10999 + 121503
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: | 10999 + 121503 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | ECPP, arithmetic progression (3,d=29766) |
| Proof-code(s): (*): | c4 : Broadhurst, Primo |
| Decimal Digits: | 1000 (log10 is 999) |
| Rank (*): | 132802 (digit rank is 51) |
| Entrance Rank (*): | 48809 |
| Currently on list? (*): | no |
| Submitted: | 8/16/2000 14:12:57 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 58893 |
| Status Flags: | Verify |
| Score (*): | 25.2688 (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 1211
Subcategory: "ECPP"
(archival tag id 178112, tag last modified 2024-04-24 05:37:26)- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: no, rank 1371, weight 29.693467414105
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 178111, 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 58893 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 Primality testing 10^999+121503 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 19, base 1+sqrt(19) Calling N-1 BLS with factored part 1.02% and helper 0.27% (3.44% proof) 10^999+121503 is Fermat and Lucas PRP! (9.550000 seconds) modified 2003-03-25 17:23:05 created 2003-01-04 05:20:41 id 60344
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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