
559 F.3d 756 (2009)
UNITED STATES of America, Plaintiff-Appellee,
v.
Michael E. NAGEL, Defendant-Appellant.
No. 08-2535.
United States Court of Appeals, Seventh Circuit.
Argued February 19, 2009.
Decided March 24, 2009.
*758 Jonathan H. Koenig (argued), Office of the United States Attorney, Milwaukee, WI, for Plaintiff-Appellee.
Robert G. Lebell (argued), Lebell Dobroski & Morgan LLP, Milwaukee, WI, for Defendant-Appellant.
Before FLAUM and WILLIAMS, Circuit Judges, and KAPALA, District Judge.[1]
KAPALA, District Judge.
Michael E. Nagel, pled guilty to attempting to entice a minor to engage in a criminal sexual act in violation of 18 U.S.C. § 2422(b) and was sentenced to the mandatory minimum ten-year term of imprisonment. On appeal, argues that the mandatory minimum sentence violates the Fifth and Eighth Amendments to the United States Constitution because it is not subject to a "safety valve" allowing for a sentence below the mandatory minimum term. We affirm.

I. Background
By indictment, the government charged that defendant violated § 2422(b) when he:
used a facility and means of interstate commerce to attempt to persuade, induce, entice, and coerce a person under eighteen years of age to engage in sexual activity for which the defendant could be charged with a criminal offense, namely, by using a computer connected to the Internet to attempt to have sexual contact and sexual intercourse with a 14-year old female known to the defendant as "Maria," in violation of Wisconsin Statute 948.02(2) (second-degree sexual assault of a child).
In reality, "Maria" was a detective with the Milwaukee Police Department.
Defendant filed a motion to dismiss the charge and to declare the mandatory minimum ten-year sentence provision in § 2422(b) unconstitutional on its face and as applied to him. Defendant argued that the mandatory minimum penalty violates the Fifth Amendment's Equal Protection guarantee because it precludes application of the "safety valve" provision contained in 18 U.S.C. § 3553(f), and that it constitutes cruel and unusual punishment in violation of the Eighth Amendment because the penalty is grossly disproportionate to the gravity of the offense.
*759 Because defendant had not been convicted, the district court found defendant's as-applied arguments unripe and addressed only defendant's facial challenges. The district court found that the legislative history provided a rational basis for the mandatory minimum sentence because it indicated that Congress contemplated a sentencing mechanism that would underscore the seriousness of the offense. The district court held further that Congress had a rational basis not to provide a safety valve because there is a rational distinction between non-violent first-time drug offenders, to which § 3553(f) applies, and offenders who prey on children, to which it does not. Citing United States v. Gross, 437 F.3d 691 (7th Cir.2006), the district court also found defendant's Eighth Amendment challenge to be without merit.
Thereafter, the parties entered a conditional plea agreement under which the government agreed to recommend the mandatory minimum ten-year sentence. The factual basis for the plea established that Nagel had extensive sexually explicit computer chats and phone conversations with "Maria," who identified herself as a 14-year-old girl from Milwaukee. During these encounters, Nagel graphically expressed his desire to have sex with Maria. Eventually, Nagel traveled from Burbank, Illinois, to Milwaukee, Wisconsin, to meet with Maria and was arrested.
After pleading guilty, but before sentencing, defendant renewed his motion to dismiss the charge on Fifth and Eighth Amendment grounds and maintained that he met all the requirements of the § 3553(f) safety valve. The district court found defendant ineligible for relief under the safety valve because he did not commit any of the offenses enumerated in § 3553(f). The district court reiterated its previous conclusion that there was a rational basis for enacting the mandatory minimum sentence in § 2422(b) without regard to any safety valve provision and, therefore, the statute did not violate equal protection principles. The district court rejected defendant's Eighth Amendment as-applied argument that his sentence was unduly harsh in light of his criminal history, characteristics, and his unlikeliness of repeating the offense. The district court also continued to reject defendant's facial challenge to the statute on cruel and unusual punishment grounds. The district court sentenced defendant to 120 months' imprisonment, but made clear that it viewed the mandatory minimum sentence provision as "draconian" in nature and stated that, but for the mandatory minimum provision in § 2422(b), it would have sentenced defendant to a sentence within the otherwise applicable advisory Sentencing Guidelines range of 46 to 57 months. Defendant now appeals.

II. Analysis
On appeal, defendant argues that § 2422(b)'s mandatory minimum ten-year sentence, which is not subject to the safety valve provision of § 3553(f), violates the Fifth and Eighth Amendments to the United States Constitution. We review de novo constitutional challenges to a sentence. United States v. Figueroa-Espana, 511 F.3d 696, 705 (7th Cir.2007).

A. Fifth Amendment
Defendant continues to advance the same facial equal protection argument that he made in the district court: that there is no rational basis to punish more severely those who have been convicted of violating § 2422(b) than those who have been convicted of the controlled substance offenses enumerated in § 3553(f).[2] Like the district court, we have little difficulty perceiving of a rational basis for the classification.
*760 The Supreme Court has noted that while the Fourteenth Amendment applies only to the states, the Fifth Amendment applies to the federal government and also "contains an equal protection component." S.F. Arts & Athletics, Inc. v. U.S. Olympic Comm., 483 U.S. 522, 542 n. 21, 107 S.Ct. 2971, 97 L.Ed.2d 427 (1987). The approach to Fifth Amendment equal protection claims has "`been precisely the same as to equal protection claims under the Fourteenth Amendment.'" Id. (quoting Weinberger v. Wiesenfeld, 420 U.S. 636, 638 n. 2, 95 S.Ct. 1225, 43 L.Ed.2d 514 (1975)). Equal protection of the laws means that all persons similarly situated should be treated alike. See Plyler v. Doe, 457 U.S. 202, 216, 102 S.Ct. 2382, 72 L.Ed.2d 786 (1982).
Defendant concedes on appeal that his equal protection challenge is subject to the rational-basis test. Under that lenient standard, the statute will be upheld "if there is a rational relationship between the disparity of treatment and some legitimate governmental purpose." Smith v. City of Chi., 457 F.3d 643, 652 (7th Cir. 2006) (quotation marks omitted). The party challenging the statute has the burden of eliminating any reasonably conceivable state of facts that could provide a rational basis for the classification. Id.
The offense to which defendant pleaded guilty provides:
Whoever, using the mail or any facility or means of interstate or foreign commerce... 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). The "safety valve" provision of § 3553(f) applies only to the controlled substance offenses specifically enumerated therein and "allow[s] certain non-violent first-time drug offenders to avoid the application of statutory minimum mandatory sentences if they cooperated with the government." United States v. Olivas-Ramirez, 487 F.3d 512, 516 (7th Cir.2007) (quotation marks omitted).
Defendant's equal protection argument fails because criminal defendants who violate § 2422(b) are not similarly situated for sentencing purposes with criminal defendants who violate the controlled substance offenses enumerated in § 3553(f). See Smith ex rel. Smith v. Severn, 129 F.3d 419, 429 (7th Cir.1997) ("An equal protection violation occurs only when different legal standards are arbitrarily applied to similarly situated individuals."). Therefore, Congress is not required to treat such disparate individuals in the same manner. The following distinctions demonstrate this point.
As noted by the district court, the Joint Explanatory Statement of the Committee of Conference for The Protection of Children from Sexual Predators Act of 1998 (PROTECT Act), Pub.L. No. 105-314 § 203(a)(1), 112 Stat. 2974 (1998), evinces a congressional recognition of the seriousness of attempted sexual enticement of a minor.[3]See H.R.Rep. No. 108-66, at 51 *761 (2003) (Conf.Rep.), as reprinted in 2003 U.S.C.C.A.N. 683, 685. Congress also perceived a need to prevent judicial leniency, especially in cases where there is no actual child victim. Id. Because individuals who violate § 2422(b) always present a serious danger to children, it was entirely rational for Congress to conclude that violations of § 2422(b) are always serious enough to require a mandatory minimum sentence. In contrast, while the drug offenses enumerated in § 3553(f) are also serious, particular drug offenders present varying degrees of risk to the community depending upon the circumstances. Congress also believed that violators of § 2422(b) were being sentenced too leniently. In contrast, Congress apparently believed that certain non-violent drug offenders were being sentenced too harshly. See United States v. Williams, 299 F.3d 250, 259 (3rd Cir.2002) ("[P]roviding a safety valve for nonviolent, first-time drug offenders has a rational relationship to the legitimate government goal of providing exceptions to draconian mandatory minimum sentences for such individuals."). Thus, both the relative seriousness of the offense and the leniency problem are two rational bases for withholding the safety valve from those convicted of violating § 2422(b) while permitting the operation of a safety valve in sentencing qualified violators of the offenses enumerated in § 3553(f).[4]
The court also agrees with the government that the need for cooperation in drug prosecutions provides a rational basis for affording the safety valve to qualified drug offenders and not to offenders who attempt to sexually entice minors. Often, there are multiple offenders involved in the distribution of controlled substances and, consequently, in appropriate cases there is a need to encourage qualified drug offenders to cooperate with the government in drug prosecutions. See United States v. Marin, 144 F.3d 1085, 1090 (7th Cir.1998) (holding that the safety valve provision of § 3553(f) "allows less knowledgeable and less culpable defendants who have fully assisted the government by providing all of the information they have to avoid the application of the statutory mandatory minimum sentences"). The same need typically is not present in prosecutions for attempted sexual enticement of a minor because such offenders ordinarily act alone. For this reason, the public's interest in preventing drug trafficking is advanced by affording the safety valve provision of § 3553(f) to qualifying drug offenders, while no such interest is advanced by affording the safety valve to those who violate § 2422(b).
Another rational basis for the disparity in application of the safety valve is that § 2422(b) is designed to protect children while the drug offenses specifically enumerated in § 3553(f) were not designed exclusively for the protection of children. As the Supreme Court has stated: "It is evident beyond the need for elaboration that [the government's] interest in safeguarding the physical and psychological well-being of a minor is compelling." Osborne v. Ohio, 495 U.S. 103, 109, 110 S.Ct. *762 1691, 109 L.Ed.2d 98 (1990) (quotation marks omitted).
In sum, we agree with the district court that there is a rational distinction between first time, non-violent, drug offenders who have cooperated with the government and those offenders who have attempted to prey on children. This distinction provides a rational basis for the sentencing disparity that defendant challenges. Therefore, defendant has not carried his burden of eliminating any reasonably conceivable state of facts to support a rational basis for withholding the safety valve provision of § 3553(f) from those who violate § 2422(b). See Smith, 457 F.3d at 652. Consequently, defendant's equal protection challenge to § 2422(b)'s ten-year mandatory minimum sentence fails.

B. Eighth Amendment
Defendant also argues that the ten-year mandatory minimum sentence provision of § 2422(b) is grossly disproportionate to the offense and therefore violates the Eighth Amendment's proscription of cruel and unusual punishment both as applied to him and on its face. In response, the government argues that the ten-year mandatory minimum sentence is not disproportionate to the offense of attempted sexual enticement of a minor and, therefore, does not violate the Eighth Amendment.
This court has yet to rule on an Eighth Amendment disproportionate penalty argument with respect to the ten-year mandatory minimum sentence of § 2422(b). Last December, however, we rejected such a claim in dicta. See United States v. Davey, 550 F.3d 653, 658 (7th Cir.2008) (concluding that defendant's argument that his 126-month sentence violated the Eighth Amendment was barred by his appeal waiver, but stating, "[e]ven if Davey's Eighth Amendment argument somehow escapes his appeal waiver ... we would reject it"). Our rationale in Davey is consistent with the Tenth Circuit's opinion in United States v. Munro, 394 F.3d 865, 873 (10th Cir.2005), holding that the former five-year mandatory minimum sentence of § 2422(b) does not constitute cruel and unusual punishment. Id. at 873; see also United States v. Butters, 267 Fed. Appx. 773, 778 (10th Cir.2008) (holding that § 2422(b)'s mandatory minimum ten-year sentence does not violate the Eighth Amendment). For the following reasons, we now hold that the ten-year mandatory minimum sentence provision in § 2422(b) is not grossly disproportionate to the crime of attempting to entice a minor to engage in a criminal sexual act and therefore does not violate the Eighth Amendment's prohibition of cruel and unusual punishment.
The Supreme Court has recognized that, "[t]he Eighth Amendment ... contains a narrow proportionality principle that applies to noncapital sentences." Ewing v. Cal., 538 U.S. 11, 20, 123 S.Ct. 1179, 155 L.Ed.2d 108 (2003) (quotation marks omitted). The Eighth Amendment's Cruel and Unusual Punishment Clause prohibits sentences that are grossly disproportionate to the crime committed. Solem v. Helm, 463 U.S. 277, 284, 103 S.Ct. 3001, 77 L.Ed.2d 637 (1983). Three factors are relevant in determining whether a sentence is so disproportionate to the crime committed that the sentence violates the Eighth Amendment: "(i) the gravity of the offense and the harshness of the penalty; (ii) the sentences imposed on other criminals in the same jurisdiction; and (iii) the sentences imposed for commission of the same crime in other jurisdictions." Id. at 292, 103 S.Ct. 3001. However, it is clear that "our first task is to ascertain whether [the defendant's] case is `the rare case in which a threshold comparison of the crime committed and the sentence imposed leads to an inference of gross disproportionality.'" *763 Gross, 437 F.3d at 692-93 (quoting Ewing, 538 U.S. at 20, 123 S.Ct. 1179). "Absent such an inference, we need not conduct any comparative analysis within and between jurisdictions." Id. at 693 (quotation marks omitted). Successful proportionality challenges to noncapital sentences have been exceedingly rare. Ewing, 538 U.S. at 21, 123 S.Ct. 1179. "[T]he fixing of prison terms for specific crimes involves a substantive penological judgment that, as a general matter, is properly within the province of legislatures, not courts." Harmelin v. Michigan, 501 U.S. 957, 998, 111 S.Ct. 2680, 115 L.Ed.2d 836 (1991) (Kennedy, J., concurring in part and concurring in the judgment) (quotation marks omitted).
As for his as-applied challenge, defendant argues that under his particular circumstances his case is the rare occurrence which renders his sentence grossly disproportionate. Specifically, defendant maintains that he has no criminal history, let alone a history of sex offending, the evidence at the sentencing hearing shows that he has a low risk for recidivism, and in his case there was no actual minor victim. For the reasons that follow, we conclude that these circumstances do not raise an inference of gross disproportionality.
In Gross, we rejected the defendant's as-applied argument that the fifteen-year mandatory minimum sentence for distribution of child pornography constituted cruel and unusual punishment. In doing so, we highlighted various decisions of the Supreme Court rejecting Eighth Amendment disproportionate sentence arguments:
The Court's precedent in this area reflects how high the bar is set. See [Ewing, 538 U.S.] at 28-3, [123 S.Ct. 1179, 155 L.Ed.2d 108] (affirming sentence of 25 years to life imposed for felony grand theft of three golf clubs under three strikes law); Harmelin, 501 U.S. at 961, 996, [111 S.Ct. 2680, 115 L.Ed.2d 836] (affirming life in prison without the possibility of parole for first-time offender possessing 672 grams of cocaine); Davis, 454 U.S. at 370-71, [102 S.Ct. 703, 70 L.Ed.2d 556] (no constitutional error in two consecutive terms of 20 years in prison for possession with intent to distribute and distribution of 9 ounces of marijuana); Rummel v. Estelle, 445 U.S. 263, 265-66, 100 S.Ct. 1133, 63 L.Ed.2d 382 (1980) (upholding life in prison without the possibility of parole under three strikes law where triggering offense was obtaining $120.75 by false pretenses and the loss amount of the two previous fraud felonies was $80, and $28.36, respectively). But see Solem v. Helm, 463 U.S. 277, 296-97, 103 S.Ct. 3001, 77 L.Ed.2d 637 (1983) (holding that the Eighth Amendment prohibited a sentence of life without the possibility of parole where the defendant had previously committed six "minor" and "nonviolent" felonies and his triggering offense was uttering a "no account" check for $100).
Gross, 437 F.3d at 693 (parallel citations omitted). We concluded that "[u]nder this precedent, it is clear that [the defendant's] case is not the rare one in which comparing the gravity of the offense to the harshness of the sentence leads to an inference of gross disproportionality." Id. Similarly, we conclude that the instant case does not lead to an inference of gross disproportionality.
While defendant may have had no criminal history prior to the events that led to the instant prosecution, in this case he pled guilty to attempting to meet with a girl that he believed to be 14 years old and with whom he intended to have sexual intercourse. Employing sexually graphic language, defendant arranged this would-be rendezvous over the Internet, which he also used to send video images of his genitals *764 and anus to the person he thought was a 14-year-old girl. For this he received a ten-year sentence, the statutory minimum. Defendant has not demonstrated how his ten-year sentence for attempting to entice a minor to engage in a criminal sexual act is any more disproportionate than the life sentence without the possibility of parole imposed on a first-time offender for possessing 672 grams of cocaine. See Harmelin, 501 U.S. at 1021, 111 S.Ct. 2680 (White, J., dissenting). Suffice it to say that defendant's sentence is less severe that the sentence imposed in Harmelin where the Supreme Court rejected an Eighth Amendment proportionality challenge, and does not resemble the life sentence for multiple non-violent felonies struck down as disproportionate in Solem.
Defendant's reliance on the clinical psychologist's report presented at sentencing, which indicated that defendant is unlikely to reoffend, also is misplaced. Even if there was no need to incapacitate or rehabilitate defendant, as this evidence seems to suggest, defendant's ten-year sentence continues to serve the purposes of societal retribution and deterring others from engaging in similar conduct. See Ewing, 538 U.S. at 25, 123 S.Ct. 1179 ("A sentence can have a variety of justifications, such as incapacitation, deterrence, retribution, or rehabilitation."). Thus, even if the psychologist's predictions that defendant will not reoffend prove true, an inference of gross disproportionality does not arise.
Defendant's "no actual minor victim" argument also fails to raise an inference of gross disproportionality. The type of crime defendant pled guilty to does not require an actual minor victim but, rather, only that the defendant believed the victim was a minor. See, e.g., United States v. Morris, 549 F.3d 548, 550 (7th Cir.2008); United States v. Coté, 504 F.3d 682, 687 (7th Cir.2007), cert. denied, ___ U.S. ___, 128 S.Ct. 2519, 171 L.Ed.2d 800 (U.S. May 27, 2008) (No. 07-10525). It is clear that Congress contemplated a mandatory minimum sentence whether there is an actual minor involved or not. As indicated above, the legislative history clearly indicates a congressional belief that attempted sexual enticement of a minor is a serious offense even where a law enforcement agent poses as the minor victim and that it did not want those who commit the offense under those circumstances to receive lenient sentences. See H.R.Rep. No. 108-66, at 51; see also, Butters, 267 Fed.Appx. at 778 ("[A]ttempted sexual enticement of a minor is a serious offense whether or not the defendant has successfully contacted an actual minor or has preyed on children in the past."). The fact that defendant had not actually victimized a minor, therefore, raises no inference that his ten-year sentence was grossly disproportionate to the crime he committed.
The only Eighth Amendment facial challenge that we can glean from defendant's briefs is that the ten-year mandatory minimum sentence in § 2422(b) is grossly disproportionate to the offense of attempted sexual enticement of a minor. In order to mount a successful facial attack, "the challenger must establish that no set of circumstances exists under which the [statute] would be valid." United States v. Salerno, 481 U.S. 739, 745, 107 S.Ct. 2095, 95 L.Ed.2d 697 (1987). As noted above, the Eighth Amendment forbids extreme sentences that are "grossly disproportionate to the crime." See Harmelin, 501 U.S. at 995, 111 S.Ct. 2680. The Supreme Court has recognized the theoretical possibility of finding a statute facially disproportionate in violation of the Eighth Amendment. See Rummel, 445 U.S. at 274 n. 11, 100 S.Ct. 1133 ("This is not to say that a proportionality principle would not come into play in the extreme example ... [where] a legislature made *765 overtime parking a felony punishable by life imprisonment."). In this case, defendant has failed to establish gross disproportionality on the face of § 2422(b) because a ten-year sentence for attempted sexual enticement of a minor does not approach the theoretical possibility mentioned in Rummel. In addition, as discussed above, the ten-year mandatory minimum sentence defendant received is not grossly disproportionate to his offense; therefore, defendant is unable to succeed on his Eighth Amendment facial challenge. See Salerno, 481 U.S. at 745, 107 S.Ct. 2095.
We conclude that neither the ten-year mandatory minimum sentence provision of § 2422(b) itself, nor the ten-year sentence defendant received in this case, lead to an inference of gross disproportionality. Therefore, defendant's facial and as-applied Eighth Amendment challenges to § 2422(b) fail. Because we have determined that defendant's case does not lead to an inference of gross disproportionality we do not need to conduct any comparative analysis of sentences within and between jurisdictions. See Gross, 437 F.3d at 694.

III. Conclusion
Based on the foregoing, we AFFIRM defendant's sentence and the district court's order rejecting defendant's constitutional challenges under the Fifth and Eighth Amendments.
NOTES
[1]  The Honorable Frederick J. Kapala of the United States District Court for the Northern District of Illinois, sitting by designation.
[2]  In his brief, defendant purported to advance both facial and as-applied equal protection challenges to the statute. However, counsel for defendant represented at oral argument that defendant was proceeding only on his facial challenge. Accordingly, we will only review defendant's facial challenge.
[3]  The PROTECT Act changed the sentence for a violation of § 2422(b) from a maximum of fifteen years imprisonment to a mandatory minimum of five years and a maximum of thirty years. On July 27, 2006, Congress passed the Adam Walsh Child Protection and Safety Act of 2006 (Adam Walsh Act), Pub.L. No. 109-248, § 203, 120 Stat. 587, 613 (2006), amending § 2422(b) to include a mandatory minimum of ten years imprisonment and a maximum of life.
[4]  In his opening brief, defendant makes the effort to point out that while the Joint Explanatory Statement of the PROTECT Act has been used extensively to find a rational basis, there is no comparable explanatory statement for the provision of the Adam Walsh Act which increased the mandatory minimum sentence of § 2422(b) from five years to ten years. Defendant does not, however, develop any argument in support of this effort. To the extent defendant is arguing that there can be no rational basis if Congress does not expressly state that basis when a law is promulgated, he is incorrect. See Smith, 457 F.3d at 652 ("The government need not have articulated a reason for the challenged action at the time the decision was made.").
