ORDER AND JUDGMENT*
Frank W. Lewis pled guilty to six counts of bank robbery under 18 U.S.C. § 2113(a). After determining that Mr. Lewis’s advisory guideline range for sentencing was 63 to 78 months of imprisonment, the district court imposed a variant sentence of 120 months. We AFFIRM.
Mr. Lewis appeals his sentence on two grounds. He first argues the district court violated 18 U.S.C. § 3582(a) by increasing his sentence in part to promote his rehabilitation. He relies on the fact that in explaining its decision to vary upwards from the guidelines, the district court stated:
I conclude ultimately on this record considered as a whole, that to provide just punishment, to promote respect for the law, to protect the public from further crimes, to provide adequate deterrence, to provide Mr. Lewis with an opportunity for rehabilitation both in and out of prison, and to avoid unwarranted sentencing disparities that I should vary upwards to impose a sentence of 120 months on each of the six counts of conviction.
Rec., vol. II at 69-70 (emphasis added). Because Mr. Lewis did not raise this argument below, we review for plain error. United States v. Cordery, 656 F.3d 1103, 1105 (10th Cir.2011). To establish plain error, Mr. Lewis “must demonstrate the district court (1) committed error, (2) the error was plain, and (3) the plain error affected his substantial rights.” Id. (citing United States v. Cotton, 535 U.S. 625, 631, 122 S.Ct. 1781, 152 L.Ed.2d 860 (2002)). *744“If these factors are met, we may exercise discretion to correct the error if (4) it seriously affects the fairness, integrity, or public reputation of judicial proceedings.” Id.
“A sentence is procedurally unreasonable if it is based on consideration of an impermissible factor.” United States v. Story, 635 F.3d 1241, 1244 (10th Cir.2011). Section 3582(a) states that in selecting sentences, district courts “shall consider the factors set forth in [18 U.S.C. § ] 3553(a) to the extent that they are applicable, recognizing that imprisonment is not an appropriate means of promoting correction and rehabilitation.” 18 U.S.C. § 3582(a) (emphasis added). Subsequent to the decision of the district court in this case, the Supreme Court analyzed § 3582(a) in Tapia v. United States, — U.S.-, 131 S.Ct. 2382, 180 L.Ed.2d 357 (2011). It held that the statute “precludes sentencing courts from imposing or lengthening a prison term to promote an offender’s rehabilitation.” Id. at 2391. The Court concluded that a sentencing court acts improperly when it calculates a defendant’s sentence to ensure that he receive rehabilitative services. Id. at 2392-93; see also Cordery, 656 F.3d at 1105-08 (finding plain error and remanding for resentenc-ing where district court considered rehabilitative goals in sentencing defendant).
“[A]n error is ‘plain’ if it is clear or obvious at the time of the appeal.... ” United States v. Gonzalez-Huerta, 403 F.3d 727, 732 (10th Cir.2005) (citing Johnson v. United States, 520 U.S. 461, 468, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997)); see also Cordery, 656 F.3d at 1106-07 (discussing rule). Here, the district court specifically stated the upward variance would “provide Mr. Lewis with an opportunity for rehabilitation both in and out of prison.” Rec., vol. II at 70. Under § 3582(a) and Tapia, the district court committed plain error when it imposed Mr. Lewis’s sentence in part to promote his rehabilitation.
In determining whether this error affected Mr. Lewis’s substantial rights, “we ask only whether there is a reasonable probability that, but for the error claimed, the result of the proceeding would have been different.” United States v. Hasan, 526 F.3d 653, 665 (10th Cir.2008) (internal quotation marks omitted). “A reasonable probability is a probability sufficient to undermine confidence in the outcome.” Id. (internal quotation marks omitted). But “[t]he reasonable-probability standard is not the same as, and should not be confused with, a requirement that a defendant prove by a preponderance of the evidence that but for error things would have been different.” United States v. Dominguez Benitez, 542 U.S. 74, 83 n. 9, 124 S.Ct. 2333, 159 L.Ed.2d 157 (2004). Importantly, “[i]t is the defendant rather than the Government who bears the burden of persuasion with respect to prejudice.” United States v. Olano, 507 U.S. 725, 734, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993).
Mr. Lewis has not satisfied his burden of showing that the error affected his substantial rights. While the district court admittedly mentioned rehabilitation as one ground for imposing its sentence, Mr. Lewis has suggested nothing in the record to indicate that, absent this error, the district court would have imposed a lower sentence. Rather, the only time the court mentioned rehabilitation was in a concluso-ry listing of the statutory purposes of sentencing set out in 18 U.S.C. § 3553(a)(2). See Tapia, 131 S.Ct. at 2387-88 (comparing purposes of sentencing in § 3553(a)(2) with factors described in § 3582(a)(2) which may or may not be considered in determining whether to impose a term of imprisonment or the length of the term).
*745Prior to the statement on which Mr. Lewis relies, the district court discussed numerous valid reasons for the upward variance. First, the court observed the seriousness of Mr. Lewis’s bank robberies. Although Mr. Lewis did not use a weapon during the robberies, the court noted “[a]ll were committed during business hours while the bank was open for business. Innocent bank employees and customers were present and in harm’s way.” Rec., vol. II at 65. The court also noted Mr. Lewis admitted he had “terrified the tellers that he was robbing.” Id.
Second, the district court emphasized that besides pleading guilty to six bank robberies, it was undisputed that Mr. Lewis was implicated in six additional robberies for which he would pay restitution. The court expressed its concern that a sentence “within the guideline range unreasonably depreciates the seriousness of these multiple bank robberies.” Id. at 69. Moreover, the court found that but for his arrest, it was more probable than not that Mr. Lewis would have continued robbing banks.
Third, the court noted that Mr. Lewis was disciplined for possessing a dangerous weapon while in pretrial detention.
Fourth, the court found that Mr. Lewis had no excuses for his behavior. It observed that Mr. Lewis was bright and articulate, that he did not have a disadvantaged childhood, that he had a disrespect for authority, and that he had repeatedly tried to take shortcuts throughout his life, dropping out of high school, college, and the military. While Mr. Lewis claimed he was forced to rob banks after becoming unemployed, the court found there was “no credible evidence in this record that the defendant spent any time seeking lawful gainful employment,” id. at 68, nor had he made any efforts to apply for public benefits. The court’s conclusions about Mr. Lewis’s character are well supported by the presentence investigation report.
For all of these reasons, the district court concluded that a within-guideline sentence “will not provide just or complete punishment for these six bank robberies, will not promote but instead likely [will] undermine respect for the law, will not provide or have the possibility to provide adequate deterrence, and certainly will not provide adequate protection to the public.” Id. at 69. It was only after making all of these findings that the court made its one reference to the “opportunity for rehabilitation” as a reason for the variant sentence. Thus, this case is unlike Tapia, where the Supreme Court expressed concern about the district court’s several statements suggesting that it might have calculated the length of the sentence in order to ensure access to rehabilitative services. Tapia, 131 S.Ct. at 2392-93. Nor is it like Cordery, 656 F.3d 1103. There, we concluded the Tapia error affected the defendant’s substantial rights where the district court had carefully explained that the sentence it was imposing needed to be of a particular length in order to ensure eligibility for the Rehabilitative Drug Abuse Program. Id. at 1108.
Accordingly, on this record, we are not persuaded there is any reasonable likelihood that the outcome would be different if we reversed Mr. Lewis’s sentence and remanded the case to the district court for reconsideration based on this error. Because we cannot say the error in this case affected Mr. Lewis’s substantial rights, we need not consider whether to exercise our discretion to correct the error.
Mr. Lewis also argues his sentence was substantively unreasonable. He claims the district court improperly increased his sentence because his sentences for past crimes had been lenient. Prior to his sen*746tence in the instant case, Mr. Lewis had served just one weekend in jail and had otherwise never been imprisoned. He contends his past sentencing history does not support the district court’s conclusion that an upward variance was needed for additional deterrence. In his view, because he “has never been subject to the deterrent effect that a meaningful prison term would carry,” there is no “reason to think that a quite lengthy prison term is needed to deter him.... ” Aplt. Br. at 17. Mr. Lewis relies on the following statement of the district court about his prior offenses when it denied his motion for a downward departure:
The disposition^] ... of these prior offenses[] have been relatively lenient, perhaps too lenient. They consist largely of suspended sentences and probation, supervised and unsupervised. However, those disposition^] for those crimes have clearly failed to deter or reform Mr. Lewis.
Rec., vol. II at 66-67. The court also explained in its judgment that it imposed a variance, in part, because Mr. Lewis “was treated leniently in the past.” Rec., vol. I at 91.
We review the substantive reasonableness of a sentence for abuse of discretion. United States v. Sayad, 589 F.3d 1110, 1116 (10th Cir.2009). We give substantial deference to district courts, meaning that “a district court’s sentence is substantively unreasonable only if it is arbitrary, capricious, whimsical, or manifestly unreasonable.” Id. (internal quotation marks omitted). “Unlike procedural reasonableness review, which focuses on the permissibility of relying on a particular factor, substantive reasonableness review broadly looks to whether the district court abused its discretion in weighing permissible § 3553(a) factors in light of the ‘totality of the circumstances.’ ” Id. at 1118 (quoting Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007)). Although we may not apply a presumption of unreasonableness where a sentence is outside the advisory guideline range, we “may consider the extent of the deviation,” Gall, 552 U.S. at 51, 128 S.Ct. 586, and a “major departure should be supported by a more significant justification than a minor one.” Id. at 50, 128 S.Ct. 586.
In this case, we concede that the district court’s reasoning regarding prior lenient sentences failing to deter Mr. Lewis is arguably curious. See, e.g., United States v. Mishoe, 241 F.3d 214, 220 (2d Cir.2001) (explaining that a shorter sentence now “might be expected to have the requisite deterrent effect” where defendant has previously served “no time or only a few months for the prior offenses”); United States v. Qualls, 373 F.Supp.2d 873, 877 (E.D.Wis.2005) (“Generally, a lesser period of imprisonment is required to deter a defendant not previously subject to lengthy incarceration than is necessary to deter a defendant who has already served serious time yet continues to re-offend.”) (emphasis added). Nonetheless, we cannot say that the district court’s resulting sentence was “arbitrary, capricious, whimsical, or manifestly unreasonable.” Sayad, 589 F.3d at 1116. The court provided a reasoned analysis for why it viewed the guidelines sentence as inadequate punishment for Mr. Lewis. Regardless of whether the leniency Mr. Lewis previously received constitutes a logical reason by itself to sentence Mr. Lewis for a longer period for the current crimes, the fact that Mr. Lewis committed twelve bank robberies in a relatively short period of time supports the need for deterrence. We conclude the district court did not abuse its discretion in imposing a variant sentence of 120 months.
For the foregoing reasons, we AFFIRM.