primV(8781)

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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:	primV(8781)
Verification status (*):	Proven
Official Comment (*):	Lucas primitive part
Proof-code(s): (*):	DK : Dubner, Keller, Cruncher
Decimal Digits:	1223 (log₁₀ is 1222.811586032)
Rank (*):	120406 (digit rank is 9)
Entrance Rank (*):	7641
Currently on list? (*):	no
Submitted:	7/1995
Last modified:	2/4/2026 10:32:01 UTC
Database id:	46232
Status Flags:	none
Score (*):	25.9011 (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 primitive part (archivable *)
Prime on list: no, rank 131
Subcategory: "Lucas primitive part"
(archival tag id 195704, tag last modified 2024-10-11 22:37:11)

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 46232

person_id 9

machine Using: Digital Ocean Droplet

what prime

notes PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 6480164520...7562600561 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000305907224.txt
trial

Running N-1 test using base 11
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 4063-bit number
Running N-1 test using base 17
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 4063-bit number
Running N+1 test using discriminant 41, base 10+sqrt(41)
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 4063-bit number
Calling N-1 BLS with factored part 100.00% and helper 0.57% (300.57% proof)

6480164520...7562600561 is prime! (0.1918s+0.0003s)
[Elapsed time: 5.00 seconds]

Helper File:
2
3
5
7
13
23
29
37
47
89
113
199
419
487
1097
1103
2927
3457
4513
8783
9349
19763
38039
42293
102481
117041
229769
263521
793487
988681
4832521
5815009
9321929
10225307
21291929
21791641
36999271
267197569
555003497
10694421739
14686239709
20669776469
22276861069
2152958650459
5600748293801
9428861799143
24848660119363
351301301942501
533975715909289
3198068921977967
42883754064158701
475966345230891901
52471477541626010209
14297347971975757800833
2959707364050967146316591
256134602178198608164284137
5500902230146438151405489047
7181634929637355776701081412683
728433505395160404002954964176389
33986746072920049431867434646693841
57314120955051297736679165379998262001
65681302014984838931368740317052761650259332806397127
327712844392821667947488867904004765588576642587744285678664548442859
10247075908997617728211332571828570020871219332351727249528819157744921519
724901011535214037845874972824565483006757602317236033423370083435767781234797
6441437021434315318928919220679668071260908685659726779571317918500059856365893629903
89141306861189919373622069885880781...(111 digits)...99337711097101194312538214688008561
50877742282160052294074710988405763...(167 digits)...51574687033060585811040461758478383
197
21841

modified 2026-02-04 10:32:01

created 2026-02-04 10:31:51

id 187700

field	value
prime_id	46232
person_id	9
machine	Using: Digital Ocean Droplet
what	prime
notes	PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing 6480164520...7562600561 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper_1100000000305907224.txt trial Running N-1 test using base 11 Generic modular reduction using generic reduction FMA3 FFT length 384 on A 4063-bit number Running N-1 test using base 17 Generic modular reduction using generic reduction FMA3 FFT length 384 on A 4063-bit number Running N+1 test using discriminant 41, base 10+sqrt(41) Generic modular reduction using generic reduction FMA3 FFT length 384 on A 4063-bit number Calling N-1 BLS with factored part 100.00% and helper 0.57% (300.57% proof) 6480164520...7562600561 is prime! (0.1918s+0.0003s) [Elapsed time: 5.00 seconds] Helper File: 2 3 5 7 13 23 29 37 47 89 113 199 419 487 1097 1103 2927 3457 4513 8783 9349 19763 38039 42293 102481 117041 229769 263521 793487 988681 4832521 5815009 9321929 10225307 21291929 21791641 36999271 267197569 555003497 10694421739 14686239709 20669776469 22276861069 2152958650459 5600748293801 9428861799143 24848660119363 351301301942501 533975715909289 3198068921977967 42883754064158701 475966345230891901 52471477541626010209 14297347971975757800833 2959707364050967146316591 256134602178198608164284137 5500902230146438151405489047 7181634929637355776701081412683 728433505395160404002954964176389 33986746072920049431867434646693841 57314120955051297736679165379998262001 65681302014984838931368740317052761650259332806397127 327712844392821667947488867904004765588576642587744285678664548442859 10247075908997617728211332571828570020871219332351727249528819157744921519 724901011535214037845874972824565483006757602317236033423370083435767781234797 6441437021434315318928919220679668071260908685659726779571317918500059856365893629903 89141306861189919373622069885880781...(111 digits)...99337711097101194312538214688008561 50877742282160052294074710988405763...(167 digits)...51574687033060585811040461758478383 197 21841
modified	2026-02-04 10:32:01
created	2026-02-04 10:31:51
id	187700

field value

prime_id 46232

person_id 9

machine Linux PII 200

what prp

notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Reading factors from helper file helper Error opening file helper Running N-1 test using base 11 Primality testing primV(8781) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Calling Brillhart-Lehmer-Selfridge with factored part 6.65% primV(8781) is PRP! (7.170000 seconds)

modified 2003-03-25 17:22:48

created 2003-01-07 04:38:59

id 63832

field	value
prime_id	46232
person_id	9
machine	Linux PII 200
what	prp
notes	PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Reading factors from helper file helper Error opening file helper Running N-1 test using base 11 Primality testing primV(8781) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Calling Brillhart-Lehmer-Selfridge with factored part 6.65% primV(8781) is PRP! (7.170000 seconds)
modified	2003-03-25 17:22:48
created	2003-01-07 04:38:59
id	63832

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.