(210169 - 1)/10402314702094700470118039921523041260063
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: | (210169 - 1)/10402314702094700470118039921523041260063 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Mersenne cofactor, ECPP |
| Proof-code(s): (*): | c8 : Broadhurst, Water, Primo |
| Decimal Digits: | 3022 (log10 is 3021.1568959186) |
| Rank (*): | 99382 (digit rank is 2) |
| Entrance Rank (*): | 28029 |
| Currently on list? (*): | no |
| Submitted: | 7/8/2002 22:55:37 UTC |
| Last modified: | 2/4/2026 10:27:10 UTC |
| Database id: | 29464 |
| Status Flags: | none |
| Score (*): | 28.7224 (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.
- Mersenne cofactor (archivable *)
- Prime on list: no, rank 47
Subcategory: "Mersenne cofactor"
(archival tag id 175401, tag last modified 2026-01-31 06:37:12)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 783
Subcategory: "ECPP"
(archival tag id 175400, 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 29464 person_id 9 machine Using: Digital Ocean Droplet what prime notes PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (2^10169-1)/1040231470...3041260063 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000013051153.txt
trial
Running N-1 test using base 5
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 10037-bit number
Running N-1 test using base 17
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 10037-bit number
Running N+1 test using discriminant 23, base 2+sqrt(23)
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 10037-bit number
Calling N-1 BLS with factored part 100.00% and helper 0.63% (300.63% proof)
(2^10169-1)/1040231470...3041260063 is prime! (0.5874s+0.0001s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
11
10169
18196183
967157656641434911
84378863865072796590580864089115538...(2988 digits)...83671092931161803326609379169091017
365455507
14868965623modified 2026-02-04 10:27:10 created 2026-02-04 10:27:05 id 187691
field value prime_id 29464 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 5 Primality testing (2^10169-1)/1040231470...3041260063 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Running N+1 test using discriminant 23, base 2+sqrt(23) Calling N-1 BLS with factored part 0.26% and helper 0.01% (0.80% proof) (2^10169-1)/1040231470...3041260063 is Fermat and Lucas PRP! (135.500000 seconds) modified 2003-03-25 17:22:57 created 2003-01-04 21:57:53 id 61886
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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