On the many prime number investigation sites across the web I haven't been able to find the answer. Also my math isn't good enough to compute it from first principles.
So, what is the least prime that has 32
1-bits? Of course this refers to its base 2, i.e., binary representation. Programmer-speak for this would be, "32 'set' bits.'
Layperson explanation of the logic behind finding the answer would be an appreciated bonus.