JULIE CARNES, Circuit Judge:

Defendant James Mathurin appeals his conviction and 685-month sentence for multiple armed robbery and carjacking crimes committed while he was a juvenile. After careful review of the record, and having heard oral argument, we affirm.

BACKGROUND

On December 12, 2007, just four months shy of his eighteenth birthday, Defendant was arrested for a robbery and carjacking he had committed that day. Defendant later confessed to the carjacking and, over the course of the next several months, he provided additional information about a string of other violent crimes he recently had committed.

Because both sides hoped to negotiate a plea agreement, federal prosecutors did not immediately indict Defendant. When the negotiations eventually fell apart, the Government indicted Defendant and the parties proceeded to trial. The jury convicted Defendant on a number of armed robbery and weapons charges, and the district court imposed a 492-month term of imprisonment.

Defendant appealed his conviction to this Court, successfully arguing that the Government did not indict him within the time required by the Speedy Trial Act. We vacated Defendant's conviction and remanded the case back to the district court with instructions to determine whether the indictment should be dismissed with or without prejudice. See United States v. Mathurin, 690 F.3d 1236, 1243 (11th Cir. 2012). The district judge concluded that the indictment should be dismissed without prejudice, and the Government re-indicted Defendant on charges of conspiracy, two counts of carjacking, twelve Hobbs Act robberies, one attempted Hobbs Act robbery, and twelve counts of brandishing a firearm in furtherance of a crime of violence. The district judge then recused herself, and the case proceeded to a second trial before a new judge.

At trial, the Government introduced evidence that Defendant had committed a spree of violent crimes beginning on July 26, 2007. The evidence showed that on that date, Defendant and five other men broke into a home and awakened a teenaged girl who was napping in an adjoining bedroom. One of the men fired a gunshot at the girl, missing her by only four inches.

A little over a week later, on August 7, 2007, Defendant entered a Cellular Hut store, pointed a gun at the clerk, and demanded money while his accomplices posed as customers and urged the clerk to comply. Immediately after this robbery, Defendant went to another Cellular Hut store and demanded money from the store clerk. When the clerk laughed at him, Defendant fired a round from his gun to show he was serious.

On August 16, Defendant and an accomplice, armed with a gun, entered a Subway restaurant and demanded money from the cashier. Two days later, on August 18, Defendant entered a Max Communications store with a gun and demanded money from the clerk. Less than a month after that, on September 10, Defendant fired gunshots at the back wall of another Cellular Hut as he entered the store. He then demanded money from the clerk and a patron of the store.

During the above robberies, Defendant was aided by a group of young men who performed various roles, such as transporting Defendant to the store or pretending to be customers. After the September 10 robbery, Defendant had a falling out with these individuals and recruited a different set of accomplices. On September 21, Defendant, accompanied by a friend who was armed with a gun, robbed an Electronics Direct Telephone store. On that same day, Defendant and his friends also robbed a Hello Cellular store, this time with Defendant carrying a gun.

On October 2, Defendant shot his gun into the air as he entered a Boston Market with an accomplice. His accomplice ordered everyone to get on the floor as Defendant demanded money from an employee. On October 6, Defendant and an accomplice walked into the LaPavillion Restaurant where Defendant shot a round into the ceiling, shattering the glass in the ceiling. Defendant then opened the cash register and took money, in addition to robbing a patron of his cell phone. On October 13, Defendant fired a gunshot as he and an accomplice entered a 7-Eleven and took money from the cash register.

Defendant subsequently committed a robbery and two carjackings without any assistance. On December 11, while armed with a gun, Defendant approached the driver of a vehicle and demanded the keys to the car and the driver's money. The victim acquiesced and Defendant took his car. The next day, December 12, Defendant robbed a 7-Eleven at gunpoint and fired his gun at the wall directly behind the clerk. On that same day, Defendant carjacked a second victim outside a check-cashing store and fled in the victim's car. After the second carjacking, Defendant finally was apprehended by the police.

The jury in Defendant's second trial convicted him of all but one count in the indictment.1 At sentencing, the district judge acknowledged that the first judge had imposed a 492-month sentence. Nevertheless, having heard the evidence against Defendant in the second trial, this second judge thought that a higher sentence was necessary to safeguard the public. The judge explained his thinking in some detail:

(emphasis added). Given his concerns about the safety of the public, the judge sentenced Defendant to 685 months in prison.

On appeal, Defendant asserts various evidentiary grounds for vacating his conviction. He also argues that the district court erred by dismissing his former indictment without prejudice, which thereby allowed the Government to re-indict Defendant. Assuming the conviction stands, Defendant argues that his sentence must be vacated under the Supreme Court's holding in Graham v. Florida, 560 U.S. 48, 130 S.Ct. 2011, 176 L.Ed.2d 825 (2010), that a juvenile cannot be sentenced to life without parole for nonhomicide offenses. Defendant also argues that the sentence was imposed as punishment for his prior appeal, in violation of the Supreme Court's holding in North Carolina v. Pearce, 395 U.S. 711, 89 S.Ct. 2072, 23 L.Ed.2d 656 (1969). For the reasons discussed below, we affirm both the conviction and the sentence.

DISCUSSION

I. Defendant does not assert any valid ground for vacating his conviction.

In support of the appeal of his conviction, Defendant argues that the district court erred by (1) denying various motions to suppress evidence, (2) admitting improper and prejudicial evidence, and (3) denying Defendant's motion to dismiss the initial indictment against him with prejudice under the Speedy Trial Act. Defendant also argues that his second indictment violated the applicable statute of limitations. We are not persuaded by any of these arguments.

A. The district court did not err in its suppression rulings.

In reviewing the district court's suppression rulings, "we review factual findings for clear error and the court's application of law to those facts de novo." United States v. Goddard, 312 F.3d 1360, 1362 (11th Cir. 2002). We construe the facts "in the light most favorable to the prevailing party." Id.

1. Post-Arrest Statements

Defendant argues that his post-arrest statements should have been suppressed because there was no probable cause for his arrest. This argument fails because it is clear that there was, in fact, probable cause for Defendant's arrest. Prior to the arrest, police set up a perimeter outside of a check-cashing store to investigate a report that a robbery had occurred there. An officer working the perimeter stopped and questioned Defendant after observing him emerge from between two houses in the area. The officer detained Defendant after he produced a checkbook that belonged to the robbery victim. While Defendant was detained at the scene, the victim positively identified him as the robber. These facts are more than adequate to provide probable cause for Defendant's arrest. See Feliciano v. City of Miami Beach, 707 F.3d 1244, 1251 (11th Cir. 2013) ("Probable cause to arrest exists when the facts and circumstances within an officer's knowledge are sufficient to warrant a reasonable belief that the suspect had committed or was committing a crime." (internal quotation marks omitted)).

2. Plea Negotiations

Defendant also argues that certain statements should have been suppressed because he made them in the course of plea negotiations. Under Rule 410 of the Federal Rules of Evidence, statements "made during plea discussions with an attorney for the prosecuting authority" are "not admissible against the defendant." Fed. R. Evid. 410(a)(4). A statement is inadmissible under Rule 410 if the defendant "exhibited an actual subjective expectation to negotiate a plea" when he made the statement and the "expectation was reasonable given the totality of the objective circumstances." United States v. Merrill, 685 F.3d 1002, 1013 (11th Cir. 2012) (internal quotation marks omitted). The district court concluded that "any expectation of a plea negotiation ... was unreasonable" as to the statements at issue in Defendant's suppression motion because Defendant was advised that no promises or negotiations would be made in the meetings during which Defendant made the statements. This conclusion is fully supported by the record.

3. Voluntariness

Defendant next asserts that the district court should have suppressed inculpatory statements he made to the police after his arrest because the statements were not made voluntarily. In support of this argument, Defendant contends that (1) his mother was not immediately notified of his arrest as required by Florida Statute § 985.101, (2) a waiver form Defendant signed did not indicate that he had a right to an attorney prior to questioning, and (3) Defendant was questioned alone after he had been appointed an attorney.

A delay in notifying Defendant's mother does not render Defendant's statements involuntary. See Neely v. State, 126 So.3d 342, 346 (Fla. App. 2013) ("[T]he failure to comply with this statutory requirement does not render a confession involuntary."). Nor does the waiver-form challenge have any basis, given the uncontested trial testimony that Defendant had been provided — and signed — Miranda waiver forms prior to the initiation of any questioning. Those forms advised Defendant that he had a right to a lawyer if he wanted one "now or at anytime during the questioning." Furthermore, the district court concluded that "law enforcement officers read the defendant his Miranda rights each time they spoke with him." Thus, Defendant's questioning outside the presence of an attorney does not require the exclusion of his statements made in response. See Montejo v. Louisiana, 556 U.S. 778, 786, 129 S.Ct. 2079, 173 L.Ed.2d 955 (2009) ("[W]hen a defendant is read his Miranda rights (which include the right to have counsel present during interrogation) and agrees to waive those rights, that typically does the trick.").

4. Eyewitness Identification

Finally, Defendant argues that the district court erred by failing to suppress five different instances of eyewitness identification. "The Court uses a two-step process to determine whether an out-of-court identification was proper. First, we ask whether the original identification procedure was unduly suggestive. If we conclude that it was, we then consider whether, under the totality of the circumstances, the identification was nonetheless reliable." United States v. Perkins, 787 F.3d 1329, 1344 (11th Cir. 2015) (internal quotation marks omitted). Defendant points to various aspects of the eyewitness identifications that he says impugn their reliability, including gaps in time between a sighting and an identification and less than full certainty by the witness making the identification. Defendant, however, cites no evidence to satisfy the first step of the inquiry, which requires a showing that the identification procedure, itself, was unduly suggestive. That being so, we find no error in admission of the evidence.

B. The district court properly dismissed Defendant's original indictment without prejudice.

We review the district court's factual findings made pertinent to the remedy for a Speedy Trial Act violation for clear error and its application of those findings to the law de novo. United States v. Williams, 314 F.3d 552, 556 (11th Cir. 2002). Applying that standard, we find no error in the district court's decision to dismiss the indictment without prejudice to the Government's right to seek a new indictment. As required by the Speedy Trial Act, the district court considered the following factors in making its decision: (1) the seriousness of Defendant's crimes, (2) the facts and circumstances that led to dismissal under the Speedy Trial Act, and (3) the impact of prosecuting Defendant a second time. See 18 U.S.C. § 3162(a)(1). Analyzing those factors, the district court determined that Defendant's crimes were "extremely serious" because he was charged with "forty-nine robbery, carjacking, and firearms offenses," many of which "involved violence to others." See United States v. Mathurin, Case No. 1:09-21075-cr-cooke, Dkt. No. 317 at p. 4 (S.D. Fla. Nov. 19, 2012). As to the second factor, the court noted that the Government "did not intentionally delay the filing of the indictment for some tactical or other improper purpose," but instead that the delay was "a result of a good faith effort to attempt to resolve this matter short of trial." Id. at p. 5-6. Finally, the court concluded that Defendant would suffer only minimal prejudice from the delay. Id. at p. 6-7. All of these findings and conclusions are fully supported by the record.

C. Defendant's second indictment was timely.

Defendant's statute of limitations argument likewise fails. Defendant contends that the statute of limitations for all but two of his robbery counts had expired by the time his original indictment was dismissed without prejudice. However, under 18 U.S.C. § 3288:

18 U.S.C. § 3288. See also Zedner v. United States, 547 U.S. 489, 499, 126 S.Ct. 1976, 164 L.Ed.2d 749 (2006) ("When an indictment is dismissed without prejudice, the prosecutor may of course seek — and in the great majority of cases will be able to obtain — a new indictment, for even if the period prescribed by the applicable statute of limitations has expired, a new indictment may be returned within six calendar months of the date of the dismissal." (internal quotation marks and alterations omitted)). Here, the new indictment was filed only ten days after the original indictment was dismissed, well within the applicable time period.

D. The district court's evidentiary rulings do not warrant reversal.

Defendant argues that the district court committed two additional evidentiary errors that warrant reversal. We review the district court's evidentiary rulings under an abuse of discretion standard. United States v. Brown, 415 F.3d 1257, 1264 (11th Cir. 2005).

First, at his first trial, as to three of the Hobbs Act robbery counts, Defendant had been convicted on those counts, but acquitted on their accompanying 18 U.S.C. § 924(c) counts (possession, brandishing, or use of a firearm during a crime of violence). Over Defendant's objection at the second trial, the district court allowed the Government to introduce witness testimony setting out a complete factual recounting of what transpired during these three robberies, including evidence concerning the use of a firearm by one of the robbers during the robberies. (Obviously, given Defendant's acquittal on these three firearm counts at the first trial, the latter were not presented to the second jury for a verdict.) Defendant argues that because he had been acquitted of these particular firearms counts, albeit he had been convicted of involvement in their underlying robberies, the Government should have been required to sanitize its presentation of the evidence to eliminate any reference to the use of a gun during the robbery.

The legal hook he uses to make this argument is his interpretation of the collateral estoppel principle embedded in the Double Jeopardy Clause; that is, according to Defendant, acquittal in a prior trial of charges involving certain conduct means there can be no mention of that conduct at a subsequent trial on any remaining charges. Defendant's argument, however, is without legal merit. The Supreme Court has held that "the collateral-estoppel component of the Double Jeopardy Clause" does not prohibit "probative evidence that is otherwise admissible under the Rules of Evidence simply because it relates to alleged criminal conduct for which a defendant has been acquitted." Dowling v. United States, 493 U.S. 342, 348, 110 S.Ct. 668, 107 L.Ed.2d 708 (1990). Thus, Defendant's argument fails.

Next, Defendant contends that the Government committed prosecutorial misconduct by referencing in closing argument a shell casing without establishing that the casing was linked to the firearm at issue, and by failing to correct the record when a witness testified in contradiction of her prior testimony at an evidentiary hearing. "Prosecutorial misconduct requires a new trial only if we find the remarks (1) were improper and (2) prejudiced the defendant's substantive rights." United States v. Frank, 599 F.3d 1221, 1237-38 (11th Cir. 2010) (internal quotation marks and alterations omitted). On this record, we discern no misconduct, but even were there some prosecutorial impropriety, it is clear that Defendant's substantive rights were not prejudiced. Prejudice only exists when there is a reasonable probability that, but for the objectionable remarks or evidence, "the outcome of the trial would be different." Id. (internal quotation marks and alterations omitted). Given the substantial evidence establishing Defendant's guilt, we find no probability that, but for the cited errors, the verdict in this case would have been different.

II. The district court did not err in sentencing Defendant.

In addition to challenges to his conviction, Defendant argues that the 685-month sentence he received for crimes committed as a juvenile should be vacated because it violates the Eighth Amendment, as interpreted by the Supreme Court in Graham v. Florida, 560 U.S. 48, 130 S.Ct. 2011, 176 L.Ed.2d 825 (2010). Defendant also argues that the sentence was presumptively vindictive, and thus unlawful, under the rule announced in North Carolina v. Pearce, 395 U.S. 711, 89 S.Ct. 2072, 23 L.Ed.2d 656 (1969). Both arguments raise purely legal issues that are subject to de novo review. See United States v. Register, 182 F.3d 820, 841 (11th Cir. 1999).

A. Defendant's sentence complies with Graham v. Florida.

In Graham, the Supreme Court held that the Eighth Amendment categorically prohibits the imposition of a "life without parole sentence on a juvenile nonhomicide offender." Graham, 560 U.S. at 75, 130 S.Ct. 2011. The Court indicated that its holding was motivated by distinctions it perceived between juvenile and adult offenders, including the decreased culpability — and increased capacity for rehabilitation — of juveniles as a result of their immaturity. Id. at 68-75, 130 S.Ct. 2011. Due to these differences, the Court determined that the Eighth Amendment bars a sentencing court from making an irrevocable pronouncement — via the imposition of a life without parole sentence — that a juvenile nonhomicide offender "never will be fit to reenter society." Id. at 75, 130 S.Ct. 2011. Rather, the Court explained, the sentence imposed on a juvenile who has not committed homicide must afford the juvenile "some meaningful opportunity to obtain release based on demonstrated maturity and rehabilitation." Id.

Defendant argues that the 685-month sentence he received for multiple violent, but non-homicide, crimes committed while he was a juvenile violates the rule set out in Graham because the sentence exceeds his expected life span. Defendant's reliance on Graham prompts several questions about how that case should be applied in contexts other than the one before the Supreme Court. First is the question whether the rule announced in Graham applies to a lengthy non-parolable term-of-years sentence that is not designated as being "life without parole," but that nonetheless will likely run longer than a juvenile offender is expected to live.2 Some courts have held that Graham does apply to such a sentence, reasoning that this kind of sentence is the functional equivalent of life without parole for purposes of Graham because it does not provide an opportunity for the juvenile offender to obtain release during his lifetime. See Henry v. State, 175 So.3d 675, 679-80 (Fla. 2015), cert. denied, ___ U.S. ___, 136 S.Ct. 1455, 194 L.Ed.2d 552 (2016) ("[T]he Graham Court had no intention of limiting its new categorical rule to sentences denominated under the exclusive term of `life in prison.'"); Moore v. Biter, 725 F.3d 1184, 1191 (9th Cir. 2013) ("[The defendant's] sentence of 254 years is materially indistinguishable from a life sentence without parole because [the defendant] will not be eligible for parole within his lifetime."). Other courts disagree, pointing out that, by its terms, Graham only applies to a sentence of "life without parole." See Bunch v. Smith, 685 F.3d 546, 551 (6th Cir. 2012) (noting that Graham "did not address juvenile offenders ... who received consecutive, fixed-term sentences for committing multiple nonhomicide offenses"); State v. Brown, 118 So.3d 332, 342 (La. 2013) ("[N]othing in Graham addresses a defendant convicted of multiple offenses and given term of year sentences, that ... equate to a possible release date when the defendant reaches the age of 86.").

For purposes of this appeal, we will assume that Graham does apply to a non-parolable term-of-years sentence that extends beyond a defendant's expected life span. Applying Graham to a term-of-years sentence, however, then gives rise to another question: how does one measure the life expectancy of an individual. Typically, actuarial tables or life expectancy data can be used to provide that answer. See Casiano v. Comm'r of Corr., 317 Conn. 52, 115 A.3d 1031, 1069 (2015) (recognizing that courts have generally relied on mortality tables to determine a juvenile's life expectancy) (Espinosa, J., dissenting). Mortality tables, at their most generic level, will usually distinguish only between male and female life expectancy at a particular age. These tables can, however, focus more granularly on numerous other distinctions that impact the life expectancy of a particular individual, such as race, income, geography, education, family history, medical history, and other factors.

Defendant was sentenced when he was 24-years old.3 He argues that in predicting how many more years he might live, we should not consider the life expectancy of 24-year old American males as a group, but instead we should focus only on the projected longevity of 24-year old American black males. Because a black male in his mid-twenties has a lesser life expectancy than does a white or Hispanic male in that same age range — and less than that of the entire male population of that age — Defendant therefore argues that a term-of-years sentence that might not effectively constitute a life sentence for a young white or Hispanic defendant could become a life sentence for a young black defendant who might be expected to die sooner.

The Government objects to Defendant's methodology, and Defendant's suggested approach does raise some questions, including whether it would be constitutional to rely on a person's race in determining how long a sentence to impose on that individual. See State v. Zuber, 227 N.J. 422, 152 A.3d 197, 214 (2017) (noting that life expectancy tables "rest on informed estimates, not firm dates, and the use of factors like race, gender, and income could raise constitutional issues"); Casiano, 115 A.3d at 1069 (stating that reliance on race and gender distinctions in juvenile sentencing "is highly problematic") (Espinosa, J., dissenting). By Defendant's reasoning, and based on the mortality table he cited in the district court, Hispanics should receive longer sentences than either whites or blacks solely because they generally live longer, and Hispanic females should receive the longest sentences of all due to their longer average life expectancy. Such an approach to sentencing would unquestionably lead to challenges from defendants from longer-living ethnic groups who would be subject to longer sentences based on that ethnicity.

Further, mortality tables shed no light on whether it is one's membership in a certain racial or ethnic population that, as a biological matter, determines life expectancy or whether instead it is the social, economic, medical, and cultural factors associated with a particular ethnic identity that primarily determine how long an individual can be expected to live.4 If it is the latter, Defendant fails to account for the possibility that incarceration of a young person for a prolonged period of time could reduce the impact of those social and economic factors that, for good or for ill, give rise to the particular life expectancy ascribed to a male member of the particular ethnic group at a given age. See, e.g., Casiano, 115 A.3d at 1070 ("Although incarceration may lower the life expectancy for an advantaged juvenile, it very well may increase the life expectancy of a juvenile who comes from a disadvantaged economic class and background.") (Espinosa, J., dissenting).

Nevertheless, in resolving this case, we do not need to decide whether Defendant's granular approach to calculating life expectancy should carry the day for purposes of a Graham analysis because even assuming the accuracy of his proffered lower life expectancy for black males in their mid-twenties, as opposed to the life expectancy of all males in their mid-twenties, we conclude that Defendant's Graham challenge fails.

Here are the numbers we are working with. In imposing its sentence, the district court noted that, but for the fact that Defendant was seventeen when he committed his many crimes, the court would be required to impose an approximately 300-year sentence, which term is arrived at by imposition of the many consecutive mandatory-minimum sentences that Defendant's convictions called for. Nevertheless, because Defendant was under the age of 18, albeit barely, by the time his crime spree ended with his capture, the court concluded that such a sentence "would violate Supreme Court preceden[t] since the defendant is a juvenile and [it] would result in effectively a mandatory life sentence." Instead, after considering the actuarial tables presented by the parties, the court sentenced Defendant to 685 months' imprisonment, which translates to a sentence of 57 years and one month. The question then becomes whether a 57-year sentence constituted a life sentence in this case.

According to the actuarial table created by the National Vital Statistics System and presented by Defendant at sentencing,5 a generic 25-year old American male can on average be expected to live 52.2 more years (or until he is 77.2 years old) whereas a 25-year old American black male can be expected to live only 48.1 years (or until he is 73.1 years old). Extrapolating from the table, a 24-year old black male could expect to live until he is 73 years old.6 Actuarially then, and not accounting for any other factors, a 24-year old black male can be expected to live about 4 years less than the average male in the entire population.7

The question then becomes whether Defendant will be required to serve a sentence until he is at least 77 (which is the anticipated longevity of all 24-year old males) or until he is at least 73 (which was the Defendant's calculations of the longevity of only black males). In figuring out how much longer Defendant will necessarily have to serve, we must include in our calculations the fact that Defendant had already served 77 months of his sentence prior to this second trial and sentencing hearing. Subtracting that 77 months from the 685-month sentence imposed by the district court, Defendant's remaining sentence to serve was, at most, 608 months (50.7 years) from the date of his sentencing. See 18 U.S.C. § 3585(b) ("A defendant shall be given credit toward the service of a term of imprisonment for any time he has spent in official detention prior to the date the sentence commences ... as a result of the offense for which the sentence was imposed[.]").

Again, Defendant had just turned 24 years old when he was sentenced. A 50.7 year sentence left to serve would put him at 74.7 years of age at the time of his mandatory release date. As noted, considering only the longevity of 24-year old black males, as Defendant would have us do, means that at the moment of sentencing,8 Defendant could be expected to live until he is 73. Using the longevity of the average 24-year old male, as the Government would have us do, means that Defendant can be expected to live until he is 77. Thus, absent any other factors, Defendant's sentence would run approximately 1.7 years longer than his expected life span as determined by his methodology, but would expire approximately 2.3 years prior to his mandatory release date under a methodology looking at the life expectancy of all males.

Yet, there is one important additional factor that is absolutely pivotal to this inquiry and that Defendant does not factor into his calculations. Specifically, although there is no parole for federal sentences, Defendant has it within his power to shorten his sentence by earning good-time credit. Pursuant to 18 U.S.C. § 3624, Defendant can earn up to 54 days of credit towards his sentence for each year he serves in prison, "subject to determination by the Bureau of Prisons that, during that year, [he] has displayed exemplary compliance with institutional disciplinary regulations." 18 U.S.C. § 3624(b)(1). The Government has calculated that if Defendant earns the maximum good-time credit available, Defendant can reduce his total sentence by over 7 years and be released when he is 67 years old. Defendant has never disputed this calculation. Earning this credit means that Defendant would serve a remaining sentence of about 43.4 years, which is more than five years shorter than his own proffered life span for black males and almost ten years shorter than the projected life span for all males his age.9 Thus, Defendant's sentence provides him with a realistic opportunity to obtain release before the end of his life, as required by Graham.

It is true that Defendant may not receive all of the above good-time credit if he misbehaves and thereby forfeits some of that credit. But it is totally within Defendant's own power to shorten the sentence imposed. Graham does not require that a sentence "guarantee eventual freedom to a juvenile offender convicted of a nonhomicide crime." Graham, 560 U.S. at 75, 130 S.Ct. 2011. It just requires that the offender have a chance to show that he has earned the right to be given a second chance at liberty. The Supreme Court made the limitations of its holding in Graham clear, explaining that:

Id. (emphasis added).

Indeed, good-time credits provide a potent rehabilitative incentive for juvenile offenders subject to lengthy sentences, which, according to the Supreme Court's rationale in Graham is an important objective. Part of the reason the Court rejected life-without-parole sentences for juvenile nonhomicide offenders is that such sentences do not offer any possibility for rehabilitation. See id. at 79, 130 S.Ct. 2011 (observing that "[a] young person who knows that he or she has no chance to leave prison before life's end has little incentive to become a responsible individual"). Similar to parole, the ability to earn good-time credits serves this objective by giving the juvenile offender a reason to pursue and exhibit "maturity and rehabilitation." Id. at 75, 130 S.Ct. 2011.

In short, using only Defendant's proffered life expectancy data for black males, he is expected to live for almost 49 years after the date of his sentencing; he is projected to live another 53 years if one looks at the longevity of all males his age. Factoring in time-served credit and the opportunity to earn good-time credits, Defendant is eligible for release approximately 43.4 years after the sentencing date, which is over five years before the end of his own projected life span and almost ten years before the date projected for all males his age. Thus, Defendant has "some meaningful opportunity to obtain release" during his lifetime, as required by Graham. Id. at 75, 130 S.Ct. 2011. See also United States v. Tocco, 135 F.3d 116, 132 (2d Cir. 1998) (holding that a 435-month sentence, which exceeded defendant's life expectancy when good-time credits were not accounted for but was slightly less than his life expectancy when good-time credits were considered, did not violate a statute requiring jury recommendation for imposition of life sentence).

B. Defendant's sentence was not vindictive.

Defendant also argues that his sentence was imposed as a punishment for successfully appealing his initial conviction, in violation of the rule announced by the Supreme Court in North Carolina v. Pearce, 395 U.S. 711, 89 S.Ct. 2072, 23 L.Ed.2d 656 (1969). As explained above, Defendant was originally convicted and sentenced to a 492-month term of imprisonment. This Court vacated the conviction on Speedy Trial Act grounds and remanded Defendant's case back to the district court. After a second trial and guilty verdict before a new judge, Defendant was sentenced to 685 months.

In Pearce, the Supreme Court held that a sentence reflecting "vindictiveness against a defendant for having successfully attacked his first conviction" violates the defendant's Due Process rights. Id. at 725, 89 S.Ct. 2072. To ensure the absence of vindictiveness, the Court required that "whenever a judge imposes a more severe sentence upon a defendant after a new trial, the reasons for his doing so must affirmatively appear." Id. at 726, 89 S.Ct. 2072. "Otherwise, a presumption arises that a greater sentence has been imposed" vindictively. Alabama v. Smith, 490 U.S. 794, 798-99, 109 S.Ct. 2201, 104 L.Ed.2d 865 (1989).

The Supreme Court has indicated, and several circuit courts have held, that the presumption of vindictiveness does not arise in the "second sentencer" context. See id. at 799, 109 S.Ct. 2201; see also Texas v. McCullough, 475 U.S. 134, 140, 106 S.Ct. 976, 89 L.Ed.2d 104 (1986) ("The presumption is also inapplicable because different sentencers assessed the varying sentences that [the defendant] received."); United States v. Clark, 84 F.3d 506, 508 (1st Cir. 1996) ("In this case, the defendant's second sentence was imposed by a different judge. Thus, no presumption of vindictiveness arises."); United States v. Rodriguez, 602 F.3d 346, 358-59 (5th Cir. 2010) ("[W]e join our seven sister circuits that, as discussed below, do not apply the presumption when different judges preside over the first and second sentencing.") (collecting cases from other circuits). With a different judge imposing the sentence, there is no "reasonable likelihood that the increase in sentence is the product of actual vindictiveness on the part of the sentencing authority" and thus no reason to apply the presumption. Smith, 490 U.S. at 799, 109 S.Ct. 2201 (internal citation omitted). In addition, this Court has clarified that the presumption only arises when the second sentence is more severe and "no non-vindictive reasons for doing so `affirmatively appear' in the record." United States v. Fowler, 749 F.3d 1010, 1019 (11th Cir. 2014) (quoting Pearce, 395 U.S. at 726, 89 S.Ct. 2072).

In this case, there can be no serious assertion that the district judge acted vindictively in imposing the sentence he chose. First, this judge did not preside over the first trial and sentencing, and thus one can assume no personal pique on his part by Defendant's successful reversal of his original conviction. The district judge here presided over a new trial and sentencing hearing, drew his own conclusions about the appropriate sentence for Defendant, and provided detailed, objective reasons for his sentencing decision. Accordingly, the Pearce presumption does not apply, and Defendant must show "actual vindictiveness" to prevail on his argument. Smith, 490 U.S. at 799, 109 S.Ct. 2201. Defendant cannot make such a showing on this record. The district judge acknowledged Defendant's original sentence and "tried as best [he could] to convince [himself] to go along with that," but ultimately determined that he "just c[ouldn]'t do it" because of his impression that Defendant would still be a danger to society after any lesser sentence. Even in the age of guidelines, sentencing is not a mathematical science. It is, instead, a discretionary endeavor whose results can vary from judge to judge. See Crystal S. Yang, Have Interjudge Sentencing Disparities Increased in an Advisory Guidelines Regime? Evidence from Booker, 89 N.Y.U. L. Rev. 1268 (2014) (finding that, in a sample of seventy-four federal districts, interjudge sentencing disparities have doubled since the sentencing guidelines became advisory). There is no reason to doubt the judge's stated rationale for imposing a higher sentence on Defendant, and no evidence to suggest it was in any way vindictive.

CONCLUSION

For the reasons discussed above, we AFFIRM Defendant's conviction and sentence.

WILSON, Circuit Judge, concurring:

I concur in the result.