74844 · 4074844 + 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: | 74844 · 4074844 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Cullen |
| Proof-code(s): (*): | x37 : Zhou, LLR |
| Decimal Digits: | 119910 (log10 is 119909.45214794) |
| Rank (*): | 47810 (digit rank is 1) |
| Entrance Rank (*): | 4413 |
| Currently on list? (*): | no |
| Submitted: | 4/9/2009 15:51:35 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 87561 |
| Status Flags: | none |
| Score (*): | 40.1135 (normalized score 0.0048) |
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.
- Generalized Cullen (archivable *)
- Prime on list: no, rank 90
Subcategory: "Generalized Cullen"
(archival tag id 208969, tag last modified 2025-04-26 08:37:11)
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 87561 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 74844 40 74844 1 2>&1 [Elapsed time: 8.636 seconds] modified 2020-07-07 22:30:38 created 2009-04-09 15:52:01 id 104490
field value prime_id 87561 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"74844*40^74844+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 74844*40^74844+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) 796670 bit request FFT size=(49152,17) Calling Brillhart-Lehmer-Selfridge with factored part 56.37% 74844*40^74844+1 is prime! (1787.2600s+0.0100s) [Elapsed time: 29.95 minutes] modified 2020-07-07 22:30:38 created 2009-04-09 15:59:48 id 104491
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
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