OPINION

BOGGS, Circuit Judge.

Nathan Hughes was sentenced to prison for the mandatory minimum term of ten years after pleading guilty to attempting to entice a minor to engage in a criminal sexual act, in violation of 18 U.S.C. § 2422(b). On appeal, Hughes argues that his mandatory minimum sentence violates the Eighth Amendment because it is grossly disproportionate to his crime, and that it violates the Fifth Amendment's due process and equal protection guarantees because similarly situated defendants charged under 18 U.S.C. § 2423(b) are not subject to a mandatory minimum. Because these arguments are without merit, we affirm the district court's sentence.

I

On July 7, 8, 13, and 24, 2008, Hughes exchanged online communications with someone he thought was a 14-year-old girl. In reality, his online companion was not a child, but rather an undercover detective. In their last exchange, Hughes proposed meeting at a local park in Louisville, Kentucky for the purpose of engaging in sexual intercourse and/or oral sex. When Hughes arrived at the park, officers recognized him from online photos and the description of his vehicle. He was arrested by the Louisville Metro Police Crimes Against Children Unit, and indicted on the charge of attempting to persuade, induce, or entice a 14-year-old girl to engage in sexual activity, in violation of 18 U.S.C. § 2422(b). The statute carries a mandatory minimum sentence of ten years of imprisonment. 18 U.S.C. § 2422(b).

Hughes filed a motion to dismiss the indictment or delete the mandatory minimum sentence, claiming that the sentence constituted cruel and unusual punishment and violated his due process and equal protection rights. In a short order, the district court denied the motion, stating that the minimum sentence under 18 U.S.C. § 2422(b) is "rationally related to the legitimate interest of Congress in curtailing the coercion or enticement of minors over the internet," and "[w]hile acknowledging the severity of a ten year sentence, the Court cannot conclude that such a sentence is grossly disproportionate to the alleged offense conduct in this case." Hughes reserved the right to appeal and pled guilty. He was sentenced to the ten-year minimum and timely appealed.

II

"`A constitutional challenge to a sentence is a question of law and reviewed de novo.'" United States v. Jones, 569 F.3d 569, 573 (6th Cir. 2009) (quoting United States v. Marks, 209 F.3d 577, 583 (6th Cir. 2000)). We have not previously addressed in a published opinion whether the mandatory minimum in 18 U.S.C. § 2422(b) is constitutional. We now hold that it is.

A

Hughes argues that the ten-year mandatory minimum is grossly disproportionate to his offense, thereby violating the Eighth Amendment's protection against cruel and unusual punishment.

The Supreme Court has adopted a "narrow proportionality principle" in evaluating Eighth Amendment claims. Harmelin v. Michigan, 501 U.S. 957, 997, 111 S.Ct. 2680, 115 L.Ed.2d 836 (1991) (Kennedy, J., concurring in part and concurring in the judgment). In that case, Justice Kennedy wrote that, "[t]he Eighth Amendment does not require strict proportionality between crime and sentence. Rather, it forbids only extreme sentences that are `grossly disproportionate' to the crime." Id. at 1001, 111 S.Ct. 2680. A defendant challenging his sentence under the Eighth Amendment has a tremendously difficult burden to meet. In the last century, the Supreme Court has struck down only a handful of non-capital sentences under the Eighth Amendment, and those cases have been egregious in the extreme. For example, the Court found a life sentence without the possibility of parole unconstitutional for the crime of uttering a "no account" check for $100. Solem v. Helm, 463 U.S. 277, 103 S.Ct. 3001, 77 L.Ed.2d 637 (1983). In Harmelin, by contrast, the Supreme Court upheld a mandatory life sentence without the possibility of parole for possession of more than 650 grams of cocaine even where the defendant had no prior felony convictions. 501 U.S. at 961, 994, 111 S.Ct. 2680.

In light of this precedent, Hughes's ten-year sentence for attempting to entice a minor into sexual relations raises no inference that it is "grossly disproportionate."

The penalty in Solem was much more severe than the ten-year term to which Hughes was sentenced, and the defendant's conduct in that case was relatively trivial. Although he was a habitual offender, all of his offenses were nonviolent in nature, and the Court described his crime of uttering a worthless check as "viewed by society as among the less serious offenses." 463 U.S. at 297, 103 S.Ct. 3001. Hughes bears a far greater similarity to the Harmelin defendant. Both defendants lack a serious criminal history, but both were convicted of very serious crimes. Hughes attempted to induce a minor to engage in sexual acts with him. As we recently recognized, federal courts have consistently noted the seriousness of crimes involving the sexual exploitation of minors. United States v. Dobrowolski, 406 Fed.Appx. 11, at 12-13, 2010 WL 4723779, at *2 (6th Cir. 2010) (unpublished). Hughes's penalty of only ten years for this serious offense is substantially less severe than the life sentence without the possibility of parole that the Supreme Court upheld for the drug offense in Harmelin. Therefore, his argument fails. In so holding, we join the other circuits to decide the question. United States v. Nagel, 559 F.3d 756 (7th Cir. 2009); United States v. Butters, 267 Fed.Appx. 773 (10th Cir. 2008); see also United States v. Farley, 607 F.3d 1294, 1343 (11th Cir. 2010) (holding that the thirty-year mandatory minimum sentence for crossing a state line with intent to engage in a sexual act with a person under the age of twelve, in violation of § 2241(c), does not violate the Eighth Amendment).

Because the defendant's sentence raises no inference of gross disproportionality, we need not consider the punishments available under other federal statutes or in other jurisdictions. Harmelin, 501 U.S. at 1005, 111 S.Ct. 2680 ("[I]ntrajurisdictional and interjurisdictional analyses are appropriate only in the rare case in which a threshold comparison of the crime committed and the sentence imposed leads to an inference of gross disproportionality.").

B

The Supreme Court has noted that the Fifth Amendment contains an equal protection component that applies to the federal government. San Francisco Arts Athletics, Inc. v. U.S. Olympic Committee, 483 U.S. 522, 543 n. 21, 107 S.Ct. 2971, 97 L.Ed.2d 427 (1987). The analysis of a Fifth Amendment equal protection claim is identical to an equal protection claim under the Fourteenth Amendment. Ibid. In the district court and on appeal, Hughes focused his equal protection argument on the disparity between himself and similar defendants who were prosecuted under 18 U.S.C. § 2423(b). He admits that he is not part of a suspect class, and therefore must show that the alleged government classification lacks a rational basis. He cannot meet this burden.

The statute under which Hughes was charged and convicted reads:

Whoever, using the mail or any facility or means of interstate or foreign commerce, or within the special maritime and territorial jurisdiction of the United States knowingly persuades, induces, entices, or coerces any individual who has not attained the age of 18 years, to engage in prostitution or any sexual activity for which any person can be charged with a criminal offense, or attempts to do so, shall be fined under this title and imprisoned not less than 10 years or for life.

18 U.S.C. § 2422(b). Hughes points to several defendants who committed acts very similar to his — that is, they used the Internet to chat with undercover law enforcement officers masquerading as young girls, arranged meetings for the express purpose of sexual activity, and were subsequently arrested and convicted. However, these defendants were not subject to the ten-year minimum sentence of § 2422(b) because they were instead convicted under 18 U.S.C. § 2423(b), entitled "Transportation of minors":

A person who travels in interstate commerce or travels into the United States, or a United States citizen or an alien admitted for permanent residence in the United States who travels in foreign commerce, for the purpose of engaging in any illicit sexual conduct with another person shall be fined under this title or imprisoned not more than 30 years, or both.

For the purpose of § 2423, "illicit sexual conduct" is confined to sex with minors. 18 U.S.C. § 2423(f). Hughes argues that the only difference between these statutes is that § 2423(b) requires interstate travel, while § 2422(b) does not. He summarizes, "if Hughes drove out of state to meet the minor, rather than drive to a park in Kentucky, he would have avoided the 10 year mandatory minimum prescribed by § 2422(b) and would have been subject instead to a maximum of 30 years under § 2423(b)." Appellant's Br. at 20.

This argument fails. As a technical matter, Hughes is not similarly situated to the theoretical defendant who commits a violation of § 2423(b) because they commit separate crimes encompassing different elements. Most notably, § 2423(b) requires interstate travel and intent to engage in sexual conduct, but has no requirement that there be an element of enticement or coercion. Section 2422(b), on the other hand, requires that a defendant "persuades, induces, entices, or coerces" a minor to perform illicit sexual activity, or attempts to do so. We have held that § 2422(b) does not require proof of a specific intent to actually engage in sexual activity. United States v. Bailey, 228 F.3d 637, 639 (6th Cir. 2000) ("While it may be rare for there to be a separation between the intent to persuade and the follow-up intent to perform the act after persuasion, they are two clearly separate and different intents and the Congress has made a clear choice to criminalize persuasion and the attempt to persuade."). Section 2422(b), in other words, was designed to protect children from the act of solicitation itself — a harm distinct from that proscribed by § 2423(b). Indeed, had Hughes driven out of state to meet the minor, he would not "have avoided the 10 year mandatory minimum," as he could have been charged with both crimes. See, e.g., United States v. Angwin, 560 F.3d 549, 551 (6th Cir. 2009) (noting that the defendant was indicted and convicted under both § 2422(b) and § 2423(b)).

But even to the extent that both Hughes and a § 2423(b) offender would be similarly situated, in that they are both guilty of federal sex crimes, we perceive a rational basis for the different punishments. Congress could reasonably have decided that attempting to induce, or otherwise compel a minor to engage in sexual activity was a more serious crime than merely crossing state lines with the intent to engage in illicit sexual conduct with a minor. Section 2422(b) essentially requires proof that the defendant attempted to communicate with the minor, and through that communication, transform the minor into his victim. Section 2423(b) does not. This distinction is a rational basis on which Congress could have decided to punish the crimes differently.

Insofar as Hughes claims an equal protection violation because he was similarly situated to actual defendants prosecuted under § 2423(b), who in fact committed all the elements of a § 2422(b) offense, that is a claim for selective prosecution. Hughes has not argued any invidious discrimination, so this claim fails.

C

Hughes argues that his prosecution under § 2422(b) and the severity of his ten-year sentence violate both substantive and procedural due process because "they are arbitrary and irrational and thereby `shock the conscience.'" This argument fails.

The only procedural due process claim that Hughes appears to be making is that he was prosecuted under § 2422(b) as opposed to some other statute with no mandatory minimum. However, it is well established that prosecutors have broad discretion in charging decisions. Gardenhire v. Schubert, 205 F.3d 303, 319 (6th Cir. 2000). Absent some more pertinent allegation such as selective enforcement, the decision to charge Hughes under § 2422(b) falls within the broad range of discretion afforded prosecutors.

As for his substantive due process claim, Hughes appears to argue that his lengthy sentence, in light of his criminal history and the lack of a minor victim, "shocks the conscience." This argument is more properly presented as an Eighth Amendment claim, which we have already rejected. The test for a substantive due process claim is whether there is a fundamental right at stake, and if not, whether there exists a rational basis for the deprivation. Doe v. Mich. Dept. of State Police, 490 F.3d 491, 501 (6th Cir. 2007). We have noted, however, that "enactments that do not encroach upon fundamental rights [are] endowed with a presumption of legislative validity, and the burden is on [the challenger] to show that there is no rational connection between the enactment and a legitimate government interest." Sheffield v. City of Fort Thomas, 620 F.3d 596, 613 (6th Cir. 2010) (citation and quotation marks omitted) (alterations in original).

In this case, Hughes has no fundamental right at stake. See Chapman v. United States, 500 U.S. 453, 465, 111 S.Ct. 1919, 114 L.Ed.2d 524 (1991) (holding that there is no fundamental right to liberty once a person has been justly convicted). Further, there are a number of rational explanations for why Congress would want to sentence an attempted sexual predator to ten years in jail. The crime Hughes sought to commit is very serious, and his intended victim — a minor — was especially vulnerable. By prescribing a severe punishment, Congress could have acted to keep Hughes away from children and deter those similar to Hughes from committing the same crime. In merely reiterating his Eighth Amendment claim, Hughes has failed to establish that the legislature lacked a rational basis for imposing the mandatory minimum.

Finally, Hughes makes a generalized challenge to mandatory minimums, arguing that they deprive district courts of the ability to consider the factors in 18 U.S.C. § 3553(a). This argument essentially asks us to invalidate congressionally mandated minimum sentences on separation of powers. grounds, which we have already declined to do. United States v. Cecil, 615 F.3d 678, 695 (6th Cir. 2010) ("When a court and a mandatory minimum are in conflict, the minimum wins.").

III

Hughes's constitutional challenges to the ten-year mandatory minimum sentence under 18 U.S.C. § 2422(b) fail. We therefore AFFIRM the district court's sentence.