(47354621 - 1)/4734
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: | (47354621 - 1)/4734 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Generalized repunit |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | CH3 : Broadhurst, Water, OpenPFGW, Primo, CHG |
| Decimal Digits: | 16980 (log10 is 16979.978414757) |
| Rank (*): | 78724 (digit rank is 1) |
| Entrance Rank (*): | 23218 |
| Currently on list? (*): | no |
| Submitted: | 9/27/2005 16:39:59 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 75726 |
| Status Flags: | Verify |
| Score (*): | 34.0798 (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.
- Generalized Repunit (archivable *)
- Prime on list: no, rank 51
Subcategory: "Generalized Repunit"
(archival tag id 192409, tag last modified 2025-09-11 16:37:14)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
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 75726 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"(4735^4621-1)/4734" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (4735^4621-1)/4734 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 5088043 Running N-1 test using base 17 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(7168,21) to FFT(7168,20) Reduced from FFT(7168,20) to FFT(7168,19) Reduced from FFT(7168,19) to FFT(7168,18) Reduced from FFT(7168,18) to FFT(7168,17) Reduced from FFT(7168,17) to FFT(7168,16) 112822 bit request FFT size=(7168,16) Running N-1 test using base 47 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(7168,21) to FFT(7168,20) Reduced from FFT(7168,20) to FFT(7168,19) Reduced from FFT(7168,19) to FFT(7168,18) Reduced from FFT(7168,18) to FFT(7168,17) Reduced from FFT(7168,17) to FFT(7168,16) 112822 bit request FFT size=(7168,16) Running N+1 test using discriminant 73, base 18+sqrt(73) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(7168,21) to FFT(7168,20) Reduced from FFT(7168,20) to FFT(7168,19) Reduced from FFT(7168,19) to FFT(7168,18) Reduced from FFT(7168,18) to FFT(7168,17) Reduced from FFT(7168,17) to FFT(7168,16) 112830 bit request FFT size=(7168,16) Calling N-1 BLS with factored part 1.50% and helper 0.00% (4.50% proof) (4735^4621-1)/4734 is Fermat and Lucas PRP! (372.0748s+0.0116s) [Elapsed time: 372 seconds] modified 2020-07-07 22:30:43 created 2005-09-27 16:53:00 id 80902
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.