If you were to call a mathematician friend of mine, who lives in Raleigh, NC, he might tell you that 919 is one of those rare primes in which the sum of the digits is equal to the count of the letters in its description.

How do you find out stuff like that (the 919 thing)?

937

953

The 21 consecutive primes from 7 to 89 sum to the prime number 953.

971

31 squared PLUS
3 squared PLUS
1 squared

983

It's the largest member of the set {983, 823, 569}, which is the largest triple of three-digit primes that can be concatenated in any order that will always result in a 9-digit prime.

991

where are you getting this information?

997

= 10^3-3. The first instance where 10^n-n is prime.

I come up with stuff myself or find it in the internet. I've got a great one for 1289, should we ever get that far...

1013

2^1013 + 3^1013 + 5^1013 + 7^1013 is prime. (2,3,5,7 being the first 4 primes).