primV(6044)

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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(6044)
Verification status (*):	Proven
Official Comment (*):	Lucas primitive part
Proof-code(s): (*):	DK : Dubner, Keller, Cruncher
Decimal Digits:	1263 (log₁₀ is 1262.2761996309)
Rank (*):	119039 (digit rank is 38)
Entrance Rank (*):	7266
Currently on list? (*):	no
Submitted:	7/1995
Last modified:	2/4/2026 10:31:40 UTC
Database id:	44857
Status Flags:	none
Score (*):	26.0003 (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 129
Subcategory: "Lucas primitive part"
(archival tag id 195702, 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 44857

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 1888859395...1298676801 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000002950687.txt
trial

Running N-1 test using base 31
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 4194-bit number
Running N-1 test using base 79
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 4194-bit number
Running N-1 test using base 89
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 4194-bit number
Running N+1 test using discriminant 113, base 4+sqrt(113)
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 4194-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 40/8320 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 113, base 4+sqrt(113)
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 4194-bit number
Calling N-1 BLS with factored part 67.95% and helper 25.83% (229.67% proof)

1888859395...1298676801 is prime! (0.3103s+0.0003s)
[Elapsed time: 5.00 seconds]

Helper File:
2
3
5
7
11
13
17
19
23
29
41
47
53
83
107
109
167
211
281
379
421
503
1009
1103
1427
1511
2267
3023
5737
5779
6263
14503
19009
30241
31249
32507
36241
38933
85429
95131
103681
912871
1461601
11128427
35239681
65740583
109734721
447901921
764940961
1258740001
1639145771
2510797801
10745088481
10749957121
70963651961
95305716283
177962167367
4322424761927
48265838239823
571385160581761
4259753026115161
955921950316735037
115613939510481515041
217533000184835774779
28670176851485891563801
780066371941922766847301
793343398694591469557681
2811666624525811646469915877
471991644996070811213117005172115579281
3263431473266519156894217972558849512533251151838024867101
717183675566658213132761730294626635650067479275923957352582406983301023453681347576121
76827807946814787200616161579347844...(93 digits)...63471356153278846031859145179203921
39983014912279391817618548836896915...(112 digits)...61143916814142602476105295172951001
223
449
769
863
2161
2207
3167
3623
6047
18143
895127
5261761
233210881
416187743
1034748641
1368322369
7182393521
10162500226001
303039789569567
1154149773784223
1292528726309580481
73842573103586899487
115561578124838522881
79914045929576045795423
10212497762794624073474270529086495...(113 digits)...46957740926235528660257230687861761

modified 2026-02-04 10:31:40

created 2026-02-04 10:31:30

id 187699

field	value
prime_id	44857
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 1888859395...1298676801 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper_1100000000002950687.txt trial Running N-1 test using base 31 Generic modular reduction using generic reduction FMA3 FFT length 384 on A 4194-bit number Running N-1 test using base 79 Generic modular reduction using generic reduction FMA3 FFT length 384 on A 4194-bit number Running N-1 test using base 89 Generic modular reduction using generic reduction FMA3 FFT length 384 on A 4194-bit number Running N+1 test using discriminant 113, base 4+sqrt(113) Generic modular reduction using generic reduction FMA3 FFT length 384 on A 4194-bit number Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 40/8320 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a1 switch) Running N+1 test using discriminant 113, base 4+sqrt(113) Generic modular reduction using generic reduction FMA3 FFT length 512 on A 4194-bit number Calling N-1 BLS with factored part 67.95% and helper 25.83% (229.67% proof) 1888859395...1298676801 is prime! (0.3103s+0.0003s) [Elapsed time: 5.00 seconds] Helper File: 2 3 5 7 11 13 17 19 23 29 41 47 53 83 107 109 167 211 281 379 421 503 1009 1103 1427 1511 2267 3023 5737 5779 6263 14503 19009 30241 31249 32507 36241 38933 85429 95131 103681 912871 1461601 11128427 35239681 65740583 109734721 447901921 764940961 1258740001 1639145771 2510797801 10745088481 10749957121 70963651961 95305716283 177962167367 4322424761927 48265838239823 571385160581761 4259753026115161 955921950316735037 115613939510481515041 217533000184835774779 28670176851485891563801 780066371941922766847301 793343398694591469557681 2811666624525811646469915877 471991644996070811213117005172115579281 3263431473266519156894217972558849512533251151838024867101 717183675566658213132761730294626635650067479275923957352582406983301023453681347576121 76827807946814787200616161579347844...(93 digits)...63471356153278846031859145179203921 39983014912279391817618548836896915...(112 digits)...61143916814142602476105295172951001 223 449 769 863 2161 2207 3167 3623 6047 18143 895127 5261761 233210881 416187743 1034748641 1368322369 7182393521 10162500226001 303039789569567 1154149773784223 1292528726309580481 73842573103586899487 115561578124838522881 79914045929576045795423 10212497762794624073474270529086495...(113 digits)...46957740926235528660257230687861761
modified	2026-02-04 10:31:40
created	2026-02-04 10:31:30
id	187699

field value

prime_id 44857

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 31 Primality testing primV(6044) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 79 Calling Brillhart-Lehmer-Selfridge with factored part 9.21% primV(6044) is PRP! (8.700000 seconds)

modified 2003-03-25 17:22:48

created 2003-01-07 04:39:58

id 63837

field	value
prime_id	44857
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 31 Primality testing primV(6044) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 79 Calling Brillhart-Lehmer-Selfridge with factored part 9.21% primV(6044) is PRP! (8.700000 seconds)
modified	2003-03-25 17:22:48
created	2003-01-07 04:39:58
id	63837

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.