Germain Primes:        Number of Germain primes; Comparison of spacings b/w Germain primes to Poissonian Behavior

 

 Inverse mod p:           Is x to 1/x mod p "random"; Comparison of length of longest increasing subsequence to Tracy-Widom

 

 Ramanujan Graphs:   Is the random three regular graph Ramanujan; Comparison of second largest eigenvalue to Tracy-Widom