23322 + 845219106973
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: | 23322 + 845219106973 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Consecutive primes arithmetic progression (1,d=600) |
| Proof-code(s): (*): | c30 : Andersen, Fougeron, Rosenthal, Primo |
| Decimal Digits: | 1001 (log10 is 1000.0216456) |
| Rank (*): | 132738 (digit rank is 29) |
| Entrance Rank (*): | 62130 |
| Currently on list? (*): | no |
| Submitted: | 9/22/2003 01:40:54 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 66311 |
| Status Flags: | Verify |
| Score (*): | 25.272 (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 87
Subcategory: "Consecutive primes in arithmetic progression (1,d=*)"
(archival tag id 185294, tag last modified 2023-07-02 12:37:20)- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: no, rank 1352
Subcategory: "Arithmetic progression (1,d=*)"
(archival tag id 185295, tag last modified 2023-07-02 12:37:19)
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 66311 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"2^3322+845219106973" 2>&1 PFGW Version 20030811.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 233812 Running N-1 test using base 2 Primality testing 2^3322+845219106973 [N-1/N+1, Brillhart-Lehmer-Selfridge] Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(384,22) to FFT(384,21) Reduced from FFT(384,21) to FFT(384,20) Reduced from FFT(384,20) to FFT(384,19) Reduced from FFT(384,19) to FFT(384,18) 6654 bit request FFT size=(384,18) Running N+1 test using discriminant 5, base 5+sqrt(5) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(384,22) to FFT(384,21) Reduced from FFT(384,21) to FFT(384,20) Reduced from FFT(384,20) to FFT(384,19) Reduced from FFT(384,19) to FFT(384,18) 6662 bit request FFT size=(384,18) Calling N-1 BLS with factored part 0.48% and helper 0.24% (1.78% proof) 2^3322+845219106973 is Fermat and Lucas PRP! (0.9111s+0.0002s) modified 2020-07-07 22:30:47 created 2003-09-22 01:53:00 id 71199
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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