(32 · 106959 - 23)/99
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: | (32 · 106959 - 23)/99 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | ECPP, palindrome |
| Proof-code(s): (*): | c17 : Rosenthal, Primo |
| Decimal Digits: | 6959 (log10 is 6958.5095147837) |
| Rank (*): | 91260 (digit rank is 1) |
| Entrance Rank (*): | 24471 |
| Currently on list? (*): | no |
| Submitted: | 7/11/2003 20:01:17 UTC |
| Last modified: | 2/4/2026 12:20:00 UTC |
| Database id: | 65486 |
| Status Flags: | Verify |
| Score (*): | 31.3155 (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.
- Palindrome (archivable *)
- Prime on list: no, rank 267
Subcategory: "Palindrome"
(archival tag id 194733, tag last modified 2024-12-09 16:37:19)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 490
Subcategory: "ECPP"
(archival tag id 194732, 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 65486 person_id 9 machine Using: Digital Ocean Droplet what prp notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper_1100000000014808894.txt -q"(32*10^6959-23)/99" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (32*10^6959-23)/99 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000014808894.txt
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 2560 on A 23123-bit number
Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 2560 on A 23123-bit number
Running N-1 test using base 5
Generic modular reduction using generic reduction FMA3 FFT length 2560 on A 23123-bit number
Running N+1 test using discriminant 13, base 2+sqrt(13)
Generic modular reduction using generic reduction FMA3 FFT length 2560 on A 23123-bit number
Calling N+1 BLS with factored part 0.27% and helper 0.24% (1.05% proof)
(32*10^6959-23)/99 is Fermat and Lucas PRP! (3.8228s+0.0002s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
3703907
277348937
1637
4051
191129277187modified 2026-02-04 12:20:00 created 2026-02-04 12:19:55 id 187746
field value prime_id 65486 person_id 9 machine Linux P4 2.8GHz what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Primality testing (32*10^6959-23)/99 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 5 Running N+1 test using discriminant 13, base 2+sqrt(13) Calling N+1 BLS with factored part 0.10% and helper 0.02% (0.34% proof) (32*10^6959-23)/99 is Fermat and Lucas PRP! (70.000000 seconds) modified 2020-07-07 22:30:47 created 2003-07-12 11:40:13 id 70315
Query times: 0.0004 seconds to select prime, 0.003 seconds to seek comments.
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