prog.sf

#!/usr/bin/ruby

# Least k such that k * M(n) * M(n+1) + 1 is prime where M(n) = A000668(n).
# https://oeis.org/A098917

# Known terms:
#   2, 6, 4, 16, 36, 6, 42, 24, 172, 18, 52, 54, 6, 130, 2488, 1344, 12420, 5596, 364, 178, 3382, 10516, 44328, 30342, 25770

# Mersenne exponents are given by A000043(n)

# A000043(24) = 19937
# A000043(25) = 21701

# a(24) corresponds to a 12539-digit prime:
#   30342 * (2**19937 - 1) * (2**21701 - 1) + 1

# A000043(25) = 21701
# A000043(26) = 23209

# a(25) corresponds to a 13524-digit prime:
#   25770 * (2**21701 - 1) * (2**23209 - 1) + 1

# A000043(26) = 23209
# A000043(27) = 44497

# New terms found:
#   a(26) = 47146

# a(26) corresponds to a 20387-digit prime:
#   47146 * (2**23209 - 1) * (2**44497 - 1) + 1

var n = 26
var t = ((2**23209 - 1) * (2**44497 - 1))

for k in (1..1e9) {
    say "Testing: #{k}"
    if (t*k + 1 -> is_prob_prime) {
        die "\na(#{n}) = #{k}\n"
    }
}

__END__
a(26) = 47146
sidef prog.sf  14369.19s user 128.69s system 95% cpu 4:14:05.46 total