One day my friend Ru He asked me a question.
What is the first 10-digit prime found in consecutive digits of e?
This is an easy problem with the help of Mathematica. The following is the Mathematica code I wrote to solve this question. It actually solves the general problem of first n-digit prime in consecutive digits of e.
(*
@param k: number of digits of the prime to be found in e*)
@param n: number of digits of e to be used
*)
PrimeInE[k_: 10, n_: 10000] := Module[{app, temp, i, flag},
app = N[E, n];
flag = 0;
For[i = 1, i <= n - k, i++,
temp = app*10^(k - 1);
temp = Floor[temp];
flag++;
If[PrimeQ[temp], Return[], app = (app - Floor[app]) 10]];
Print["Please choose a bigger value for argument \"n\" in order to find the first ", k, "-digit prime in e."]
]
PrimeInE[10]
7427466391
PrimeInE[30]
182845904523536028747135266249