482787103228021316582127269999999

enzocreti · 2019-05-03, 10:22

482787103228021316582127269999999 is the lesser of a twin prime pair.

It is 5#*7#*11#*13#*17#*19#*23#-1

A challenge for somebody of you:

to find other pairs of twin primes of the form 5#*7#*11#...*p# +/- 1, greater than that.

paulunderwood · 2019-05-03, 10:55

See: https://www.mersenneforum.org/showpo...58&postcount=6

Dylan14 · 2019-05-04, 01:19

Code used to check this (in Mathematica):

Code:

Primorial[n_] := Product[Prime[i], {i, n}]
For[i = 0, i <= 130, i++, 
 If[PrimeQ[Product[Primorial[3 + x], {x, 0, i}] - 1] && 
   PrimeQ[Product[Primorial[3 + x], {x, 0, i}] + 1], Print[i]]]

Through a product of 5#*7#*11#*...*751# (which has 18572 digits and corresponds to i = 130 in this code), the only twin primes of this form are
5# +/- 1 (corresponding to i=0)
5#*7# +/- 1 (i = 1)
and the example that enzocreti gave (i=6). I will not go further, simply because the time it takes to run the PrimeQ quickly becomes prohibitive (at i = 130 it takes about 19 * 2 seconds to test for primality, plus a small amount of time to compute the product (*)).

(*) yes we could sieve the candidates here to reduce the overhead but I am not sure how we could code this efficiently using the MTsieve framework.

2019-05-03, 10:22	#1
enzocreti Mar 2018 212₁₆ Posts	482787103228021316582127269999999 482787103228021316582127269999999 is the lesser of a twin prime pair. It is 5#7#11#13#17#19#23#-1 A challenge for somebody of you: to find other pairs of twin primes of the form 5#7#11#...p# +/- 1, greater than that. Last fiddled with by enzocreti on 2019-05-03 at 10:23*

2019-05-04, 01:19	#3
Dylan14 "Dylan" Mar 2017 3·193 Posts	Code used to check this (in Mathematica): Code: Primorial[n_] := Product[Prime[i], {i, n}] For[i = 0, i <= 130, i++, If[PrimeQ[Product[Primorial[3 + x], {x, 0, i}] - 1] && PrimeQ[Product[Primorial[3 + x], {x, 0, i}] + 1], Print[i]]] Through a product of 5#7#11#...751# (which has 18572 digits and corresponds to i = 130 in this code), the only twin primes of this form are 5# +/- 1 (corresponding to i=0) 5#7# +/- 1 (i = 1) and the example that enzocreti gave (i=6). I will not go further, simply because the time it takes to run the PrimeQ quickly becomes prohibitive (at i = 130 it takes about 19 2 seconds to test for primality, plus a small amount of time to compute the product ()). () yes we could sieve the candidates here to reduce the overhead but I am not sure how we could code this efficiently using the MTsieve framework.

2019-05-03, 10:55	#2
paulunderwood Sep 2002 Database er0rr 3,739 Posts	See: https://www.mersenneforum.org/showpo...58&postcount=6