See A066272 for definition of antidivisor.
Jon Perry calls these antiprimes.
From Max Alekseyev, Jul 23 2007: (Start)
Except for the term 4, the elements of A066466 have form 2^k*p where p is odd prime and both 2^(k+1)*p1, 2^(k+1)*p+1 are prime (i.e., twin primes). In other words, this sequence, omitting 4, is a subsequence of A040040 containing elements of the form 2^k*p with prime p.
Furthermore, since 2^(k+1)*p1, 2^(k+1)*p+1 must equal 1 and +1 modulo 3, the number 2^(k+1)*p must be 0 modulo 3, implying that p=3. Therefore every element 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.
According to these tables: http://web.archive.org/web/20161028080239/http://www.prothsearch.net/riesel.html and http://web.archive.org/web/20161028021640/http://www.prothsearch.net/riesel2.html there are no other such k up to 5*10^6. Therefore the next element of A066466 (if it exists) is greater than 3*2^(5*10^6) ~= 10^1505150. (End)
From Daniel Forgues, Nov 23 2009: (Start)
The 2 last known antiprimes seem to relate to the Fermat primes (coincidence?):
96 = 3 * 2^5 = 3 * 2^F_1 = 3 * 2^[2^(2^1) + 1] and
393216 = 3 * 2^17 = 3 * 2^F_2 = 3 * 2^[2^(2^2) + 1],
where F_k is the kth Fermat prime. (End)
