Phi(3261, - 10)
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(3261, - 10) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Unique, APR-CL assisted |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | F2 : Broadhurst, OpenPFGW, Primo, VFYPR |
| Decimal Digits: | 2173 (log10 is 2172.0409586077) |
| Rank (*): | 107585 (digit rank is 9) |
| Entrance Rank (*): | 27407 |
| Currently on list? (*): | no |
| Submitted: | 2/11/2001 22:02:37 UTC |
| Last modified: | 2/4/2026 10:02:28 UTC |
| Database id: | 33929 |
| Status Flags: | none |
| Score (*): | 27.6944 (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.
User comments about this prime (disclaimer):
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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 33929 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper_1100000000005551252.txt -q"Phi(3261,-10)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(3261,-10) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000005551252.txt
Prime_Testing_Warning,
Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 768 on A 7216-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 35.29%
Phi(3261,-10) is prime! (0.1346s+0.0048s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
11
37
1087
12671
13757
1429397
28865519
995130761
4411725823
9822131521
16814655289
414479952329
53626715893973
4883002285136971
1467439874822650361
34712893020518440729
73897947065047207693
124016216479696838809
3923435197184939035671283
4063238920032381354306386614023999095656711243
25777735562862028866275893860507358474449690283
484165712170909795871964783465540188248186710475652666425207
25900548863672930451831053961363718303143744545008210388536104834284881
57813769227978665304109403799291636496876923883191635824278127299864929561
778918424933155393480511088578762495409547716376329687166271120021739022042090054703
43802165346296010499240898793751822...(138 digits)...08485764810227154150678965468226079
66182298069357042371041913724627286...(197 digits)...98154908973645214837925427979563331
85461444657765270893407150603527324...(204 digits)...86426232608794708662531148460347289
101
9055670033modified 2026-02-04 10:02:28 created 2026-02-04 10:02:23 id 187678
field value prime_id 33929 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 2 Primality testing Phi(3261,-10) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N+1 test using discriminant 13, base 2+sqrt(13) Calling N-1 BLS with factored part 0.75% and helper 0.11% (2.37% proof) Phi(3261,-10) is Fermat and Lucas PRP! (76.210000 seconds) modified 2003-03-25 17:22:59 created 2003-01-04 19:09:02 id 61626
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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