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# 46

This number is a composite.

The 46th prime is 199. Let C = the number of combinations of a group of 199 objects taken 46 at a time. Note that 199!/[46!(199-46)!] has 46 digits and C ± 1 are both primes! [Hartley]

The least even number 2*k* such that SOP(2, P(*k*)) is divisible
by 2*k*, i.e., SOP(2, P(*k*)) is congruent to 0 mod (2*k*).
Note that SOP(2, P(*k*)) = the sum of primes from 2 to the prime P(*k*). [Rivera]

Mersenne wrongly thought 2^67-1 was prime. 46 is the
smallest base *b* for which
(*b*^67-1)/(*b*-1) is actually prime.

(There are 5 curios for this number that have not yet been approved by an editor.)

Printed from the PrimePages <t5k.org> © G. L. Honaker and Chris K. Caldwell