Phi(3273, - 100)

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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:	Phi(3273, - 100)
Verification status (*):	PRP
Official Comment (*):	Unique, ECPP
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	c8 : Broadhurst, Water, Primo
Decimal Digits:	4361 (log₁₀ is 4360.0043209395)
Rank (*):	96634 (digit rank is 3)
Entrance Rank (*):	28555
Currently on list? (*):	no
Submitted:	4/7/2003 18:46:57 UTC
Last modified:	2/4/2026 12:19:43 UTC
Database id:	64312
Status Flags:	Verify
Score (*):	29.8635 (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.

Unique (archivable *)
Prime on list: no, rank 34
Subcategory: "Unique"
(archival tag id 210384, tag last modified 2025-08-23 01:37:16)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 642
Subcategory: "ECPP"
(archival tag id 210383, tag last modified 2026-01-31 06:37:12)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

David Broadhurst writes (11 Sep 2014): (report abuse)

certificate

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 64312

person_id 9

machine Using: Digital Ocean Droplet

what prp

notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper_1100000000014715446.txt -q"Phi(3273,-100)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(3273,-100) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000014715446.txt
Prime_Testing_Warning,

Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 14484-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 32.67%

Phi(3273,-100) is PRP! (0.6625s+0.0050s)
[Elapsed time: 5.00 seconds]

Helper File:
2
3
5
11
41
101
271
1091
3541
9091
20929
27961
143881
1192679
34895261
83941717007
2755580006681
1107565782360491
3338786746233023
4346911038633671
49369369412784246809
211723317507540088631
712767480971213008079
942341755086403716271
5295275348767234696493
35701893527078181712481
170571534068289207623071
1809124652597219199454921
1359322464803502776636005411
7884537470256430322347573586201
14060959683864286267405933000927102019
7152063279176360267550161080960805856216521
19364383321148719295180578853325741855858987848620134943
246829743984355435962408390910378218537282105150086881669547
18654253320890865029653562871534686...(165 digits)...68302687189633740722184126124790381
60839049349772467210931538101301612...(352 digits)...73103186599449037494993789898657351
27640599640615475767368816052252050...(365 digits)...36116334970247889572939387577135801
73
137
433
593

modified 2026-02-04 12:19:43

created 2026-02-04 12:19:38

id 187743

field	value
prime_id	64312
person_id	9
machine	Using: Digital Ocean Droplet
what	prp
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper_1100000000014715446.txt -q"Phi(3273,-100)" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing Phi(3273,-100) [N-1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper_1100000000014715446.txt Prime_Testing_Warning, Running N-1 test using base 2 Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 14484-bit number Calling Brillhart-Lehmer-Selfridge with factored part 32.67% Phi(3273,-100) is PRP! (0.6625s+0.0050s) [Elapsed time: 5.00 seconds] Helper File: 2 3 5 11 41 101 271 1091 3541 9091 20929 27961 143881 1192679 34895261 83941717007 2755580006681 1107565782360491 3338786746233023 4346911038633671 49369369412784246809 211723317507540088631 712767480971213008079 942341755086403716271 5295275348767234696493 35701893527078181712481 170571534068289207623071 1809124652597219199454921 1359322464803502776636005411 7884537470256430322347573586201 14060959683864286267405933000927102019 7152063279176360267550161080960805856216521 19364383321148719295180578853325741855858987848620134943 246829743984355435962408390910378218537282105150086881669547 18654253320890865029653562871534686...(165 digits)...68302687189633740722184126124790381 60839049349772467210931538101301612...(352 digits)...73103186599449037494993789898657351 27640599640615475767368816052252050...(365 digits)...36116334970247889572939387577135801 73 137 433 593
modified	2026-02-04 12:19:43
created	2026-02-04 12:19:38
id	187743

field value

prime_id 64312

person_id 9

machine Linux P4 2.8GHz

what prp

notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Primality testing Phi(3273,-100) [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 0.79% Phi(3273,-100) is PRP! (4.640000 seconds)

modified 2020-07-07 22:30:48

created 2003-04-08 12:42:50

id 69181

field	value
prime_id	64312
person_id	9
machine	Linux P4 2.8GHz
what	prp
notes	PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Primality testing Phi(3273,-100) [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 0.79% Phi(3273,-100) is PRP! (4.640000 seconds)
modified	2020-07-07 22:30:48
created	2003-04-08 12:42:50
id	69181

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.