21262679382290 · 2399# + 19423
At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.
This prime's information:
| Description: | 21262679382290 · 2399# + 19423 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Quintuplet (2), ECPP |
| Proof-code(s): (*): | c18 : Luhn, Primo |
| Decimal Digits: | 1037 (log10 is 1036.3449024003) |
| Rank (*): | 130099 (digit rank is 68) |
| Entrance Rank (*): | 93908 |
| Currently on list? (*): | no |
| Submitted: | 9/30/2011 09:14:52 UTC |
| Last modified: | 2/4/2026 11:10:48 UTC |
| Database id: | 102259 |
| Status Flags: | none |
| Score (*): | 25.3837 (normalized score 0) |
Archival tags:
There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper. Such primes are tracked with archival tags.
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 1208
Subcategory: "ECPP"
(archival tag id 213511, tag last modified 2026-01-31 06:37:12)- Quintuplet (archivable class *)
- Prime on list: no, rank 20
Subcategory: "Quintuplet (2)"
(archival tag id 213512, tag last modified 2026-02-15 09:37:13)
Verification data:
The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions. We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.
field value prime_id 102259 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper_1100000002650805142.txt -q"21262679382290*2399#+19423" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 21262679382290*2399#+19423 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000002650805142.txt
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 320 on A 3443-bit number
Running N+1 test using discriminant 5, base 1+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 320 on A 3443-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 62/3444 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 5, base 1+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3443-bit number
Running N+1 test using discriminant 5, base 2+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 320 on A 3443-bit number
Calling N+1 BLS with factored part 97.30% and helper 0.87% (292.79% proof)
21262679382290*2399#+19423 is prime! (0.0751s+0.0002s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
13
83
258733
607
140557
35147648599880957219
18446117170264038320500164252384169...(1009 digits)...44501039061149785711869526712565651modified 2026-02-04 11:10:48 created 2026-02-04 11:10:43 id 187725
field value prime_id 102259 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 21262679382290 2399 # 19423 2>&1 [Elapsed time: 145.120 seconds] modified 2020-07-07 22:30:30 created 2011-09-30 09:22:54 id 134105
field value prime_id 102259 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -q"21262679382290*2399#+19423" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 21262679382290*2399#+19423 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 1+sqrt(5) Calling N+1 BLS with factored part 0.81% and helper 0.35% (2.82% proof) 21262679382290*2399#+19423 is Fermat and Lucas PRP! (0.3552s+0.0003s) [Elapsed time: 0.00 seconds] modified 2020-07-07 22:30:30 created 2011-09-30 09:23:02 id 134107
Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.
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