primU(10025)

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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(10025)
Verification status (*):	Proven
Official Comment (*):	Fibonacci primitive part
Proof-code(s): (*):	DK : Dubner, Keller, Cruncher
Decimal Digits:	1672 (log₁₀ is 1671.9046388051)
Rank (*):	112108 (digit rank is 1)
Entrance Rank (*):	4866
Currently on list? (*):	no
Submitted:	7/1995
Last modified:	2/4/2026 10:22:27 UTC
Database id:	38380
Status Flags:	none
Score (*):	26.8781 (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 67
Subcategory: "Fibonacci Primitive Part"
(archival tag id 176480, 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 38380

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 8028581217...4744275001 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000305619107.txt
trial

Running N-1 test using base 13
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5554-bit number
Running N-1 test using base 17
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5554-bit number
Running N+1 test using discriminant 23, base 6+sqrt(23)
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5554-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 298/5568 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 23, base 6+sqrt(23)
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 5554-bit number
Calling N-1 BLS with factored part 41.15% and helper 0.18% (123.64% proof)

8028581217...4744275001 is prime! (0.2631s+0.0003s)
[Elapsed time: 5.00 seconds]

Helper File:
2
3
5
7
11
31
41
47
61
101
151
251
269
401
1601
2011
2161
3041
4001
4021
116849
124001
570601
667321
1429913
6996001
9125201
82892501
82974811
112128001
763170871
1353439001
5738108801
11635785751
14073087361
24994118449
28143378001
81035662501
83086383091
1603158458731
3014307972001
5465167948001
7718835665940241
10496059430146001
1102501826040037981
1402587705167164001
84817574770589638001
158414167964045700001
3160438834174817356001
38856705409546629457212001
47420297430047911698194931398915971
754443521566594151546570042623791984775588648001
1249976481751054211089356699940265657412260237297720289437904001
9372625568572722938847095612481183137496995522804466421273200001
10997061097092427532544917221341458994887154863443084531915173089761744886170366141
631

modified 2026-02-04 10:22:27

created 2026-02-04 10:22:17

id 187688

field	value
prime_id	38380
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 8028581217...4744275001 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper_1100000000305619107.txt trial Running N-1 test using base 13 Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5554-bit number Running N-1 test using base 17 Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5554-bit number Running N+1 test using discriminant 23, base 6+sqrt(23) Generic modular reduction using generic reduction FMA3 FFT length 512 on A 5554-bit number Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 298/5568 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a1 switch) Running N+1 test using discriminant 23, base 6+sqrt(23) Generic modular reduction using generic reduction FMA3 FFT length 640 on A 5554-bit number Calling N-1 BLS with factored part 41.15% and helper 0.18% (123.64% proof) 8028581217...4744275001 is prime! (0.2631s+0.0003s) [Elapsed time: 5.00 seconds] Helper File: 2 3 5 7 11 31 41 47 61 101 151 251 269 401 1601 2011 2161 3041 4001 4021 116849 124001 570601 667321 1429913 6996001 9125201 82892501 82974811 112128001 763170871 1353439001 5738108801 11635785751 14073087361 24994118449 28143378001 81035662501 83086383091 1603158458731 3014307972001 5465167948001 7718835665940241 10496059430146001 1102501826040037981 1402587705167164001 84817574770589638001 158414167964045700001 3160438834174817356001 38856705409546629457212001 47420297430047911698194931398915971 754443521566594151546570042623791984775588648001 1249976481751054211089356699940265657412260237297720289437904001 9372625568572722938847095612481183137496995522804466421273200001 10997061097092427532544917221341458994887154863443084531915173089761744886170366141 631
modified	2026-02-04 10:22:27
created	2026-02-04 10:22:17
id	187688

field value

prime_id 38380

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 13 Primality testing primU(10025) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Calling Brillhart-Lehmer-Selfridge with factored part 3.44% primU(10025) is PRP! (13.840000 seconds)

modified 2003-03-25 17:22:47

created 2003-01-07 05:12:09

id 63876

field	value
prime_id	38380
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 13 Primality testing primU(10025) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Calling Brillhart-Lehmer-Selfridge with factored part 3.44% primU(10025) is PRP! (13.840000 seconds)
modified	2003-03-25 17:22:47
created	2003-01-07 05:12:09
id	63876

Query times: -0.9997 seconds to select prime, 0.0004 seconds to seek comments.