
theorem
  9787 is prime
proof
  now
    9787 = 2*4893 + 1; hence not 2 divides 9787 by NAT_4:9;
    9787 = 3*3262 + 1; hence not 3 divides 9787 by NAT_4:9;
    9787 = 5*1957 + 2; hence not 5 divides 9787 by NAT_4:9;
    9787 = 7*1398 + 1; hence not 7 divides 9787 by NAT_4:9;
    9787 = 11*889 + 8; hence not 11 divides 9787 by NAT_4:9;
    9787 = 13*752 + 11; hence not 13 divides 9787 by NAT_4:9;
    9787 = 17*575 + 12; hence not 17 divides 9787 by NAT_4:9;
    9787 = 19*515 + 2; hence not 19 divides 9787 by NAT_4:9;
    9787 = 23*425 + 12; hence not 23 divides 9787 by NAT_4:9;
    9787 = 29*337 + 14; hence not 29 divides 9787 by NAT_4:9;
    9787 = 31*315 + 22; hence not 31 divides 9787 by NAT_4:9;
    9787 = 37*264 + 19; hence not 37 divides 9787 by NAT_4:9;
    9787 = 41*238 + 29; hence not 41 divides 9787 by NAT_4:9;
    9787 = 43*227 + 26; hence not 43 divides 9787 by NAT_4:9;
    9787 = 47*208 + 11; hence not 47 divides 9787 by NAT_4:9;
    9787 = 53*184 + 35; hence not 53 divides 9787 by NAT_4:9;
    9787 = 59*165 + 52; hence not 59 divides 9787 by NAT_4:9;
    9787 = 61*160 + 27; hence not 61 divides 9787 by NAT_4:9;
    9787 = 67*146 + 5; hence not 67 divides 9787 by NAT_4:9;
    9787 = 71*137 + 60; hence not 71 divides 9787 by NAT_4:9;
    9787 = 73*134 + 5; hence not 73 divides 9787 by NAT_4:9;
    9787 = 79*123 + 70; hence not 79 divides 9787 by NAT_4:9;
    9787 = 83*117 + 76; hence not 83 divides 9787 by NAT_4:9;
    9787 = 89*109 + 86; hence not 89 divides 9787 by NAT_4:9;
    9787 = 97*100 + 87; hence not 97 divides 9787 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9787 & n is prime
  holds not n divides 9787 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
