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The primorial \$p_n\#\$ is the product of the first \$n\$ primes. The sequence begins \$2, 6, 30, 210, 2310\$.
A Fortunate number, \$F_n\$, is the smallest integer \$m > 1\$ such that \$p_n\# + m\$ is prime. For example \$F_7 = 19\$ as:
$$p_7\# = 2\times3\times5\times7\times11\times13\times17 = 5...