Phi(1087, - 10000)

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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(1087, - 10000)
Verification status (*):	Proven
Official Comment (*):	Unique, ECPP
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	c8 : Broadhurst, Water, Primo
Decimal Digits:	4344 (log₁₀ is 4343.9999565727)
Rank (*):	96612 (digit rank is 1)
Entrance Rank (*):	26438
Currently on list? (*):	no
Submitted:	11/15/2002 21:52:48 UTC
Last modified:	2/4/2026 12:19:32 UTC
Database id:	60802
Status Flags:	none
Score (*):	29.8521 (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 35
Subcategory: "Unique"
(archival tag id 210387, tag last modified 2025-08-23 01:37:16)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 645
Subcategory: "ECPP"
(archival tag id 210386, 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 60802

person_id 9

machine Using: Digital Ocean Droplet

what prime

notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper_1100000000014701599.txt -q"Phi(1087,-10000)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(1087,-10000) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000014701599.txt
Prime_Testing_Warning,

Running N-1 test using base 19
Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 14431-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.41%

Phi(1087,-10000) is prime! (0.7324s+0.0049s)
[Elapsed time: 5.00 seconds]

Helper File:
2
3
5
7
11
13
37
101
1087
8689
9901
12671
13033
13757
2402233
28865519
99990001
436973821
928417781
995130761
9822131521
16814655289
414479952329
469968172441
2136569912461
14034695261869
15470952779187481
37795566859212829
117703209545178769
1467439874822650361
34712893020518440729
73897947065047207693
124016216479696838809
192453118504107893353
3467369151629862044701
2022926961077521870116793
3923435197184939035671283
54688276128174703204513489
314547891171506427278717744569
4063238920032381354306386614023999095656711243
22780106292572351730658730234738216404394547689
25777735562862028866275893860507358474449690283
484165712170909795871964783465540188248186710475652666425207
25900548863672930451831053961363718303143744545008210388536104834284881
57813769227978665304109403799291636496876923883191635824278127299864929561
778918424933155393480511088578762495409547716376329687166271120021739022042090054703
43802165346296010499240898793751822...(138 digits)...08485764810227154150678965468226079
66182298069357042371041913724627286...(197 digits)...98154908973645214837925427979563331
85461444657765270893407150603527324...(204 digits)...86426232608794708662531148460347289
27630577081016864430329072556708703...(214 digits)...97867258088089212682054699054590801
998707609

modified 2026-02-04 12:19:32

created 2026-02-04 12:19:27

id 187741

field	value
prime_id	60802
person_id	9
machine	Using: Digital Ocean Droplet
what	prime
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper_1100000000014701599.txt -q"Phi(1087,-10000)" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing Phi(1087,-10000) [N-1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper_1100000000014701599.txt Prime_Testing_Warning, Running N-1 test using base 19 Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 14431-bit number Calling Brillhart-Lehmer-Selfridge with factored part 33.41% Phi(1087,-10000) is prime! (0.7324s+0.0049s) [Elapsed time: 5.00 seconds] Helper File: 2 3 5 7 11 13 37 101 1087 8689 9901 12671 13033 13757 2402233 28865519 99990001 436973821 928417781 995130761 9822131521 16814655289 414479952329 469968172441 2136569912461 14034695261869 15470952779187481 37795566859212829 117703209545178769 1467439874822650361 34712893020518440729 73897947065047207693 124016216479696838809 192453118504107893353 3467369151629862044701 2022926961077521870116793 3923435197184939035671283 54688276128174703204513489 314547891171506427278717744569 4063238920032381354306386614023999095656711243 22780106292572351730658730234738216404394547689 25777735562862028866275893860507358474449690283 484165712170909795871964783465540188248186710475652666425207 25900548863672930451831053961363718303143744545008210388536104834284881 57813769227978665304109403799291636496876923883191635824278127299864929561 778918424933155393480511088578762495409547716376329687166271120021739022042090054703 43802165346296010499240898793751822...(138 digits)...08485764810227154150678965468226079 66182298069357042371041913724627286...(197 digits)...98154908973645214837925427979563331 85461444657765270893407150603527324...(204 digits)...86426232608794708662531148460347289 27630577081016864430329072556708703...(214 digits)...97867258088089212682054699054590801 998707609
modified	2026-02-04 12:19:32
created	2026-02-04 12:19:27
id	187741

field value

prime_id 60802

person_id 9

machine Linux PII 200

what prp

notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 19 Primality testing Phi(1087,-10000) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 23 Running N+1 test using discriminant 47, base 1+sqrt(47) Calling N-1 BLS with factored part 0.81% and helper 0.01% (2.45% proof) Phi(1087,-10000) is Fermat and Lucas PRP! (295.680000 seconds)

modified 2003-03-25 17:22:56

created 2003-01-05 05:33:54

id 62170

field	value
prime_id	60802
person_id	9
machine	Linux PII 200
what	prp
notes	PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 19 Primality testing Phi(1087,-10000) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 23 Running N+1 test using discriminant 47, base 1+sqrt(47) Calling N-1 BLS with factored part 0.81% and helper 0.01% (2.45% proof) Phi(1087,-10000) is Fermat and Lucas PRP! (295.680000 seconds)
modified	2003-03-25 17:22:56
created	2003-01-05 05:33:54
id	62170

Query times: 0.0005 seconds to select prime, 0.0004 seconds to seek comments.