1103 · 2^3558177 - 503 · 2^1092022 - 1

This prime's information:

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)

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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:

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