197418203 · 225000 + 6089
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: | 197418203 · 225000 + 6089 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | ECPP, consecutive primes arithmetic progression (3,d=6090) |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | FE4 : Broadhurst, Morain, OpenPFGW, FastECPP |
| Decimal Digits: | 7535 (log10 is 7534.04527879) |
| Rank (*): | 85689 (digit rank is 22) |
| Entrance Rank (*): | 30346 |
| Currently on list? (*): | no |
| Submitted: | 2/26/2005 23:35:01 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 73546 |
| Status Flags: | Verify |
| Score (*): | 31.562 (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 420
Subcategory: "ECPP"
(archival tag id 194567, tag last modified 2024-04-19 02:37:11)- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: no, rank 162, weight 36.996895568025
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 194566, tag last modified 2023-03-11 16:02:30)- Consecutive Primes in Arithmetic Progression (archivable class *)
- Prime on list: no, rank 15
Subcategory: "Consecutive primes in arithmetic progression (3,d=*)"
(archival tag id 194565, tag last modified 2023-03-11 15:53:59)
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 73546 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"197418203*2^25000+6089" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 197418203*2^25000+6089 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 2115178 Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3072,21) to FFT(3072,20) Reduced from FFT(3072,20) to FFT(3072,19) Reduced from FFT(3072,19) to FFT(3072,18) Reduced from FFT(3072,18) to FFT(3072,17) 50064 bit request FFT size=(3072,17) Running N+1 test using discriminant 11, base 1+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3072,21) to FFT(3072,20) Reduced from FFT(3072,20) to FFT(3072,19) Reduced from FFT(3072,19) to FFT(3072,18) Reduced from FFT(3072,18) to FFT(3072,17) 50072 bit request FFT size=(3072,17) Calling N+1 BLS with factored part 0.19% and helper 0.02% (0.60% proof) 197418203*2^25000+6089 is Fermat and Lucas PRP! (98.5591s+0.0003s) modified 2020-07-07 22:30:44 created 2005-02-26 23:55:31 id 78564
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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