"16282536218213511214...(5838 other digits)...95781943818436478311"
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: | "16282536218213511214...(5838 other digits)...95781943818436478311" |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | ECPP, stop gap |
| Proof-code(s): (*): | c28 : Pardo, Primo |
| Decimal Digits: | 5878 (log10 is 5877.21172205) |
| Rank (*): | 92969 (digit rank is 1) |
| Entrance Rank (*): | 24637 |
| Currently on list? (*): | no |
| Submitted: | 2/15/2003 00:52:59 UTC |
| Last modified: | 2/4/2026 12:19:54 UTC |
| Database id: | 64797 |
| Blob database id: | 92 |
| Status Flags: | Verify |
| Score (*): | 30.7912 (normalized score 0) |
Description: (from blob table id=92)
From Marcel Martin's page (23 May 2003):The certification of this End Gap number, done during September 2002/February 2003 by Jose Luis Gomez Pardo with Primo 2.0.0 beta 3, took 22 weeks using Primo with an AMD XP1800 + processor. ... To download the primality certificate: ecpp5878.zip (3223 KB). Thanks to François Morain who checked the certificate with his own code.
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.
- Gap Primes (tolerated *)
- Prime on list: no, rank 3
Subcategory: "Gap Primes"
(archival tag id 194937, tag last modified 2023-03-11 15:53:59)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 547
Subcategory: "ECPP"
(archival tag id 194936, tag last modified 2026-01-31 06:37:12)
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 64797 person_id 9 machine Using: Digital Ocean Droplet what prp notes PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 1628253621...8436478311 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000488464224.txt
trial
Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 2K on A 19524-bit number
Running N+1 test using discriminant 19, base 1+sqrt(19)
Generic modular reduction using generic reduction FMA3 FFT length 2K on A 19524-bit number
Calling N+1 BLS with factored part 0.46% and helper 0.10% (1.50% proof)
1628253621...8436478311 is Fermat and Lucas PRP! (1.7930s+0.0009s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
67709
13
23
109
179
673
25148869
2075580817modified 2026-02-04 12:19:54 created 2026-02-04 12:19:49 id 187745
field value prime_id 64797 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality Running N-1 test using base 3 0559754855...8436478311 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 19, base 1+sqrt(19) Calling N+1 BLS with factored part 0.17% and helper 0.10% (0.64% proof) 1628253621...8436478311 is Fermat and Lucas PRP! (366.270000 seconds) modified 2020-07-07 22:30:47 created 2003-05-24 16:25:51 id 69651
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.