482787103228021316582127269999999
 

[URL="http://factordb.com/index.php?id=1100000001293391644"][COLOR=#000000]482787103228021316582127269999999[/COLOR][/URL] 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.

See: [url]https://www.mersenneforum.org/showpost.php?p=515558&postcount=6[/url] :raman:

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]]][/CODE]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.