How many prime numbers n exist such that 90 < n < 106 and n is a factor of 99999919? Pick
A) Zero B) One C) Two D) Three E) More than three
There are 3 primes in the range: 97, 101 and 103.   99,999,919=10^8−81=(10^4+9)(10^4−9)   =(10^4+9)(10^2+3)(10^2−3)   =10,009∗10^3∗97   97 and 103 are factors of 99,999,919 but 101 is not a factor of 10,009. Thus 2 primes from the range are factors of 99,999,919.   Answer: Two.
<result>C</result>
How many prime numbers n exist such that 90 < n < 106 and n is a factor of 99999919?