173028555 · 226993 + 1
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: | 173028555 · 226993 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Cunningham chain 2nd kind (p) |
| Proof-code(s): (*): | L983 : Wu_T, LLR |
| Decimal Digits: | 8134 (log10 is 8133.9407907388) |
| Rank (*): | 84848 (digit rank is 1) |
| Entrance Rank (*): | 47098 |
| Currently on list? (*): | no |
| Submitted: | 2/19/2010 23:29:25 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 91917 |
| Status Flags: | none |
| Score (*): | 31.7997 (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.
- Cunningham Chains (2nd kind) (archivable class *)
- Prime on list: no, rank 40, weight 21.961901993812
Subcategory: "Cunningham chain 2nd kind (p)"
(archival tag id 212443, tag last modified 2023-11-26 09:37:13)
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 91917 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 173028555 2 26993 1 2>&1 [Elapsed time: 7.878 seconds] modified 2020-07-07 22:30:36 created 2010-02-19 23:35:01 id 113203
field value prime_id 91917 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -t -q"173028555*2^26993+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 173028555*2^26993+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3584,21) to FFT(3584,20) Reduced from FFT(3584,20) to FFT(3584,19) Reduced from FFT(3584,19) to FFT(3584,18) Reduced from FFT(3584,18) to FFT(3584,17) Reduced from FFT(3584,17) to FFT(3584,16) 54050 bit request FFT size=(3584,16) Calling Brillhart-Lehmer-Selfridge with factored part 99.90% 173028555*2^26993+1 is prime! (3.5900s+0.0000s) [Elapsed time: 3.00 seconds] modified 2020-07-07 22:30:36 created 2010-02-19 23:38:01 id 113209
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
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