
theorem
  9551 is prime
proof
  now
    9551 = 2*4775 + 1; hence not 2 divides 9551 by NAT_4:9;
    9551 = 3*3183 + 2; hence not 3 divides 9551 by NAT_4:9;
    9551 = 5*1910 + 1; hence not 5 divides 9551 by NAT_4:9;
    9551 = 7*1364 + 3; hence not 7 divides 9551 by NAT_4:9;
    9551 = 11*868 + 3; hence not 11 divides 9551 by NAT_4:9;
    9551 = 13*734 + 9; hence not 13 divides 9551 by NAT_4:9;
    9551 = 17*561 + 14; hence not 17 divides 9551 by NAT_4:9;
    9551 = 19*502 + 13; hence not 19 divides 9551 by NAT_4:9;
    9551 = 23*415 + 6; hence not 23 divides 9551 by NAT_4:9;
    9551 = 29*329 + 10; hence not 29 divides 9551 by NAT_4:9;
    9551 = 31*308 + 3; hence not 31 divides 9551 by NAT_4:9;
    9551 = 37*258 + 5; hence not 37 divides 9551 by NAT_4:9;
    9551 = 41*232 + 39; hence not 41 divides 9551 by NAT_4:9;
    9551 = 43*222 + 5; hence not 43 divides 9551 by NAT_4:9;
    9551 = 47*203 + 10; hence not 47 divides 9551 by NAT_4:9;
    9551 = 53*180 + 11; hence not 53 divides 9551 by NAT_4:9;
    9551 = 59*161 + 52; hence not 59 divides 9551 by NAT_4:9;
    9551 = 61*156 + 35; hence not 61 divides 9551 by NAT_4:9;
    9551 = 67*142 + 37; hence not 67 divides 9551 by NAT_4:9;
    9551 = 71*134 + 37; hence not 71 divides 9551 by NAT_4:9;
    9551 = 73*130 + 61; hence not 73 divides 9551 by NAT_4:9;
    9551 = 79*120 + 71; hence not 79 divides 9551 by NAT_4:9;
    9551 = 83*115 + 6; hence not 83 divides 9551 by NAT_4:9;
    9551 = 89*107 + 28; hence not 89 divides 9551 by NAT_4:9;
    9551 = 97*98 + 45; hence not 97 divides 9551 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9551 & n is prime
  holds not n divides 9551 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
