(10665261037744209 · 4001# · (205881 · 4001# + 1) + 210) · (205881 · 4001# - 1)/35 + 7
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: | (10665261037744209 · 4001# · (205881 · 4001# + 1) + 210) · (205881 · 4001# - 1)/35 + 7 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Arithmetic progression (5,d=(681402540*205881*4001#*(205881*4001#+1)*(205881*4001#-1)/35)) |
| Proof-code(s): (*): | p179 : DavisK, APTreeSieve, OpenPFGW |
| Decimal Digits: | 5132 (log10 is 5131.6842365155) |
| Rank (*): | 90803 (digit rank is 19) |
| Entrance Rank (*): | 40191 |
| Currently on list? (*): | no |
| Submitted: | 2/9/2007 12:44:09 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 79365 |
| Status Flags: | none |
| Score (*): | 30.3699 (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.
- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: no, rank 146, weight 44.763805253411
Subcategory: "Arithmetic progression (5,d=*)"
(archival tag id 195115, tag last modified 2023-03-11 15:53:59)
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 79365 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"(51803036889*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+7" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] (51803036889*205881*4001#.........10)*(205881*4001 1/1 trial factoring to 1394925 (51803036889*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+7 has no small factor. [Elapsed time: 0.709 seconds] modified 2020-07-07 22:30:41 created 2007-02-09 12:52:01 id 87824
field value prime_id 79365 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -tc -q"(51803036889*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+7" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (51803036889*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+7 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2048,21) to FFT(2048,20) Reduced from FFT(2048,20) to FFT(2048,19) Reduced from FFT(2048,19) to FFT(2048,18) Reduced from FFT(2048,18) to FFT(2048,17) 34104 bit request FFT size=(2048,17) Running N+1 test using discriminant 11, base 2+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2048,21) to FFT(2048,20) Reduced from FFT(2048,20) to FFT(2048,19) Reduced from FFT(2048,19) to FFT(2048,18) Reduced from FFT(2048,18) to FFT(2048,17) 34112 bit request FFT size=(2048,17) Calling N-1 BLS with factored part 33.34% and helper 0.11% (100.15% proof) (51803036889*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+7 is prime! (20.6800s+0.0000s) [Elapsed time: 21 seconds] modified 2020-07-07 22:30:41 created 2007-02-09 13:04:56 id 87829
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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