19891919890 · R(15600)/R(10) + 1
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: | 19891919890 · R(15600)/R(10) + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Palindrome |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | x30 : Broadhurst, Dubner |
| Decimal Digits: | 15601 (log10 is 15600.298676702) |
| Rank (*): | 80120 (digit rank is 1) |
| Entrance Rank (*): | 9223 |
| Currently on list? (*): | no |
| Submitted: | 10/5/2001 07:22:50 UTC |
| Last modified: | 2/4/2026 11:27:36 UTC |
| Database id: | 11776 |
| Status Flags: | none |
| Score (*): | 33.8175 (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.
- Palindrome (archivable *)
- Prime on list: no, rank 213
Subcategory: "Palindrome"
(archival tag id 192484, tag last modified 2024-12-09 16:37:19)
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 11776 person_id 9 machine Using: Digital Ocean Droplet what prime notes PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 19891919890*R(15600)/R(10)+1 [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000002731718067.txt
Prime_Testing_Warning,
Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 5K on A 51824-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.39%
19891919890*R(15600)/R(10)+1 is prime! (10.8010s+0.0002s)
[Elapsed time: 15.00 seconds]
Helper File:
2
3
5
7
13
17
31
37
53
61
73
79
101
131
137
151
157
211
241
251
313
401
521
601
859
1201
1249
1301
1601
1951
2081
2161
3121
3541
4201
5051
5851
6397
9901
15601
15667
19501
21401
25601
27961
32401
49297
60101
77351
107251
109201
126967
200201
216451
257401
261301
300977
648961
925081
1101673
1580801
1676321
2311921
2906161
3903901
4188901
4271801
5070721
5882353
5990401
6160961
7019801
39526741
66365521
99990001
148068337
265371653
431684501
1058313049
1132716961
5020298401
5964848081
10662171313
14852911841
24592788001
35081393881
82009322851
162503518711
168290119201
182521213001
388847808493
14103673319201
32233075296001
38609381516161
53397071018461
78875943472201
156481560378001
325807801400017
360924572424391
686402214033121
758429752282801
1680588011350901
4347195468174001
9999999900000001
90827204742518401
201721695849323521
1031498834064949381
4487398067478973921
9160020509281917601
12763852652999774041
25074091038628125301
249227787818677482257
280672874149406424401
318942474614140390001
1159572853677397520401
1358074433371719716641
1900381976777332243781
12119730504567977254081
291593563046646669491593
900900900900990990990991
3377783567534940293548001
19721061166646717498359681
23098714167966114959599501
112359026146134915822246001
261765253942256632280403601
281259985248437790051014401
429140220995081117770103701
2685647186330706081032050321
23281905657338518494799021801
31388506438433752927908678241
2737820036624672031089487008281
6060517860310398033985611921721
100009999999899989999000000010001
4711806100010561082466291127577601
8927366651782745402485106538825301
15763985553739191709164170940063151
38654658795718156456729958859629701
5538396997364024056286510640780600481
120920505705101252491925533049923433521
3733209604853765522511798189559871765401
10000099999999989999899999000000000100001
203939065707819971348847334277829768072001
632527440202150745090622412245443923049201
3475700719926956233659563848134955052440801
7323941687838105624847742701467683590147273
44612114135261049915172448202991314405938701
455488632818255423618294643103015306628392801
8396862596258693901610602298557167100076327481
108656831497374119645419435740256864429622885281
175067038724863563854848045107963303611128869041
4482637729513780747000872935673625025127940754401
722385356046094043901164020994302748085851637026401
6279815040943032407714418831204387527919360005277361
7523020307427066273763456609903850552762967576510974081
333632766438409011274705987026407639670042305536743429073
14051485220127306539558738857309372503949399323665750407976449
44933275139025237741442164195375614371497219389368548160257661491391
129694419029057750551385771184564274499075700947656757821537291527196801
14162999157973809346330858715610116834650947071716927166725815643512203761
14612365731240570382005793941286349536257260783370326347124974631092755601
515598058349426893425512324539506997710608203280700351680904729473604464893512426851
63054129911571801941639263405768461425999152026392552531582926655481271974023945336611
13835932649870514134658378951951589...(99 digits)...62990060463305717055848920585883537
11699030147674713906318389910782999...(108 digits)...68627241615756780789663364521811201
16184717413009579260371945398681770...(114 digits)...43195331250705338664714884091786251
14176580788140166982612662932269638...(155 digits)...95571176996529118267301590082336151
99289375637786344255515599181595884...(206 digits)...15000933748377623448310239241465001
77636448947195236747133013143811675...(237 digits)...15756342052306072869338993143889701
16693373281688487965997601829994352...(1914 digits)...68486550399547542810573115222169601
6581modified 2026-02-04 11:27:36 created 2026-02-04 11:27:21 id 187728
field value prime_id 11776 person_id 9 machine WinXP Athlon 1.3GHz what prp notes PFGW Version 20021217.Win_Dev (Beta 'caveat utilitor') [FFT v22.7 w/P4] Running N-1 test using base 2 Primality testing 19891919890*R(15600)/R(10)+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 1.57% 19891919890*R(15600)/R(10)+1 is PRP! (144.838000 seconds) modified 2003-03-25 17:23:32 created 2002-12-29 00:18:29 id 56280
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.