25000 + 37442785
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: | 25000 + 37442785 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Consecutive primes arithmetic progression (2,d=588) |
| Proof-code(s): (*): | c14 : Fougeron, Primo |
| Decimal Digits: | 1506 (log10 is 1505.1499783199) |
| Rank (*): | 112613 (digit rank is 9) |
| Entrance Rank (*): | 30896 |
| Currently on list? (*): | no |
| Submitted: | 10/26/2000 11:55:37 UTC |
| Last modified: | 1/27/2026 13:26:22 UTC |
| Database id: | 39116 |
| Status Flags: | none |
| Score (*): | 26.5501 (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.
- Consecutive Primes in Arithmetic Progression (archivable class *)
- Prime on list: no, rank 45
Subcategory: "2/3"
(archival tag id 238772, tag last modified 2025-02-16 14:52:00)- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: no, rank 166
Subcategory: "2/3"
(archival tag id 234983, tag last modified 2025-02-16 14:52:00)
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 39116 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000007617824446 -q"2^5000+37442785" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 2^5000+37442785 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000007617824446
trial
Running N-1 test using base 3
Special modular reduction using generic reduction FMA3 FFT length 512 on 2^5000+37442785
Running N-1 test using base 7
Special modular reduction using generic reduction FMA3 FFT length 512 on 2^5000+37442785
Running N+1 test using discriminant 17, base 12+sqrt(17)
Special modular reduction using generic reduction FMA3 FFT length 512 on 2^5000+37442785
Calling N-1 BLS with factored part 100.00% and helper 0.90% (300.90% proof)
2^5000+37442785 is prime! (0.1522s+0.0004s)
[Elapsed time: 5.00 seconds]
Helper File:
2
5
8581
1716941
59919069948455538471314044124385906...(1493 digits)...73673203534862545782381024906339131
3
7
13
23
1077101041modified 2026-01-27 13:26:22 created 2026-01-27 13:26:16 id 187593
field value prime_id 39116 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 3 Running N+1 test using discriminant 7, base 1+sqrt(7) Running N+1 test using discriminant 7, base 2+sqrt(7) Primality testing 2^5000+37442785 [N-1/N+1, Brillhart-Lehmer-Selfridge] Calling N-1 BLS with factored part 0.40% and helper 0.30% (1.52% proof) 2^5000+37442785 is Fermat and Lucas PRP! (24.450000 seconds) modified 2003-03-25 17:23:00 created 2003-01-04 17:11:40 id 61326
Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.
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