primV(10821)

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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(10821)
Verification status (*):	Proven
Official Comment (*):	Lucas primitive part
Proof-code(s): (*):	DK : Dubner, Keller, Cruncher
Decimal Digits:	1508 (log₁₀ is 1507.034776772)
Rank (*):	112870 (digit rank is 11)
Entrance Rank (*):	5203
Currently on list? (*):	no
Submitted:	1995
Last modified:	2/4/2026 10:28:34 UTC
Database id:	39090
Status Flags:	none
Score (*):	26.554 (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 126
Subcategory: "Lucas primitive part"
(archival tag id 195699, 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 39090

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 1083369917...7048838211 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000306341416.txt
trial

Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5007-bit number
Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5007-bit number
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5007-bit number
Calling N-1 BLS with factored part 79.40% and helper 0.32% (238.59% proof)

1083369917...7048838211 is prime! (0.2432s+0.0004s)
[Elapsed time: 5.00 seconds]

Helper File:
2
3
5
7
43
89
163
199
263
307
881
967
2789
3607
6011
16829
21649
59369
306511
800483
855997
928157
4274579
62043169
350207569
370248451
3444245657
23515719083
30048040741
7878454669361
9838425675437
28278965692309
22549039789436761
194370916721445668453
1027729298220237292846693
594781729148710899627586567069
2684571411430027028247905903965201
26315372138382470904009809410251331242219701
389192962225654291671474159761046390844386713
666146992336447094037882680026427177876016818933
17732745322135163936648351820424253379372467026985685021596123
150091893275938965565142165169464683420682759092285062166834604838859194179
56909671435221082533169582520085662884377962564222829999842181652894123123019
19664644211826977261258200244938258...(92 digits)...69016674440337439189171248007621961
97903429242000349002888933691465744...(96 digits)...92481134336750695323180049770154871
79242603382498978143878749618315218...(109 digits)...31093891098279396811260320046888441
22360525253034883018624489654276404...(120 digits)...50502532827604799013828233565326309
36645269041465497098749680120289063...(140 digits)...46035698985849240337576788325219929
137
197

modified 2026-02-04 10:28:34

created 2026-02-04 10:28:24

id 187694

field	value
prime_id	39090
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 1083369917...7048838211 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper_1100000000306341416.txt trial Running N-1 test using base 2 Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5007-bit number Running N-1 test using base 3 Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5007-bit number Running N+1 test using discriminant 7, base 1+sqrt(7) Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5007-bit number Calling N-1 BLS with factored part 79.40% and helper 0.32% (238.59% proof) 1083369917...7048838211 is prime! (0.2432s+0.0004s) [Elapsed time: 5.00 seconds] Helper File: 2 3 5 7 43 89 163 199 263 307 881 967 2789 3607 6011 16829 21649 59369 306511 800483 855997 928157 4274579 62043169 350207569 370248451 3444245657 23515719083 30048040741 7878454669361 9838425675437 28278965692309 22549039789436761 194370916721445668453 1027729298220237292846693 594781729148710899627586567069 2684571411430027028247905903965201 26315372138382470904009809410251331242219701 389192962225654291671474159761046390844386713 666146992336447094037882680026427177876016818933 17732745322135163936648351820424253379372467026985685021596123 150091893275938965565142165169464683420682759092285062166834604838859194179 56909671435221082533169582520085662884377962564222829999842181652894123123019 19664644211826977261258200244938258...(92 digits)...69016674440337439189171248007621961 97903429242000349002888933691465744...(96 digits)...92481134336750695323180049770154871 79242603382498978143878749618315218...(109 digits)...31093891098279396811260320046888441 22360525253034883018624489654276404...(120 digits)...50502532827604799013828233565326309 36645269041465497098749680120289063...(140 digits)...46035698985849240337576788325219929 137 197
modified	2026-02-04 10:28:34
created	2026-02-04 10:28:24
id	187694

field value

prime_id 39090

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 2 Primality testing primV(10821) [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 3.36% primV(10821) is PRP! (7.040000 seconds)

modified 2003-03-25 17:22:48

created 2003-01-07 05:06:02

id 63863

field	value
prime_id	39090
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 2 Primality testing primV(10821) [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 3.36% primV(10821) is PRP! (7.040000 seconds)
modified	2003-03-25 17:22:48
created	2003-01-07 05:06:02
id	63863

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