(2157457 - 1)/1651348995090599153173927
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: | (2157457 - 1)/1651348995090599153173927 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | ECPP, Mersenne cofactor |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | E18 : Kruse, CM |
| Decimal Digits: | 47376 (log10 is 47375.062188397) |
| Rank (*): | 65536 (digit rank is 1) |
| Entrance Rank (*): | 65519 |
| Currently on list? (*): | yes |
| Submitted: | 1/29/2026 07:18:00 UTC |
| Last modified: | 1/31/2026 06:37:10 UTC |
| Database id: | 141512 |
| Status Flags: | Verify |
| Score (*): | 37.2506 (normalized score 0.0001) |
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: yes, rank 12
Subcategory: "ECPP"
(archival tag id 239734, tag last modified 2026-01-31 06:37:12)- Mersenne cofactor (archivable *)
- Prime on list: yes, rank 3
Subcategory: "Mersenne cofactor"
(archival tag id 239735, tag last modified 2026-01-31 06:37:12)
User comments about this prime (disclaimer):
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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 141512 person_id 9 machine Using: Digital Ocean Droplet what prp notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"(2^157457-1)/1651348995090599153173927" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (2^157457-1)/1651348995...9153173927 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 5
Generic modular reduction using generic reduction FMA3 FFT length 15K, Pass1=320, Pass2=48, clm=2 on A 157377-bit number
Running N+1 test using discriminant 11, base 1+sqrt(11)
Generic modular reduction using generic reduction FMA3 FFT length 15K, Pass1=320, Pass2=48, clm=2 on A 157377-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 39/157426 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 11, base 1+sqrt(11)
Generic modular reduction using generic reduction FMA3 FFT length 16K, Pass1=256, Pass2=64, clm=2 on A 157377-bit number
Calling N-1 BLS with factored part 0.04% and helper 0.02% (0.13% proof)
(2^157457-1)/1651348995...9153173927 is Fermat and Lucas PRP! (139.0965s+0.0006s)
[Elapsed time: 2.33 minutes]modified 2026-01-31 06:08:13 created 2026-01-31 06:05:53 id 187615
Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
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