V(5711)/456881

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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:	V(5711)/456881
Verification status (*):	Proven
Official Comment (*):	Lucas cofactor
Proof-code(s): (*):	c8 : Broadhurst, Water, Primo
Decimal Digits:	1188 (log₁₀ is 1187.86861037)
Rank (*):	122010 (digit rank is 13)
Entrance Rank (*):	54042
Currently on list? (*):	no
Submitted:	3/7/2004 11:40:44 UTC
Last modified:	2/4/2026 10:56:21 UTC
Database id:	69404
Status Flags:	none
Score (*):	25.8104 (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.

Lucas cofactor (archivable *)
Prime on list: no, rank 61
Subcategory: "Lucas cofactor"
(archival tag id 179935, tag last modified 2024-08-04 11:37:22)

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 69404

person_id 9

machine Using: Digital Ocean Droplet

what prime

notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper_1100000000216931938.txt -q"V(5711)/456881" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing V(5711)/456881 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000216931938.txt
trial

Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3947-bit number
Running N-1 test using base 7
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3947-bit number
Running N+1 test using discriminant 19, base 1+sqrt(19)
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3947-bit number
Running N+1 test using discriminant 19, base 3+sqrt(19)
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3947-bit number
Calling N+1 BLS with factored part 100.00% and helper 1.29% (301.29% proof)

V(5711)/456881 is prime! (0.1584s+0.0048s)
[Elapsed time: 5.00 seconds]

Helper File:
2
3
17
103
5711
69262069
5
36819583
155943913
16086926954329297972860390650984663...(1171 digits)...70283101986552081887813993673459499

modified 2026-02-04 10:56:21

created 2026-02-04 10:56:16

id 187721

field	value
prime_id	69404
person_id	9
machine	Using: Digital Ocean Droplet
what	prime
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper_1100000000216931938.txt -q"V(5711)/456881" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing V(5711)/456881 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper_1100000000216931938.txt trial Running N-1 test using base 3 Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3947-bit number Running N-1 test using base 7 Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3947-bit number Running N+1 test using discriminant 19, base 1+sqrt(19) Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3947-bit number Running N+1 test using discriminant 19, base 3+sqrt(19) Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3947-bit number Calling N+1 BLS with factored part 100.00% and helper 1.29% (301.29% proof) V(5711)/456881 is prime! (0.1584s+0.0048s) [Elapsed time: 5.00 seconds] Helper File: 2 3 17 103 5711 69262069 5 36819583 155943913 16086926954329297972860390650984663...(1171 digits)...70283101986552081887813993673459499
modified	2026-02-04 10:56:21
created	2026-02-04 10:56:16
id	187721

field value

prime_id 69404

person_id 9

machine Linux P4 2.8GHz

what prp

notes Command: /home/caldwell/client/pfgw -f -tc -q"V(5711)/456881" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing V(5711)/456881 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 282483 Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(448,22) to FFT(448,21) Reduced from FFT(448,21) to FFT(448,20) Reduced from FFT(448,20) to FFT(448,19) Reduced from FFT(448,19) to FFT(448,18) 7902 bit request FFT size=(448,18) Running N-1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(448,22) to FFT(448,21) Reduced from FFT(448,21) to FFT(448,20) Reduced from FFT(448,20) to FFT(448,19) Reduced from FFT(448,19) to FFT(448,18) 7902 bit request FFT size=(448,18) Running N+1 test using discriminant 19, base 1+sqrt(19) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(448,22) to FFT(448,21) Reduced from FFT(448,21) to FFT(448,20) Reduced from FFT(448,20) to FFT(448,19) Reduced from FFT(448,19) to FFT(448,18) 7910 bit request FFT size=(448,18) Calling N-1 BLS with factored part 0.63% and helper 0.15% (2.10% proof) V(5711)/456881 is Fermat and Lucas PRP! (0.9881s+0.0008s)

modified 2020-07-07 22:30:46

created 2004-03-07 11:53:25

id 74339

field	value
prime_id	69404
person_id	9
machine	Linux P4 2.8GHz
what	prp
notes	Command: /home/caldwell/client/pfgw -f -tc -q"V(5711)/456881" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing V(5711)/456881 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 282483 Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(448,22) to FFT(448,21) Reduced from FFT(448,21) to FFT(448,20) Reduced from FFT(448,20) to FFT(448,19) Reduced from FFT(448,19) to FFT(448,18) 7902 bit request FFT size=(448,18) Running N-1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(448,22) to FFT(448,21) Reduced from FFT(448,21) to FFT(448,20) Reduced from FFT(448,20) to FFT(448,19) Reduced from FFT(448,19) to FFT(448,18) 7902 bit request FFT size=(448,18) Running N+1 test using discriminant 19, base 1+sqrt(19) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(448,22) to FFT(448,21) Reduced from FFT(448,21) to FFT(448,20) Reduced from FFT(448,20) to FFT(448,19) Reduced from FFT(448,19) to FFT(448,18) 7910 bit request FFT size=(448,18) Calling N-1 BLS with factored part 0.63% and helper 0.15% (2.10% proof) V(5711)/456881 is Fermat and Lucas PRP! (0.9881s+0.0008s)
modified	2020-07-07 22:30:46
created	2004-03-07 11:53:25
id	74339

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