
theorem
  9511 is prime
proof
  now
    9511 = 2*4755 + 1; hence not 2 divides 9511 by NAT_4:9;
    9511 = 3*3170 + 1; hence not 3 divides 9511 by NAT_4:9;
    9511 = 5*1902 + 1; hence not 5 divides 9511 by NAT_4:9;
    9511 = 7*1358 + 5; hence not 7 divides 9511 by NAT_4:9;
    9511 = 11*864 + 7; hence not 11 divides 9511 by NAT_4:9;
    9511 = 13*731 + 8; hence not 13 divides 9511 by NAT_4:9;
    9511 = 17*559 + 8; hence not 17 divides 9511 by NAT_4:9;
    9511 = 19*500 + 11; hence not 19 divides 9511 by NAT_4:9;
    9511 = 23*413 + 12; hence not 23 divides 9511 by NAT_4:9;
    9511 = 29*327 + 28; hence not 29 divides 9511 by NAT_4:9;
    9511 = 31*306 + 25; hence not 31 divides 9511 by NAT_4:9;
    9511 = 37*257 + 2; hence not 37 divides 9511 by NAT_4:9;
    9511 = 41*231 + 40; hence not 41 divides 9511 by NAT_4:9;
    9511 = 43*221 + 8; hence not 43 divides 9511 by NAT_4:9;
    9511 = 47*202 + 17; hence not 47 divides 9511 by NAT_4:9;
    9511 = 53*179 + 24; hence not 53 divides 9511 by NAT_4:9;
    9511 = 59*161 + 12; hence not 59 divides 9511 by NAT_4:9;
    9511 = 61*155 + 56; hence not 61 divides 9511 by NAT_4:9;
    9511 = 67*141 + 64; hence not 67 divides 9511 by NAT_4:9;
    9511 = 71*133 + 68; hence not 71 divides 9511 by NAT_4:9;
    9511 = 73*130 + 21; hence not 73 divides 9511 by NAT_4:9;
    9511 = 79*120 + 31; hence not 79 divides 9511 by NAT_4:9;
    9511 = 83*114 + 49; hence not 83 divides 9511 by NAT_4:9;
    9511 = 89*106 + 77; hence not 89 divides 9511 by NAT_4:9;
    9511 = 97*98 + 5; hence not 97 divides 9511 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9511 & n is prime
  holds not n divides 9511 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
