1103 · 23558177 - 503 · 21092022 - 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:1103 · 23558177 - 503 · 21092022 - 1
Verification status (*):PRP
Official Comment (*):Arithmetic progression (3,d=1103*2^3558176-503*2^1092022)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p423 : Propper, Batalov, EMsieve, OpenPFGW
Decimal Digits:1071122   (log10 is 1071121.0494572)
Rank (*):1353 (digit rank is 1)
Entrance Rank (*):632
Currently on list? (*):short
Submitted:12/31/2022 06:34:21 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:134715
Status Flags:Verify
Score (*):46.8438 (normalized score 6.2069)

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.
Arithmetic Progressions of Primes (archivable class *)
Prime on list: yes, rank 1, weight 54.757167724718
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 227482, tag last modified 2023-03-11 16:02:32)

User comments about this prime (disclaimer):

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Serge Batalov writes (31 Dec 2022):  (report abuse)
Proof by N+1 K-P combined test, using kpp function from kppm.gp by D Broadhurst. Proof output follows:
Primality testing 1103*2^3558177-503*2^1092022-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 384K, Pass1=384, Pass2=1K, clm=4, 8 threads on A 3558189-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 30.69%
1103*2^3558177-503*2^1092022-1 is Lucas PRP! (34707.4102s+0.0026s)

Then kpp():
N=1103*2^3558177-503*2^1092022-1;
G=[2^1092022*513128186329*50227*27127];
kpp(G,N);

fraction = 306924/10^6
OK -5
OK -4
OK -3
OK -2
OK -1
OK 0
OK 1
OK 2
OK 3
OK 4
OK 5

Case 1

Round of root:
-115554051495002606365081666130572627857581267512949660...
Root OK: below the round

Round of root:
0
Root OK: above the round

Round of root:
1155540514950026063650816661305726278575812675129496607...
Root OK: above the round

Case 2

Round of root:
-283631030649275094192045077828634487369156331409673659...
Root OK: above the round

Round of root:
0
Root OK: above the round
Round of root:
2836310306492750941920450778286344873691563314096736592...
Root OK: below the round

Proof completed

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.
fieldvalue
prime_id134715
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tp -q"1103*2^3558177-503*2^1092022-1" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 1103*2^3558177-503*2^1092022-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 30.69%


1103*2^3558177-503*2^1092022-1 is Lucas PRP! (90141.2018s+0.1424s)
[Elapsed time: 25.04 hours]
modified2023-01-01 07:37:23
created2022-12-31 06:35:01
id180495

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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