Richard Vieux is a pro se federal prisoner serving a total sentence of life plus 45 years’ imprisonment for numerous federal offenses arising out of two carjackings and three armed robberies. Vieux appeals the district court’s dismissal of his 28 U.S.C. § 2241 petition for a writ of habeas corpus. After review, we affirm.
I. BACKGROUND FACTS
A. 1995 Convictions and 1996 Sentences in the Middle District of Florida
In 1995, iii the Middle District of Florida, a jury convicted Vieux of two counts of carjacking with intent to cause death or serious bodily harm, in violation of 18 U.S.C. §§ 2119 and 2 (Counts 2 and 6); three counts of use of a firearm during three robberies, in violation of 18 U.S.C. § 924(c)(1) (Counts 3, 7 and 9); three counts of possession of a firearm by a convicted felon, in violation of 18 U.S.C. § 922(g)(1) (Counts 5, 10 and 12); possession with intent to distribute cocaine, in violation of 21 U.S.C. § 841(a)(1) (Count 11); obstruction of commerce by robbery, in violation of 18 U.S.C. § 1951(a) (Count 8); and conspiracy to commit the charged substantive offenses, in violation of 18 U.S.C. § 371 (Count 1).
After grouping multiple offenses, the Presentence Investigation Report (“PSI”) showed Vieux had a combined adjusted offense level of 43 and a criminal history category of III, yielding a guidelines range sentence of life imprisonment.
The district court imposed a total sentence of life, plus 45 years. The 45 years represented the statutorily required consecutive sentences on Vieux’s § 924(c) firearm offenses consisting of: a five-year consecutive sentence on Count 3, a twenty-year sentence on Count 7 to be served consecutive to the Count 3 sentence, and a twenty-year sentence on Count 9, to be served consecutive to Count 7 sentence. The judgment does not separate all of the counts, but at a minimum the district court imposed a life sentence on Count 6, the carjacking offense that resulted in death.
At the time of Vieux’s 1996 sentencing, the federal carjacking statute, in § 2119(2), increased the statutory maximum prison term from 15 years to 25 years “if serious bodily injury ... results.” And, if “death results,” § 2119(3) increased the statutory maximum prison term to “any number of years up to life” or a death sentence. In 1995, this Court held that the “serious bodily injury” or “death” enhancements were sentencing factors that could be found by the district court at sentencing, not elements of the offense that must be proven to the jury. See United States v. Williams, 51 F.3d 1004, 1009 (11th Cir.1995), abrogated by Jones v. United States, 526 U.S. 227, 119 S.Ct. 1215, 143 L.Ed.2d 311 (1999); 18 U.S.C. § 2119(2) & (3) (and, “if death results,” providing for a prison term of).
Consistent with Williams, the sentencing court found that the carjacking in Count 2 occurred on April 13, 1995, and resulted in serious bodily injury to the victim driver. The sentencing court found the carjacking in Count 6 occurred on April 22,1995, and resulted in the death of the victim driver. As a result, the sen*893tencing court imposed prison sentences of 25 years on Count 2 and a life sentence on Count 6.
On direct appeal, Vieux did not raise any issue with respect to his enhanced sentences under § 2119(2) and (3) or argue that the facts supporting his enhanced sentences should have been charged in the indictment and found by the jury beyond a reasonable doubt.1 On March 3, 1998, this Court affirmed Vieux’s convictions and sentences. See United States v. Taylor, 138 F.3d 955 (11th Cir.1998) (table).
B. First § 2255 Motion in the Middle District of Florida
On March 5, 1999, Vieux filed his initial 28 U.S.C. § 2255 motion in the Middle District of Florida. Vieux’s § 2255 motion did not raise any claims particular to his two carjacking convictions. He did not challenge the sentencing court’s finding that his carjackings involved death and serious bodily injury to his victims.
Around the time Vieux filed his § 2255 motion, the United States Supreme Court issued two decisions implicating the federal carjacking statute, 18 U.S.C. § 2119. On March 2, 1999, the Supreme Court decided Holloway v. United States, which concluded that the intent element of § 2119 required proof only that at the moment that the defendant demanded or took control of the car, he possessed the intent to seriously harm or ldll the driver if necessary in order to steal the car. 526 U.S. 1, 3, 12, 119 S.Ct. 966, 968, 972, 143 L.Ed.2d 1 (1999). A few weeks later, on March 24, 1999, the Supreme Court decided Jones v. United States, which concluded that the enhanced penalties in subsections (2) and (3) of § 2119, when serious bodily injury or death resulted, were separate elements of the offense, not sentencing factors that could be found by the sentencing court. 526 U.S. 227, 251-52, 119 S.Ct. 1215, 1228, 143 L.Ed.2d 311 (1999).
On March 19,1999, Vieux filed a motion to amend his § 2255 motion, but did not explain what claims Vieux wanted to add to his motion, did not refer to his carjacking convictions, and did not cite Holloway, which was just decided. The motion merely asked the district court to allow him to amend his § 2255 motion, given that the court had denied his request to adopt a codefendant’s § 2255 motion. On March 29, 1999, the district court denied the motion to amend because Vieux failed to submit a proposed amended § 2255 motion along with the motion to amend.
On April 19, 1999, Vieux filed a second motion to amend, this time stating, “In the waking [sic] of Jones v. U.S., No. 97-6203 March 24, 1999, this amendment motion for Addendum to § 2255 is in good faith and not to delay the court.” On April 26, 1999, the district court denied the motion again because Vieux “did not submit a proposed amended section 2255 motion in its entirety.”
Separately, on May 7, 1999, Vieux attempted to file an “Addendum Motion Under 28 U.S.C., § 2255.” On May 11, 1999, the district court struck this pleading because Vieux “did not obtain leave of court to file the amended section 2255 motion.”2
*894On June 11, 1999, Vieux made a final attempt to amend his original § 2255 motion, again stating that the amendment was sought in the wake of Jones. On June 25, 1999, the district court denied the motion to amend, explaining that it had “previously informed Defendant as to how the proposed section 2255 motion should be presented to the Court, and Defendant has failed to do so.” The district court instructed the clerk “to return the proposed pleadings to Defendant.” The district court also directed the government to file a response to Vieux’s original § 2255 motion.
On August 5, 1999, the district court denied Vieux’s original § 2255 motion on the merits and dismissed his case with prejudice.3 Vieux filed a notice of appeal, which this Court construed as a motion for a certificate of appealability and denied. The United States Supreme Court denied Vieux’s petition for certiorari.
C.2002 Second § 2255 Motion in the Middle District of Florida
On February 25, 2002, Vieux filed a second § 2255 motion in the Middle District of Florida. Vieux’s second § 2255 motion raised three claims relating to Counts 2 and 6, the carjacking offenses, two based on Jones and one based on Holloway. The district court dismissed Vieux’s second § 2255 motion without prejudice because Vieux had not first obtained authorization from this Court to file a second or successive § 2255 motion, as required by 28 U.S.C. § 2244(b)(3)(A).
The district court, and then this Court, denied Vieux’s requests for a certificate of appealability. The U.S. Supreme Court denied Vieux’s petition for certiorari.
D. 2005 Application for Leave to File Successive § 2255 Motion
On February 18, 2005, Vieux filed with this Court an application for leave to file a second or successive § 2255 motion. This Court denied Vieux’s application because Vieux’s claims did not rely on a new rule of constitutional law made retroactive or rely on newly discovered evidence. See 28 U.S.C. § 2255(h).
E. Rule 60(b) Motion in Middle District of Florida
On December 13, 2005, Vieux returned to the Middle District of Florida and filed a motion for relief from the judgment pursuant to Federal Rule of Civil Procedure 60(b). Vieux complained that the district court “on four (4) different occasions, denied him his absolute right to amend his 1999 original § 2255,” and that he was “subsequently being subjected to the restrictive provisions of 28 U.S.C. § 2244.”
The district court filed Vieux’s Rule 60(b) motion as a separate action under *895§ 2255. In dismissing the action without prejudice, the district court noted that Vieux sought to challenge his carjacking convictions based on the Supreme Court’s Jones v. United, States, which was a claim of error in his federal conviction subject to the limitation on successive § 2255 motions. The district court explained that it lacked jurisdiction to entertain Vieux’s successive § 2255 motion without authorization from this Court.4
Vieux appealed the dismissal. Both the district court and this Court denied Vieux’s' request for a certificate of appealability. The U.S. Supreme Court denied Vieux’s petition for certiorari.
F. First § 2241 Petition in the Middle District of Pennsylvania in 2007
While incarcerated in Pennsylvania, Vieux filed his first § 2241 petition in the Middle District of Pennsylvania, seeking to invoke the savings clause in § 2255(e). See Vieux v. Williamson, 4:07-CV-0645, 2007 WL 1799712 (M.D.Pa. June 20, 2007). Vieux’s § 2241 petition challenged his carjacking convictions and sentences in light of the Supreme Court’s Jones decision and argued that he could not “challenge the legality of his sentence in a § 2255 motion because he has diligently tried to raise his claims via § 2255, but to no avail.” Id. at *3, *7. The district court in Pennsylvania dismissed Vieux’s § 2241 petition for lack of jurisdiction because his claims needed to be brought in a § 2255 motion, which must be filed in the sentencing court after obtaining permission from this Court to file a successive § 2255 motion. The district court further concluded that the denials of Vieux’s previous § 2255 motions were “insufficient to show that § 2255.remedy is inadequate or ineffective,” as required by § 2255(e). Id. at *4.
On appeal, the Third Circuit affirmed, “agree[ing] with the District Court’s determination that Vieux’s situation does not render section 2255 inadequate or ineffective.” Vieux v. Williamson, 250 F.App’x 519, 521 (3rd Cir.2007). The Third Circuit stressed that the fact that “Vieux was denied leave to amend the [original] section 2255 in the sentencing court” and “has failed thus far in obtaining authorization from the Eleventh Circuit to file another § 2255 motion does not show the inadequacy of that remedy.” Id. at 521-22. The U.S. Supreme Court denied Vieux’s petition for certiorari. Vieux v. Williamson, 553 U.S. 1012, 128 S.Ct. 2071, 170 L.Ed.2d 808 (2008).
G. 2008 Motion for Writ of Coram No-bis in the Middle District of Florida
On June 12, 2008, Vieux filed a “Writ of Error Coram Nobis” in the Middle District of Florida, again challenging his carjacking convictions and sentences citing Holloway and Jones. The district court denied Vieux’s motion, stating that Vieux was “attempting to collaterally attack his conviction and sentence which can only be brought on a Section 2255 motion not by a motion for writ of coram nobis.” The district court concluded that it was “without jurisdiction to consider a 5th such motion.” The district court denied Vieux’s request for a certificate of appealability. Later on, this Court dismissed Vieux’s appeal for lack of prosecution.
With this background,' we turn to the instant § 2241 petition before this Court.
II. SECOND § 2241 PETITION IN THE NORTHERN DISTRICT OF ALABAMA
By mid-2009, Vieux was housed at Tal-ladega FCI in Alabama. On June 24, *8962011, Vieux filed the instant § 2241 petition in ‘the Northern District of Alabama, again seeking to challenge his carjacking convictions and sentences through the savings clause in § 2255(e). Vieux’s § 2241 petition argued that the repeated denials of his motions to amend his original § 2255 motion — filed in the Middle District of Florida — to add claims based on Jones and Holloway rendered § 2255 “inadequate or ineffective” to test the legality of his “detention” and that he met the requirements of the “savings clause” in § 2255(e).
The magistrate judge’s report (“R & R”) concluded that Vieux’s § 2241 petition did not meet the requirements of § 2255(e)’s savings clause because: (1) Holloway and Jones were not retroactively applicable to cases on collateral review; (2) Holloway and Jones did not establish that Vieux was convicted of a nonexistent offense; and (3) in any event, Vieux had not shown that the district court abused its discretion in denying Vieux leave to amend his original § 2255 motion. Because Vieux could not establish that the § 2255 remedy was “inadequate or ineffective,” the district court was not authorized under § 2255(e) to entertain his claims via a § 2241 petition.
Over Vieux’s objection, the district court adopted the R & R and dismissed Vieux’s § 2241 petition with prejudice for lack of jurisdiction. The district court denied Vieux’s subsequent motion under Federal Rule of Civil Procedure 59(e) to alter or amend the judgment. Vieux filed this appeal.5
III. DISCUSSION
A. General Principles
Section 2241 habeas petitions “are generally reserved for challenges to the execution of a sentence or the nature of confinement, not the validity of the sentence itself or the fact of confinement.” Bryant v. Warden, FCC Coleman, 738 F.3d 1253, 1288 (11th Cir.2013) (emphasis omitted). Typically, once a conviction becomes final, a prisoner collaterally attacks the validity of his federal conviction or sentence by filing a § 2255 motion in the district of conviction. 28 U.S.C. § 2255; Bryant, 738 F.3d at 1256; Sawyer v. Holder, 326 F.3d 1363, 1365 (11th Cir.2003). Once the prisoner has filed a § 2255 motion, he must apply for and receive authorization from this Court before filing a successive § 2255 motion. 28 U.S.C. §§ 2255(h), 2244(b)(3); Bryant, 738 F.3d at 1260.
However, under our precedent, the “savings clause” in § 2255(e) permits a prisoner to file a § 2241 petition if the prisoner establishes that § 2255’s remedy was “inadequate or ineffective to test the legality of his detention.” 28 U.S.C. § 2255(e); Sawyer, 326 F.3d at 1365. The savings clause is a jurisdictional provision, such that a petitioner must show § 2255’s remedy is “inadequate and ineffective” before the district court has jurisdiction to review the § 2241 petition on the merits. Bryant, 738 F.3d at 1262; Williams v. Warden, 713 F.3d 1332, 1337 (11th Cir.2013), cert. denied, — U.S. -, 135 S.Ct. 52, 190 L.Ed.2d 29 (2014).6
*897To open the § 2255(e) portal to an actual-innocence conviction claim, the § 2241 petitioner must show that: (1) the petitioner’s claim is based on a retroactively applicable Supreme Court decision; (2) the holding of which establishes the petitioner was convicted of a non-existent offense; and (3) circuit law squarely foreclosed the petitioner from raising the conviction claim at “‘trial, direct appeal, or first § 2255 motion.’ ” Bryant, 738 F.3d at 1264 (quoting. Wofford v. Scott, 177 F.3d 1236, 1244 (11th Cir.1999)).
To open the § 2255(e) portal to a sentencing claim, the § 2241 petitioner must establish that: (1) binding circuit precedent squarely foreclosed the claim “throughout his sentence, direct appeal, and first § 2255 proceeding”; (2) “subsequent to his first 2255 proceeding,” a U.S. Supreme Court decision overturned that circuit precedent; (3) the rule announced in that Supreme Court decision applies retroactively on collateral review; (4) as a result of the new rule, the petitioner’s current sentence exceeds the statutory maximum penalty authorized by Congress; and (5) the savings clause reaches the petitioner’s claim. Bryant, 738' F.3d at 1274 (involving the violent felony enhancement in 18 U.S.C. § 924(e)); see also Jeanty v. Warden, 757 F.3d 1283, 1285 (11th Cir.2014) (involving the prior felony drug offense enhancement in 21 U.S.C. § 841(b)(1)(B)).
B. Vieux’s § 2241 Claims
Here, the district court did not err in dismissing Vieux’s § 2241 petition for lack of-jurisdiction. Vieux’s attack on his carjacking convictions needs to be viewed as two separate claims. The first, based on Jones, is a sentencing claim. The second, based on Holloway, is a claim of actual innocence of the carjacking offenses.
Jones held that the facts necessary to impose the enhanced prison penalties in either subsections (2) or (3) of § 2119— that the carjacking resulted in either serious bodily injury or death — were elements of the carjacking offense that needed to be charged in the indictment, submitted to the jury, and proven beyond a reasonable doubt. Jones, 526 U.S. at 251-52, 119 S.Ct. at 1228. Jones is merely a specific application to the federal carjacking statute of the general rule announced one year later in Apprendi v. New Jersey. See Apprendi 530 U.S. 466, 490, 120 S.Ct. 2348, 2362-63, 147 L.Ed.2d 435 (2000); see also United States v. Booker, 543 U.S. 220, 237, 125 S.Ct. 738, 752, 160 L.Ed.2d 621 (2005) (explaining that the general rule applied in Booker was “first considered in Jones and developed Apprendi and subsequent cases”). Because the Apprendi rule does not apply retroactively to cases on collateral review, neither does Jones, a decision applying that rule. See Dohrm-ann v. United States, 442 F.3d 1279,1281-82 (11th Cir.2006); McCoy v. United States, 266 F.3d 1245, 1258 (11th Cir.2001) (“[W]e hold that the new constitutional rule of criminal procedure announced in Apprendi does not apply retroactively on collateral review.”)'.7
Because Jones is not retroactively applicable on collateral review, Vieux has not *898satisfied Bryant’s test, and the § 2255(e) portal is not opened as to the sentencing claims in his § 2241 petition.8
Vieux’s second claim, based on Holloway, is an actual-innocence claim. In Holloway, the Supreme Court concluded that § 2119 did not require proof of an unconditional intent to kill or injure in all events, but instead required proof only that at the moment the defendant demanded or took control over the driver’s car the defendant possessed conditional intent to kill or injure if necessary to steal the car. Holloway, 526 U.S. at 3, 12, 119 S.Ct. at 968, 972. Setting aside the fact that the Supreme Court in Holloway adopted a broader reading of the intent requirement that likely would have been detrimental to Vieux, at the time that Holloway was decided, this Court had not addressed the proper interpretation of § 2119’s intent requirement. As such, this Circuit precedent did not foreclose Vieux from raising a claim as to the intent requirement at trial, on direct appeal, or in his initial § 2255 motion, and Holloway did not overturn this Circuit’s precedent. Thus, Vieux’s Holloway claim also fails to open the savings clause portal.
Vieux’s argument that the district court violated the Suspension Clause by dismissing his § 2241 petition lacks merit, too. See Gilbert v. United States, 640 F.3d 1293, 1316-17 (11th Cir.2011) (en banc) (citing Felker v. Turpin, 518 U.S. 651, 116 S.Ct. 2333, 135 L.Ed.2d 827 (1996)). Furthermore, because Vieux has not successfully opened § 2255(e)’s savings clause portal to § 2241 jurisdiction, we cannot reach Vieux’s argument based on Clisby v. Jones, 960 F.2d 925 (11th Cir.1992). See Williams, 713 F.3d at 1338-40 (explaining that the district court lacks subject matter jurisdiction if the savings clause does not apply).
For all these reasons, Vieux has not shown the inadequacy or ineffectiveness of § 2255’s remedy, and the district court did not err in dismissing his § 2241 petition for lack of jurisdiction.9 We deny Vieux’s request to recall the mandate in his 1998 direct criminal appeal because he has not shown extraordinary circumstances warranting such action. See Calderon v. Thompson, 523 U.S. 538, 550, 118 S.Ct. 1489, 1498, 140 L.Ed.2d 728 (1998).
AFFIRMED.
. The issues Vieux raised on direct appeal were: (1) whether the district judge was required to disqualify herself because one of the investigating agents in Vieux’s case was married to the district judge’s recent law clerk; (2) whether the district court erred in denying his motions for severance and for a mistrial; and (3) whether the trial evidence was insufficient to support his carjacking convictions. On the direct appeal, this Court held that "[t]he evidence of guilt in this case is overwhelming, such that a recital of the Government’s proof is altogether unnecessary.” Vieux did not testify at trial.
. It appears the "Addendum” originally was attached to Vieux’s April 19, 1999 motion to *894amend, as the district court’s order instructed the clerk "to return to Defendant the proposed addendum which is attached to the 04/19/99 motion to amend.”
. Vieux’s original § 2255 motion raised claims of (1) denial of his right of self-representation at trial; (2) constructive amendment of the indictment as to Counts 7 and 9; (3) ineffective assistance of appellate counsel for failing to raise his right of self-representation claim on direct appeal; and (4) ineffective assistance of trial counsel for failing to file a motion to suppress evidence seized during a traffic stop, failing to object to the jury instruction on Counts 7 and 9, and failing to object to the submission to the jury of an unredacted copy of the. indictment that described Vieux’s prior convictions. In denying Vieux's § 2255 motion, the district court concluded that Vieux had procedurally defaulted the first two claims because he did not raise them on direct appeal and that Vieux failed to satisfy either prong of Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), with respect to his ineffective assistance claims.
. The district court instructed the clerk to send Vieux a form application for leave to file a second or successive § 2255 motion and close the case.
. Vieux’s second § 2241 petition also raised claims with respect to his firearm convictions in Counts 9 and 12 and his controlled substance conviction in Count 11. The district court dismissed those claims as not cognizable. In his appeal brief, Vieux does not challenge the dismissal of those claims or the district court’s denial of his Rule 59(e) motion. Accordingly, those claims are abandoned. See Timson v. Sampson, 518 F.3d 870, 874 (11th Cir.2008).
. Whether a prisoner may bring a § 2241 petition under § 2255(e)'s savings clause is á question of law reviewed de novo. Williams v. Warden, 713 F.3d 1332, 1337 (11th Cir.2013).
. Vieux’s argument that Jones announced a new substantive rule that automatically applies retroactively, rather than a procedural rule that does not, lacles merit also. See Schriro v. Summerlin, 542 U.S. 348, 351-52, 124 S.Ct. 2519, 2522-23, 159 L.Ed.2d 442 (2004) (explaining that a substantive rule that is retroactive alters the range of conduct or the class of persons the law punishes, while a procedural rule that is not retroactive regulates only the manner of determining the defendant's culpability); Varela v. United States, 400 F.3d 864, 866-67 (11th Cir.2005) (explaining that Supreme Court decisions, such as Ring, Blakely, and Booker, applying Appren-di’s "prototypical procedural rule” in various contexts are not retroactive).
. We point out to Vieux that his Jones claim would fail on the merits because at trial the government presented uncontroverted evidence that the victim driver (Mr. Hanson) in Count 2 was shot (by Vieux) and seriously injured and the victim driver (Mr. Medina) in Count 6 was shot and lulled (by Vieux’s co-conspirator). Thus, any failure to submit the sentencing factors of serious bodily injury and death to the jury was harmless error. See United States v. Candelario, 240 F.3d 1300, 1307-08 (11th Cir.2001) (holding that Appren-di/Jones-based errors are subject to harmless error review, under which the error is harmless beyond a reasonable doubt if there is "uncontroverted evidence” to support the facts omitted from the indictment that increase the statutory maximum penalty); United States v. Nealy, 232 F.3d 825, 829-30 (11th Cir.2000) (concluding that Apprendi error is harmless "if the record does not contain evidence that could rationally lead to a contrary finding” with respect to the omitted sentencing fact).
. Because the district court did not address it, and the parties do not raise it on appeal, we do not consider whether Vieux's current § 2241 petition was due to be dismissed as successive under 28 U.S.C. § 2244(a). See 28 U.S.C. § 2244(a); Antonelli v. Warden, 542 F.3d 1348, 1350, 1352 (11th Cir.2008) (affirming district court's dismissal of § 2241 petition pursuant to § 2244(a) upon a finding that the claims in the § 2241 petition previously was adjudicated on the merits in a first § 2241 petition filed in a district court in Arkansas and affirmed by the Eighth Circuit). We also need not address whether this alternative ground is jurisdictional or not.