U(1493, - 1, 4621)

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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:	U(1493, - 1, 4621)
Verification status (*):	PRP
Official Comment (*):	Generalized Lucas number
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	CH3 : Broadhurst, Water, OpenPFGW, Primo, CHG
Decimal Digits:	14665 (log₁₀ is 14664.157211627)
Rank (*):	77778 (digit rank is 1)
Entrance Rank (*):	25187
Currently on list? (*):	no
Submitted:	10/5/2005 04:16:25 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	75826
Status Flags:	Verify
Score (*):	33.6259 (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 Lucas Number (archivable *)
Prime on list: no, rank 28
Subcategory: "Generalized Lucas Number"
(archival tag id 192558, tag last modified 2023-10-24 02:37:13)

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.

Chris Caldwell writes (11 Sep 2014): (report abuse)

CHG proof with ECPP helpers. The certificate of proof may be found at http://physics.open.ac.uk/~dbroadhu/cert/b4621.zip

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 75826

person_id 9

machine Linux P4 2.8GHz

what prp

notes Command: /home/caldwell/client/pfgw -f -tc -q"lucasU(1493,-1,4621)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing lucasU(1493,-1,4621) [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 4344106 Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) Reduced from FFT(6144,17) to FFT(6144,16) 97436 bit request FFT size=(6144,16) Running N-1 test using base 11 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) Reduced from FFT(6144,17) to FFT(6144,16) 97436 bit request FFT size=(6144,16) Running N+1 test using discriminant 17, base 6+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) Reduced from FFT(6144,17) to FFT(6144,16) 97444 bit request FFT size=(6144,16) Running N+1 test using discriminant 17, base 8+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) Reduced from FFT(6144,17) to FFT(6144,16) 97444 bit request FFT size=(6144,16) Running N+1 test using discriminant 17, base 10+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) Reduced from FFT(6144,17) to FFT(6144,16) 97444 bit request FFT size=(6144,16) Calling N-1 BLS with factored part 1.13% and helper 0.51% (3.92% proof) lucasU(1493,-1,4621) is Fermat and Lucas PRP! (594.2252s+0.0145s) [Elapsed time: 594 seconds]

modified 2020-07-07 22:30:43

created 2005-10-05 04:23:01

id 81012

field	value
prime_id	75826
person_id	9
machine	Linux P4 2.8GHz
what	prp
notes	Command: /home/caldwell/client/pfgw -f -tc -q"lucasU(1493,-1,4621)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing lucasU(1493,-1,4621) [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 4344106 Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) Reduced from FFT(6144,17) to FFT(6144,16) 97436 bit request FFT size=(6144,16) Running N-1 test using base 11 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) Reduced from FFT(6144,17) to FFT(6144,16) 97436 bit request FFT size=(6144,16) Running N+1 test using discriminant 17, base 6+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) Reduced from FFT(6144,17) to FFT(6144,16) 97444 bit request FFT size=(6144,16) Running N+1 test using discriminant 17, base 8+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) Reduced from FFT(6144,17) to FFT(6144,16) 97444 bit request FFT size=(6144,16) Running N+1 test using discriminant 17, base 10+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(6144,21) to FFT(6144,20) Reduced from FFT(6144,20) to FFT(6144,19) Reduced from FFT(6144,19) to FFT(6144,18) Reduced from FFT(6144,18) to FFT(6144,17) Reduced from FFT(6144,17) to FFT(6144,16) 97444 bit request FFT size=(6144,16) Calling N-1 BLS with factored part 1.13% and helper 0.51% (3.92% proof) lucasU(1493,-1,4621) is Fermat and Lucas PRP! (594.2252s+0.0145s) [Elapsed time: 594 seconds]
modified	2020-07-07 22:30:43
created	2005-10-05 04:23:01
id	81012

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.