
theorem
  3863 is prime
proof
  now
    3863 = 2*1931 + 1; hence not 2 divides 3863 by NAT_4:9;
    3863 = 3*1287 + 2; hence not 3 divides 3863 by NAT_4:9;
    3863 = 5*772 + 3; hence not 5 divides 3863 by NAT_4:9;
    3863 = 7*551 + 6; hence not 7 divides 3863 by NAT_4:9;
    3863 = 11*351 + 2; hence not 11 divides 3863 by NAT_4:9;
    3863 = 13*297 + 2; hence not 13 divides 3863 by NAT_4:9;
    3863 = 17*227 + 4; hence not 17 divides 3863 by NAT_4:9;
    3863 = 19*203 + 6; hence not 19 divides 3863 by NAT_4:9;
    3863 = 23*167 + 22; hence not 23 divides 3863 by NAT_4:9;
    3863 = 29*133 + 6; hence not 29 divides 3863 by NAT_4:9;
    3863 = 31*124 + 19; hence not 31 divides 3863 by NAT_4:9;
    3863 = 37*104 + 15; hence not 37 divides 3863 by NAT_4:9;
    3863 = 41*94 + 9; hence not 41 divides 3863 by NAT_4:9;
    3863 = 43*89 + 36; hence not 43 divides 3863 by NAT_4:9;
    3863 = 47*82 + 9; hence not 47 divides 3863 by NAT_4:9;
    3863 = 53*72 + 47; hence not 53 divides 3863 by NAT_4:9;
    3863 = 59*65 + 28; hence not 59 divides 3863 by NAT_4:9;
    3863 = 61*63 + 20; hence not 61 divides 3863 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3863 & n is prime
  holds not n divides 3863 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
