U(35999)
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: | U(35999) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Fibonacci number, cyclotomy |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | p54 : Broadhurst, Water, OpenPFGW |
| Decimal Digits: | 7523 (log10 is 7522.9965763568) |
| Rank (*): | 89272 (digit rank is 1) |
| Entrance Rank (*): | 16901 |
| Currently on list? (*): | yes |
| Submitted: | 7/24/2001 03:15:40 UTC |
| Last modified: | 2/4/2026 11:51:01 UTC |
| Database id: | 20235 |
| Status Flags: | Verify |
| Score (*): | 31.5575 (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.
- Fibonacci Number (archivable *)
- Prime on list: yes, rank 8
Subcategory: "Fibonacci Number"
(archival tag id 194580, tag last modified 2023-09-15 17:37:10)- Cyclotomy Proof (tolerated *)
- Prime on list: no, rank 68
Subcategory: "Cyclotomy Proof"
(archival tag id 194579, tag last modified 2025-08-29 21:37:20)
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.
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 20235 person_id 9 machine Using: Digital Ocean Droplet what prp notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper_1000000000012286023.txt -q"U(35999)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing U(35999) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1000000000012286023.txt
trial
Running N-1 test using base 13
Generic modular reduction using generic reduction FMA3 FFT length 2560 on A 24991-bit number
Running N-1 test using base 71
Generic modular reduction using generic reduction FMA3 FFT length 2560 on A 24991-bit number
Running N+1 test using discriminant 79, base 1+sqrt(79)
Generic modular reduction using generic reduction FMA3 FFT length 2560 on A 24991-bit number
Calling N-1 BLS with factored part 28.40% and helper 12.36% (97.55% proof)
U(35999) is Fermat and Lucas PRP! (7.9816s+0.0058s)
[Elapsed time: 10.00 seconds]
Helper File:
2
3
5
7
11
17
19
23
31
41
47
61
101
107
151
181
241
251
401
541
601
751
1103
1201
1601
1801
2161
2251
2521
3001
3041
4001
4391
8641
9001
12301
14401
18451
20641
35999
54001
79201
103681
109441
124001
126001
169501
221401
570601
673201
1948801
2009251
4925251
5208481
6996001
9125201
15608701
24327001
112128001
148669201
230686501
370248451
826061911
1353439001
2534538001
5738108801
9602982001
10749957121
10783342081
28143378001
135059760001
329233146001
615492724061
1107516928501
1599014169601
2623565892001
3014307972001
3467131047901
4319732027251
5465167948001
23735900452321
41510105455501
87129547172401
468535826053501
10496059430146001
13373763765986881
20882100086372251
1402587705167164001
9906293406944653501
84817574770589638001
87821494006817736001
158414167964045700001
186374563189054810201
792081397330050024751
3160438834174817356001
56591071305331580971201
11981661982050957053616001
38856705409546629457212001
53933118732742016819700001
427694148584338087778220001
2741744004792724568507910751
2768864177646584420637552001
10609171199508620690498181601
31693914535837935570580506001
732097782477553046683475592001
2598599460710680701179307912001
1149884364774317448679684799063561
1393078961742658514909432047447201
2563987147105929622138082038024801
37720432662731112363293109762399994510923001
13345777072640252551741515140876418537140353109
754443521566594151546570042623791984775588648001
1868365782227850502954142134626134886244458706713751
1249976481751054211089356699940265657412260237297720289437904001
9372625568572722938847095612481183137496995522804466421273200001
24296771853413907209577117179673869...(90 digits)...24632219567348601088077065692608801
23249041189463596379778767030034661...(103 digits)...68647711189175096705585942075335001
22296350187565543723832432907201912...(114 digits)...53004855859303159173049035110721501
12276479955948202195811060788005244...(122 digits)...38216273379685143062894719794402001
62027167790141724825296188911197369...(141 digits)...17785033057321791251202667886705601
23298148909270057149295222840876001...(146 digits)...84280768681886985648908424858620001
769
877
2207
2789
3167
4801
24001
59369
163309
858241
2512001
5990401
23448001
107420801
177736001
281490241
297288001
362304001
2567001601
2846184001
89322144001
1263141849553
23725145626561
51793685214662401
362660972372910721
539818905175331293
1999653272832963841
56217506866590456001
115561578124838522881
33364102626696976997761
41071004474575750019238941
2167331446169951536000056001
12842054866056446184519361561
329541040898736809891408309777
7601587101128729489773008667804801
17173718030064788332433726155286401
39529024042287185727716365292486741472001
434353132447792437313298765453570531365913726307826738327056001
27096618456036920128682868938465398341403509562400553901610581411201
81146173936753219778365521800477746...(290 digits)...85480312155483830827940489094040001modified 2026-02-04 11:51:01 created 2026-02-04 11:50:51 id 187730
field value prime_id 20235 person_id 9 machine Using: Digital Ocean Droplet what prp notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper_1000000000012286023.txt -q"U(35999)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing U(35999) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1000000000012286023.txt
trial
Running N-1 test using base 13
Generic modular reduction using generic reduction FMA3 FFT length 2560 on A 24991-bit number
Running N-1 test using base 71
Generic modular reduction using generic reduction FMA3 FFT length 2560 on A 24991-bit number
Running N+1 test using discriminant 79, base 1+sqrt(79)
Generic modular reduction using generic reduction FMA3 FFT length 2560 on A 24991-bit number
Calling N-1 BLS with factored part 28.40% and helper 12.36% (97.55% proof)
U(35999) is Fermat and Lucas PRP! (7.4072s+0.0049s)
[Elapsed time: 10.00 seconds]
Helper File:
2
3
5
7
11
17
19
23
31
41
47
61
101
107
151
181
241
251
401
541
601
751
1103
1201
1601
1801
2161
2251
2521
3001
3041
4001
4391
8641
9001
12301
14401
18451
20641
35999
54001
79201
103681
109441
124001
126001
169501
221401
570601
673201
1948801
2009251
4925251
5208481
6996001
9125201
15608701
24327001
112128001
148669201
230686501
370248451
826061911
1353439001
2534538001
5738108801
9602982001
10749957121
10783342081
28143378001
135059760001
329233146001
615492724061
1107516928501
1599014169601
2623565892001
3014307972001
3467131047901
4319732027251
5465167948001
23735900452321
41510105455501
87129547172401
468535826053501
10496059430146001
13373763765986881
20882100086372251
1402587705167164001
9906293406944653501
84817574770589638001
87821494006817736001
158414167964045700001
186374563189054810201
792081397330050024751
3160438834174817356001
56591071305331580971201
11981661982050957053616001
38856705409546629457212001
53933118732742016819700001
427694148584338087778220001
2741744004792724568507910751
2768864177646584420637552001
10609171199508620690498181601
31693914535837935570580506001
732097782477553046683475592001
2598599460710680701179307912001
1149884364774317448679684799063561
1393078961742658514909432047447201
2563987147105929622138082038024801
37720432662731112363293109762399994510923001
13345777072640252551741515140876418537140353109
754443521566594151546570042623791984775588648001
1868365782227850502954142134626134886244458706713751
1249976481751054211089356699940265657412260237297720289437904001
9372625568572722938847095612481183137496995522804466421273200001
24296771853413907209577117179673869...(90 digits)...24632219567348601088077065692608801
23249041189463596379778767030034661...(103 digits)...68647711189175096705585942075335001
22296350187565543723832432907201912...(114 digits)...53004855859303159173049035110721501
12276479955948202195811060788005244...(122 digits)...38216273379685143062894719794402001
62027167790141724825296188911197369...(141 digits)...17785033057321791251202667886705601
23298148909270057149295222840876001...(146 digits)...84280768681886985648908424858620001
769
877
2207
2789
3167
4801
24001
59369
163309
858241
2512001
5990401
23448001
107420801
177736001
281490241
297288001
362304001
2567001601
2846184001
89322144001
1263141849553
23725145626561
51793685214662401
362660972372910721
539818905175331293
1999653272832963841
56217506866590456001
115561578124838522881
33364102626696976997761
41071004474575750019238941
2167331446169951536000056001
12842054866056446184519361561
329541040898736809891408309777
7601587101128729489773008667804801
17173718030064788332433726155286401
39529024042287185727716365292486741472001
434353132447792437313298765453570531365913726307826738327056001
27096618456036920128682868938465398341403509562400553901610581411201
81146173936753219778365521800477746...(290 digits)...85480312155483830827940489094040001modified 2026-02-04 11:42:08 created 2026-02-04 11:41:58 id 187729
field value prime_id 20235 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality testing 9921477614...0278699239 Running N-1 test using base 13 6792069340...5181224001 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 71 Running N+1 test using discriminant 79, base 1+sqrt(79) Calling N-1 BLS with factored part 2.29% and helper 0.54% (7.42% proof) U(35999) is Fermat and Lucas PRP! (1007.860000 seconds) modified 2003-03-25 17:22:42 created 2003-01-08 21:49:50 id 64662
Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.