primV(5498)

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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(5498)
Verification status (*):	Proven
Official Comment (*):	Lucas primitive part
Proof-code(s): (*):	DK : Dubner, Keller, Cruncher
Decimal Digits:	1149 (log₁₀ is 1148.5369248397)
Rank (*):	124108 (digit rank is 22)
Entrance Rank (*):	8391
Currently on list? (*):	no
Submitted:	7/1995
Last modified:	2/4/2026 10:37:26 UTC
Database id:	49833
Status Flags:	none
Score (*):	25.7051 (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 132
Subcategory: "Lucas primitive part"
(archival tag id 195705, 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 49833

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 3442903416...6034270001 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000216871508.txt
trial

Running N-1 test using base 7
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3816-bit number
Running N-1 test using base 13
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3816-bit number
Running N+1 test using discriminant 19, base 6+sqrt(19)
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3816-bit number
Calling N-1 BLS with factored part 100.00% and helper 17.54% (317.56% proof)

3442903416...6034270001 is prime! (0.4180s+0.0003s)
[Elapsed time: 5.00 seconds]

Helper File:
2
3
5
11
89
101
151
199
251
331
457
661
1373
2749
3001
5501
6871
8243
27481
39161
46751
92401
474541
665501
2392501
4798009
7239101
40487201
112128001
3331306969
7927130867
15806979101
28143378001
132605449901
1820769980147
6982111964759801
43339382282472497059
125379665729217573529
158414167964045700001
964537359154707797801
47831560297620361798553
5527278404454199535821801
432239751442823624735947140379
4967694409687530204298076715216528113
104990418946773667410736999685208265866007631
6944993144158238896632132845325587544900606541
11451679269411697337009089362255999092646667621
13299334241526667283574233715912087831926676751
34098707388625115276643183984525763460112322689001
1646312266588079195968305823407601921407816872407729
501423989411370534047129625287794631465193450279153001
45209282921637859105860390756003405771874712318181696001
13939201442089338203892419708311563176158844531969070307130469089559613476929664587
7198337913009621318933598167897318851211804421713629337070104957293174053516450203301501
17346744418309288946546821505917887...(96 digits)...82787982326965619685734718473208401
31175565237203005208352565390646119...(105 digits)...48651308440951077882560893414811001
7
23
41
43
307
401
12823
55001
570601
20125601
72912401
374436983
1353439001
1003768029001
5465167948001
21380678704001
59996854928656801
84817574770589638001
268246800620554143257373290552875877832369251433833738128853733342001

modified 2026-02-04 10:37:26

created 2026-02-04 10:37:16

id 187702

field	value
prime_id	49833
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 3442903416...6034270001 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper_1100000000216871508.txt trial Running N-1 test using base 7 Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3816-bit number Running N-1 test using base 13 Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3816-bit number Running N+1 test using discriminant 19, base 6+sqrt(19) Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3816-bit number Calling N-1 BLS with factored part 100.00% and helper 17.54% (317.56% proof) 3442903416...6034270001 is prime! (0.4180s+0.0003s) [Elapsed time: 5.00 seconds] Helper File: 2 3 5 11 89 101 151 199 251 331 457 661 1373 2749 3001 5501 6871 8243 27481 39161 46751 92401 474541 665501 2392501 4798009 7239101 40487201 112128001 3331306969 7927130867 15806979101 28143378001 132605449901 1820769980147 6982111964759801 43339382282472497059 125379665729217573529 158414167964045700001 964537359154707797801 47831560297620361798553 5527278404454199535821801 432239751442823624735947140379 4967694409687530204298076715216528113 104990418946773667410736999685208265866007631 6944993144158238896632132845325587544900606541 11451679269411697337009089362255999092646667621 13299334241526667283574233715912087831926676751 34098707388625115276643183984525763460112322689001 1646312266588079195968305823407601921407816872407729 501423989411370534047129625287794631465193450279153001 45209282921637859105860390756003405771874712318181696001 13939201442089338203892419708311563176158844531969070307130469089559613476929664587 7198337913009621318933598167897318851211804421713629337070104957293174053516450203301501 17346744418309288946546821505917887...(96 digits)...82787982326965619685734718473208401 31175565237203005208352565390646119...(105 digits)...48651308440951077882560893414811001 7 23 41 43 307 401 12823 55001 570601 20125601 72912401 374436983 1353439001 1003768029001 5465167948001 21380678704001 59996854928656801 84817574770589638001 268246800620554143257373290552875877832369251433833738128853733342001
modified	2026-02-04 10:37:26
created	2026-02-04 10:37:16
id	187702

field value

prime_id 49833

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 7 Primality testing primV(5498) [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 5.69% primV(5498) is PRP! (3.890000 seconds)

modified 2003-03-25 17:22:48

created 2003-01-07 04:36:53

id 63823

field	value
prime_id	49833
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 7 Primality testing primV(5498) [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 5.69% primV(5498) is PRP! (3.890000 seconds)
modified	2003-03-25 17:22:48
created	2003-01-07 04:36:53
id	63823

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