
COMMENTS

This is to primorial (A002110) as antiprime (A092680) is to prime (A000040). Max Alekseyev points out that every element of A066466, except 4, must be of the form 3*2^k such that 3*2^(k+1)1, 3*2^(k+1)+1 are twin primes. There no such new k+1 (i.e., except known 1,2,6,18) below 1000. In other words, 3*2^n  1, 3*2^n + 1 are twin primes for n=1,2,6,18. According to these tables: http://web.archive.org/web/20161028080239/http://www.prothsearch.net/riesel.html http://web.archive.org/web/20161028021640/http://www.prothsearch.net/riesel2.html there are no other such n up to 1200000. Therefore the next element of A066466 (if it exists) is greater than 3*2^1200000 ~= 10^361236. Hence the next element of the antiprimorials (if it exists) is greater than 679477248 *3*2^1200000 ~= 679477248 * 10^361236 ~= 6 * 10^361245.
