- E(526)/359897564379184692582610493005245214013933
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: | - E(526)/359897564379184692582610493005245214013933 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Euler irregular, ECPP |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | c4 : Broadhurst, Primo |
| Decimal Digits: | 1060 (log10 is 1059.9489314478) |
| Rank (*): | 129167 (digit rank is 4) |
| Entrance Rank (*): | 51983 |
| Currently on list? (*): | no |
| Submitted: | 2/13/2002 18:43:12 UTC |
| Last modified: | 2/4/2026 10:45:21 UTC |
| Database id: | 54611 |
| Status Flags: | none |
| Score (*): | 25.4541 (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 1181
Subcategory: "ECPP"
(archival tag id 177693, tag last modified 2026-01-31 06:37:12)- Euler Irregular primes (archivable *)
- Prime on list: no, rank 33
Subcategory: "Euler Irregular primes"
(archival tag id 177692, tag last modified 2025-08-08 05:37:12)
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 54611 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 8890607709...9628411017 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000002369128792.txt
trial
Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 320 on A 3522-bit number
Running N-1 test using base 5
Generic modular reduction using generic reduction FMA3 FFT length 320 on A 3522-bit number
Running N+1 test using discriminant 11, base 1+sqrt(11)
Generic modular reduction using generic reduction FMA3 FFT length 320 on A 3522-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 325/3565 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 384 on A 3522-bit number
Calling N-1 BLS with factored part 100.00% and helper 0.82% (300.82% proof)
8890607709...9628411017 is prime! (0.1629s+0.0043s)
[Elapsed time: 5.00 seconds]
Helper File:
2
7
13
12212373227372449199537701054421324...(1058 digits)...42162879100959508464562141070918147
3
23
1395739modified 2026-02-04 10:45:21 created 2026-02-04 10:45:10 id 187717
field value prime_id 54611 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Reading factors from helper file helper Error opening file helper Running N-1 test using base 3 Primality testing -E(526)/(5062100689*7109648473...5730043997) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 0.26% -E(526)/(5062100689*7109648473...5730043997) is PRP! (4.980000 seconds) modified 2003-03-25 17:22:48 created 2003-01-07 03:35:01 id 63795
Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
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