A086827 Smaller member of a twin prime pair such that the sum sets a record for number of prime divisors (counted with multiplicity).

3, 11, 59, 71, 191, 1151, 14591, 15359, 138239, 675839, 737279, 786431, 22118399, 36175871, 63700991, 138412031, 169869311, 1321205759, 4076863487, 10871635967, 24159191039, 370440929279, 1793819934719, 2348273369087, 14637248544767, 56358560858111, 79164837199871, 659706976665599

Offset: 1

Author

Jason Earls, Aug 07 2003

Keywords

• nonn

Examples

			191:193 are twin primes and 384 has 8 prime divisors.
1151:1153 are twin primes and 2304 has 10 prime divisors.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..107

Crossrefs

Subsequence of A001359.

Cf. A001222.

Programs

PARI

g(n) = isprime(n/2 - 1) && isprime(n/2 + 1);
m = 0; forprime(n = 3, 10000, if (isprime(n + 2), c = bigomega(2*n + 2); if (c > m, m = c; print(n))));
while (m < 50, found = 0; for (i = m - 6, m, for (j = max(1, m - 1 - i), m + 4 - i, for (k = 2, 5, for (l = k, 15, n = 2^i*3^j*prime(k)*prime(l); if (g(n), if (!found || found > n, found = n)))))); t = log(found/2^m/3)/log(1.5); t = round(t); a = found/2^(m - t)/3; x = 0; i = 2^t; while (!x, if (bigomega(i) >= t, n = 2^(m - t)*3*i; if (g(n), x = n)); i++); m = bigomega(x); print(x/2 - 1)); \\ David Wasserman, Mar 30 2005

Extensions

More terms from David Wasserman, Mar 30 2005

Offset 1 from Michel Marcus, Sep 25 2023

More terms from David A. Corneth, Sep 26 2023