primU(14203)

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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:	primU(14203)
Verification status (*):	Proven
Official Comment (*):	Fibonacci primitive part
Proof-code(s): (*):	DK : Dubner, Keller, Cruncher
Decimal Digits:	2544 (log₁₀ is 2543.1015890509)
Rank (*):	101501 (digit rank is 9)
Entrance Rank (*):	4429
Currently on list? (*):	no
Submitted:	10/1996
Last modified:	2/4/2026 09:54:02 UTC
Database id:	31033
Status Flags:	none
Score (*):	28.1859 (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.

Fibonacci Primitive Part (archivable *)
Prime on list: no, rank 58
Subcategory: "Fibonacci Primitive Part"
(archival tag id 175651, tag last modified 2024-10-14 00:37:17)

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 31033

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 1263540162...2284983601 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000305791141.txt
trial

Running N-1 test using base 17
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 8449-bit number
Running N+1 test using discriminant 23, base 2+sqrt(23)
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 8449-bit number
Calling N-1 BLS with factored part 33.89% and helper 0.14% (101.82% proof)

1263540162...2284983601 is prime! (0.5865s+0.0004s)
[Elapsed time: 5.00 seconds]

Helper File:
2
3
5
7
11
29
59
71
79
233
337
521
859
911
1013
1217
2027
2029
19489
89909
90481
135721
141283
141961
514229
2629093
47472487
56470541
10069148777
12280217041
70453016089
104600155609
120196353941
194435819761
335825368481
404112157123
1322154751061
6189308414329
27276495048041
126213229732669
596107814364089
4172478655536941
5931857299161151
671040394220849329
136017283437875754181
478061565712797524641
349619996930737079890201
2586982700656733994659533
2892106995173496522201467
17340889195212892399797173
904631677874647406183595497
2748232098283374889444289976282269
628792633741009630402212166470453301
1319619372577567194301056335501698189305917359441
1405358584518002862111895840152520800694281567628127021
12683786376588169024557898918225085843290175928337986391
78860606172081877329818897864636608633384251965253851978285929
58714558803573051605831367991139340...(107 digits)...76601022792891886606183648826463681
13
223

modified 2026-02-04 09:54:02

created 2026-02-04 09:53:52

id 187675

field	value
prime_id	31033
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 1263540162...2284983601 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper_1100000000305791141.txt trial Running N-1 test using base 17 Generic modular reduction using generic reduction FMA3 FFT length 1K on A 8449-bit number Running N+1 test using discriminant 23, base 2+sqrt(23) Generic modular reduction using generic reduction FMA3 FFT length 1K on A 8449-bit number Calling N-1 BLS with factored part 33.89% and helper 0.14% (101.82% proof) 1263540162...2284983601 is prime! (0.5865s+0.0004s) [Elapsed time: 5.00 seconds] Helper File: 2 3 5 7 11 29 59 71 79 233 337 521 859 911 1013 1217 2027 2029 19489 89909 90481 135721 141283 141961 514229 2629093 47472487 56470541 10069148777 12280217041 70453016089 104600155609 120196353941 194435819761 335825368481 404112157123 1322154751061 6189308414329 27276495048041 126213229732669 596107814364089 4172478655536941 5931857299161151 671040394220849329 136017283437875754181 478061565712797524641 349619996930737079890201 2586982700656733994659533 2892106995173496522201467 17340889195212892399797173 904631677874647406183595497 2748232098283374889444289976282269 628792633741009630402212166470453301 1319619372577567194301056335501698189305917359441 1405358584518002862111895840152520800694281567628127021 12683786376588169024557898918225085843290175928337986391 78860606172081877329818897864636608633384251965253851978285929 58714558803573051605831367991139340...(107 digits)...76601022792891886606183648826463681 13 223
modified	2026-02-04 09:54:02
created	2026-02-04 09:53:52
id	187675

field value

prime_id 31033

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 17 Primality testing primU(14203) [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 2.96% primU(14203) is PRP! (19.100000 seconds)

modified 2003-03-25 17:22:47

created 2003-01-07 13:19:39

id 64030

field	value
prime_id	31033
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 17 Primality testing primU(14203) [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 2.96% primU(14203) is PRP! (19.100000 seconds)
modified	2003-03-25 17:22:47
created	2003-01-07 13:19:39
id	64030

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