Phi(211, - 204807268365921)
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(211, - 204807268365921) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized unique |
| Proof-code(s): (*): | D : Dubner, Cruncher |
| Decimal Digits: | 3006 (log10 is 3005.3825266859) |
| Rank (*): | 100059 (digit rank is 1) |
| Entrance Rank (*): | 3195 |
| Currently on list? (*): | no |
| Submitted: | 7/1996 |
| Last modified: | 2/4/2026 10:28:03 UTC |
| Database id: | 29676 |
| Status Flags: | none |
| Score (*): | 28.7061 (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.
- Generalized Unique (archivable *)
- Prime on list: no, rank 1569
Subcategory: "Generalized Unique"
(archival tag id 225613, tag last modified 2026-01-09 22:37:30)
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 29676 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper_1100000002486193144.txt -q"Phi(211,-204807268365921)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(211,-204807268365921) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000002486193144.txt
Prime_Testing_Warning,
Running N-1 test using base 17
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 9984-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.34%
1/0
Phi(211,-204807268365921) is prime! (0.5120s+0.0054s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
29
31
41
43
61
71
97
127
151
211
277
281
421
457
673
769
1153
1597
1861
2129
2311
2423
2521
2551
3037
3361
3739
4397
6961
10501
20611
33349
34297
49081
54851
67843
112129
179593
228523
244129
541531
763673
1357021
1363909
1710661
2505301
5566681
5669273
7634131
8554981
10438891
14327381
20199481
45096521
185781877
187996201
607862221
1617891397
2153847557
3732897191
17448285961
218761675441
233192109697
1634937258991
12679493500561
32865162782671
41701516562376301
144327839237553061
3544682891965876753
16889767782565690993
41292817411115912783
362352404713707042601
449600611887614196409
585536383020672712441
650288372066994222451
11998527312559507129244563471
41957105204652261671051004001
345143731957701225012010051849
11325494577817206352715859839058049
245400801012816032790937270964237881
12190776839225475272301199333493572083181
23198597614797838571822260366221413903129
147526405368937095937935995706387810707660358361
6149353079589041060716064824702973387248297003698026631631
7071843067963727429416209308068138124267474791961664591188733288275329713572131
30957288988909203586841172268329594...(115 digits)...59234134476034041506695892931383681
16206001306465224731032908049167779...(169 digits)...70887593367652775835707990243561761
23
227
3373modified 2026-02-04 10:28:03 created 2026-02-04 10:27:58 id 187693
field value prime_id 29676 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 17 Primality testing Phi(211,-204807268365921) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 23, base 14+sqrt(23) Calling N-1 BLS with factored part 5.36% and helper 0.25% (16.33% proof) Phi(211,-204807268365921) is Fermat and Lucas PRP! (120.910000 seconds) modified 2003-03-25 17:22:58 created 2003-01-04 21:40:13 id 61866
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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