primes

Prove that 10,007 is the smallest prime greater than 10,000.

Just trial and error:

10001 = 73 x 137
10002 = even
10003 = 7 x 1429
10004 = even
10005 = last digit is 5
10006 = even
10007 = prime (test by dividing through all primes up to 101)