OPINION
MAYS, District Judge.Defendant-Appellant Bryan Carthen (“Carthen”) appeals his 96-month sentence for being a felon in possession of a firearm, in violation of 18 U.S.C. § 922(g). Carthen argues that, although the district court imposed a sentence within the advisory guideline range, his sentence was substantively unreasonable because it was excessive and failed to accommodate his debilitating medical problems. For the following reasons, the judgment of the district court is AFFIRMED.
I. BACKGROUND
Carthen was arrested after a June 6, 2009 armed carjacking in Lansing, Michigan. Daniel McConnell (“McConnell”), the victim of the carjacking, reported that two unidentified men had abducted him at gunpoint in the parking lot of his apartment complex. McConnell was physically assaulted and forced into the trunk of his 2004 Chrysler Sebring. The assailants *430drove off with McConnell in the trunk, but he escaped after activating the trunk release and leaping from the car.
On July 11, 2009, Shannon Tett-Davis (“Tett-Davis”) told police that Carthen, her boyfriend, had possessed a Chrysler Sebring since June 2009. Tett-Davis made her statement while police were investigating her report that Carthen had threatened to “blow her head off.” On July 13, 2009, the Lansing Police Department located McConnell’s Chrysler Sebr-ing. Carthen’s neighbor was driving it. The neighbor told police that the car belonged to Carthen, but that Carthen could not drive because he was on probation. A short time later, officers found Carthen riding a bicycle. They took him into custody after finding 3.4 grams of marijuana.
Carthen’s mother consented to a search of her home, where Carthen also lived. Police found a .38 caliber revolver inside his bedroom closet. They brought Car-then to his mother’s home, where they interviewed him after advising him of his Miranda rights. Carthen claimed that the Sebring and the revolver belonged to his friend Bryan Bradford (“Bradford”). Car-then denied knowing that the car was stolen. He told police he had taken the revolver from the car and hidden it in his bedroom after agreeing to watch the car.
Carthen’s story changed on August 28, 2009. He told ATF special agents that, on June 6, 2009, he had met Bradford and Shay Inu, another friend, at a Lansing nightclub. Carthen claimed that the Chrysler Sebring belonged to one of his friends, but that he had agreed to watch the car for the evening. He claimed that Bradford had told him on June 7, 2009, that the car was stolen. Carthen maintained that Bradford had removed the .38 revolver from the Sebring and had given it to him in exchange for $100.
After arresting Carthen, police learned he had several prior convictions, including two felony convictions for home invasion. Carthen was indicted on November 5, 2009, and charged with being a felon in possession of a firearm, in violation of 18 U.S.C. § 922(g). (See Indictment, ECF No. 1.) After executing a written plea agreement, Carthen pled guilty. (See Plea Agreement, ECF No. 13.)
During his presentence interview, Car-then admitted his prior statements were untrue. He admitted he was present at the carjacking and saw friends force McConnell into the trunk of the Sebring. Carthen denied direct involvement in the carjacking. Later, during a proffer-protected polygraph, Carthen admitted he had taken an active role in the carjacking. He admitted forcing McConnell into the trunk at gunpoint using the .38 revolver. Car-then claimed to have purchased the revolver in May 2009 and to have brought it to the nightclub on June 6, 2009. He maintained that he had accepted $200 from Bradford to help collect a drug debt from McConnell.
The Presentence Report (“PSR”) provided that Carthen’s total offense level was 21 and' that his criminal history category was VI, yielding an advisory guideline range of 77-96 months. (PSR ¶ 101.) The PSR noted that an upward departure might be warranted under U.S.S.G. § 4A1.3(a)(4)(B), given Carthen’s “patter-nistic history of violent, aggressive, assaul-tive, and confrontational behavior.” (Id. ¶ 111.) The PSR noted that an upward variance might be warranted because of Carthen’s violent criminal history and the “disturbing” nature of the carjacking. (Id. ¶¶ 112, 113.) The PSR recommended that the district court impose a sentence of 114 months, which was above the guideline range.
*431At Carthen’s July 1, 2010 sentencing hearing, the parties agreed that Carthen’s advisory guideline range was 77-96 months. (Sent. Tr. 4-5, ECF No. 27.) The parties also stipulated that, in determining the appropriate sentence, the district court should not consider the proffer-protected information about Carthen’s involvement in the carjacking. (Id. 5-7.) Carthen’s counsel argued that the district court should impose a sentence below the guideline range because of Carthen’s difficult childhood and his poor mental and physical health. (Id. 7.) Carthen argued that a sentence of less than 77 months would be sufficient if he received counseling for anger management. (Id.) Carthen proffered letters from his physicians about his sickle cell anemia. (See Def.’s Mem. Ex. A.) Although one doctor suggested that Carthen would benefit from release on bond, his other doctor believed that Carthen’s condition could “be monitored and treated on an as needed basis whether incarcerated or at home.” (See Def.’s Mem. Ex. A. 2/16/10 Chamathy Letter.) Carthen also challenged the conclusions of the PSR, which recommended a sentence above the guidelines because of his criminal history. (Sent. Tr. 10-11.)
After considering the arguments of both parties, the district court imposed a 96-month sentence, which was at the high end of the advisory guideline range. The court sought to impose a sentence that was sufficient but not greater than necessary to comply with the purposes of the sentencing statute. The court specifically noted that 18 U.S.C. § 3558(a) required it to promote respect for the law by imposing a sentence that reflected the seriousness of the offense, the need to promote deterrence, and the need to promote rehabilitative opportunities and treatments, as well as to protect the public and promote respect for the law. (Sent. Tr. 18-19.)
The district court discussed and rejected Carthen’s arguments for a variance based on his difficult childhood, his continuing and serious medical problems, his mental health, and his lack of economic opportunities. (Sent. Tr. 19-20.) The court concluded that Carthen’s circumstances did not warrant a downward variance because they were neither unique nor unusual. The court rejected Carthen’s argument for a below-guideline sentence and concluded that counseling would not resolve his issues in less than 77 months. (Id. 20-21.) Finally, the court rejected the argument that a sentence below the guidelines would be more consistent with the sentence Car-then would have received under Michigan’s advisory guidelines. (Id. 21.) The court found that prosecuting Carthen at the federal level was a reasonable allocation of law enforcement resources and in the interest of public safety and accountability. (Id.) Ultimately, the court denied Car-then’s request for a downward variance, stating that it did not rely on any information about Carthen’s involvement in the carjacking. (Id. 21-22.)
Although a “harder question,” the district court declined to impose an above-guideline sentence. (Id. 22.) The court noted Carthen’s “really unusually significant” criminal history, which included numerous incidents of violence. (Id. 23.) In addition to five juvenile incidents, the district court considered Carthen’s prosecutions for malicious destruction of property, domestic violence, and home invasions— incidents that involved “violent, assaultive, loud, [and] angry behavior that leads to people getting hurt.” (Id. 24-25.) Although characterizing the question of varying upwards as a “very close call,” the court declined to exercise its authority and sentenced Carthen to 96 months. The district court noted that the sentence was at the high end of the guideline range but *432said that, in its view, Carthen was “in some sense getting a break.” (Id. 26.)
II.JURISDICTION
The district court had jurisdiction under 18 U.S.C. § 3231. Carthen filed a notice of appeal on July 2, 2010. (See ECF No. 40). This Court has jurisdiction under 18 U.S.C. § 3742.
III.STANDARD OF REVIEW
Challenges to the substantive reasonableness of a sentence are reviewed for abuse of discretion. United States v. Simmons, 587 F.3d 348, 358 (6th Cir.2009). “[A] sentence may be substantively unreasonable ‘when the district court selects the sentence arbitrarily, bases the sentence on impermissible factors, fails to consider pertinent § 3553(a) factors or gives an unreasonable amount of weight to any pertinent factor.’ ” United States v. Borho, 485 F.3d 904, 908 (6th Cir.2007) (quoting United States v. Collington, 461 F.3d 805, 808 (6th Cir.2006)). A sentence within the guideline range is presumptively reasonable. Simmons, 587 F.3d at 365; see also United States v. Vonner, 516 F.3d 382, 389-90 (6th Cir.2008) (en banc) (“[District courts ... deserve the benefit of the doubt when we review their sentences and the reasons given for them.”). When a sentencing judge’s determination falls within the guideline range, “that double determination significantly increases the likelihood that the sentence is a reasonable one.” Rita v. United States, 551 U.S. 338, 347, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007); accord Simmons, 587 F.3d at 365. Proving substantive unreasonableness is “no small burden and [the Court] will not generally ‘second guess’ sentences on substantive grounds when they fall in the range prescribed by the Guidelines.” Simmons, 587 F.3d at 365 (quoting United States v. Davis, 537 F.3d 611, 618 (6th Cir.2008)).
IV.ANALYSIS
The gravamen of Carthen’s argument is that the district court abused its discretion “because the facts are so clear [] that a prison term of no more than 77 months is sufficient to punish the Defendant here based on the § 3553(a) factors.” (Appellant Br. 10.) Carthen argues that his physical and mental ailments, which include sickle cell anemia and anger management, “demonstrate that [he] requires significant medical evaluation and care.” (Id. 11.) Carthen recognizes the seriousness of his offense and the extensiveness of his criminal history, but he argues that the district court’s need to protect the public “can be addressed based on a prison term of less than 96 months.” (See id.)
A. A 96-Month Sentence is Substantively Reasonable
“[M]ere allegation that the sentence imposed is greater than necessary to achieve the goals of punishment outlined in § 3553(a) is insufficient to rebut the presumption of reasonableness.” United States v. Dexta, 470 F.3d 612, 616 (6th Cir.2006). Without additional facts showing that the district court’s sentence was unreasonable, “[t]he fact that the district court did not give the defendant the exact sentence he sought is not a cognizable basis to appeal, particularly where the district court followed the mandate of § 3553(a) in all relevant respects.” Id. (quoting United States v. Jackson, 466 F.3d 537, 540 (6th Cir.2006)).
Despite Carthen’s broad allegation that his sentence was substantively unreasonable, there is no evidence that the district court selected his sentence “arbitrarily, based its determination on impermissible factors, disregarded any relevant concern, or gave unreasonable weight to *433any of the § 3553(a) factors.” Simmons, 587 F.3d at 365. The district court weighed each § 3553(a) factor and rejected Carthen’s argument for a downward variance. (See Sentencing Tr. 19-21.) According to the district court,
I have considered and thought about [Carthen’s] motion for a downward variance, and I do not intend to grant that. I do not think that this is a case that warrants a variance below the guideline range. The bases in the motion, most of which are reiterated here in one form or another, begin to focus understandably on what was a difficult youth for Mr. Carthen. There’s no dispute on that. He had medical problems that are continuing and are serious, particularly at times. He has ongoing mental health issues that require treatment. He had a difficult family setting to say the least. He didn’t have much economic or social opportunity. And, in fact, his education experience was also quite difficult ... And the conduct here is what I am focusing on. The background, the causes and effects, those things I can take into account, and I can and will take that into account overall in assessing where within the guideline range an appropriate sentence is, but I don’t think anything so significant here is of record that would warrant a variance downward.
(Sentencing Tr. 19-20.) The law of this circuit distinguishes between those sentences “that fall within a correctly calculated range and those that fall outside of it. Those sentences falling into the former category, such as that imposed on [Car-then], are entitled to a rebuttable presumption of reasonableness.” United States v. Trejo-Martinez, 481 F.3d 409, 413 (6th Cir.2007); see also United States v. Thompson, 586 F.3d 1035, 1037-38 (6th Cir.2009) (properly calculated sentences are accorded a rebuttable presumption of reasonableness); United States v. McGee, 494 F.3d 551, 554 (6th Cir.2007). Carthen does not rebut the presumption. Instead, he presents arguments that the district court considered but rejected. He does not identify any facts suggesting that the district court gave inappropriate weight to a § 3553(a) sentencing factor, or that his sentence was improper in other respects. Carthen’s desire for a more lenient sentence is “insufficient to justify [ ] disturbing the reasoned judgment of the district court.” Id.
B. The District Court Reasonably Considered Carthen’s Medical History
Carthen contends that the district court abused its discretion under § 3553(a)(2)(D) because the court did not vary downward to reflect his medical needs. Section 3553(a)(2)(D) provides that a district court must consider “the need for the sentence imposed — to provide the defendant with needed ... medical care.” Carthen argues that his 96-month sentence, given his health, is excessive and does not provide for adequate medical treatment. He bases his argument on a letter from his treating physician, who said that he needed direct contact with Carthen to provide proper treatment. (See Ex. A.)
The letter from Carthen’s physician tells only part of the story. Although one of Carthen’s physicians claimed to need direct contact to treat Carthen’s sickle cell anemia, the other physician said that Car-then’s condition could be treated in prison. (See Ex. A, Chamarthy Letter). The district court considered both letters and recommended that Carthen be placed in an appropriate facility. In other words, “[t]he district court [ ] addressed and took into account each argument that [Carthen] raised ... specifically [relating to] his medical condition.” United States v. Clark, 469 F.3d 568, 571 (6th Cir.2006). *434Once the court had considered Carthen’s health conditions, “it had discretion to vary or depart from the Guidelines range because of those conditions and refused to do so.” United States v. Carpenter, 359 Fed.Appx. 553, 558 (6th Cir.2009) (unpublished opinion). Carthen has not identified any relevant facts that the district court failed to consider in imposing his sentence. The court’s refusal to vary downward was not an abuse of discretion. See Clark, 469 F.3d at 571.
C. The Decision to Bring Federal Charges Against Carthen Was Appropriate
The Equal Protection Clause prohibits selective enforcement of laws based on race, religion, or other arbitrary classification. See United States v. Batchelder, 442 U.S. 114, 125 n. 9, 99 S.Ct. 2198, 60 L.Ed.2d 755 (1979); accord United States v. Allen, 160 F.3d 1096, 1108 (6th Cir.1998). Carthen would have faced a guideline range of 15-21 months for being a felon-in-possession in Michigan, compared to 77-96 months under federal law. Based on that disparity, Carthen argues that charging him in federal rather than state court produced an arbitrary sentence and was fundamentally unfair. (Appellant Br. 12.)
Carthen’s argument would limit prosecu-torial discretion inappropriately. United States v. Smith, 510 F.3d 603, 609 (6th Cir.2007); see also United States v. Allen, 954 F.2d 1160, 1166 (6th Cir.1992). When a prosecutor has probable cause to believe that an accused has committed an offense defined by statute, “decisions regarding whether to prosecute and what charges to file generally rest within the prosecutor’s discretion.” United States v. Brimite, 102 Fed.Appx. 952, 955 (6th Cir.2004) (unpublished opinion); see also Allen, 954 F.2d at 1166. The baseline for judging selective prosecutions is whether decisions to file and pursue charges were based on a defendant’s race, sex, religion, or exercise of a statutory or constitutional right. Allen, 954 F.2d at 1166.
Subjecting a defendant to federal rather than state law because of higher penalties is not “anything new.” See Brimite, 102 Fed.Appx. at 955. “Just as a defendant has no constitutional right to elect which of two applicable [] statutes shall be the basis for his indictment and prosecution[,] neither is he entitled to choose the penalty scheme under which he will be sentenced.” Batchelder, 442 U.S. at 125, 99 S.Ct. 2198 (rejecting a defendant’s challenge to his prosecution and sentencing under a federal statute that carried a higher penalty than a statute that carried a lower penalty). The prosecutors here had probable cause to believe that Carthen was a felon-in-possession. Officers found a .38 revolver in his bedroom closet. He had previously been charged and convicted of separate felonies. Based on that information, prosecutors concluded that charging Carthen under federal law was appropriate. That state and federal penalties differed is an insufficient basis to challenge his sentence. “The prosecutor may properly base his decision on the penalties available upon conviction when determining what offense will be charged against a defendant.” Allen, 954 F.2d at 1166 (citing Batchelder, 442 U.S. at 125, 99 S.Ct. 2198).
Y. CONCLUSION
The district court did not abuse its discretion when it sentenced Carthen within the guidelines to 96 months in prison. The judgment of the district court is AFFIRMED.