
theorem
  9587 is prime
proof
  now
    9587 = 2*4793 + 1; hence not 2 divides 9587 by NAT_4:9;
    9587 = 3*3195 + 2; hence not 3 divides 9587 by NAT_4:9;
    9587 = 5*1917 + 2; hence not 5 divides 9587 by NAT_4:9;
    9587 = 7*1369 + 4; hence not 7 divides 9587 by NAT_4:9;
    9587 = 11*871 + 6; hence not 11 divides 9587 by NAT_4:9;
    9587 = 13*737 + 6; hence not 13 divides 9587 by NAT_4:9;
    9587 = 17*563 + 16; hence not 17 divides 9587 by NAT_4:9;
    9587 = 19*504 + 11; hence not 19 divides 9587 by NAT_4:9;
    9587 = 23*416 + 19; hence not 23 divides 9587 by NAT_4:9;
    9587 = 29*330 + 17; hence not 29 divides 9587 by NAT_4:9;
    9587 = 31*309 + 8; hence not 31 divides 9587 by NAT_4:9;
    9587 = 37*259 + 4; hence not 37 divides 9587 by NAT_4:9;
    9587 = 41*233 + 34; hence not 41 divides 9587 by NAT_4:9;
    9587 = 43*222 + 41; hence not 43 divides 9587 by NAT_4:9;
    9587 = 47*203 + 46; hence not 47 divides 9587 by NAT_4:9;
    9587 = 53*180 + 47; hence not 53 divides 9587 by NAT_4:9;
    9587 = 59*162 + 29; hence not 59 divides 9587 by NAT_4:9;
    9587 = 61*157 + 10; hence not 61 divides 9587 by NAT_4:9;
    9587 = 67*143 + 6; hence not 67 divides 9587 by NAT_4:9;
    9587 = 71*135 + 2; hence not 71 divides 9587 by NAT_4:9;
    9587 = 73*131 + 24; hence not 73 divides 9587 by NAT_4:9;
    9587 = 79*121 + 28; hence not 79 divides 9587 by NAT_4:9;
    9587 = 83*115 + 42; hence not 83 divides 9587 by NAT_4:9;
    9587 = 89*107 + 64; hence not 89 divides 9587 by NAT_4:9;
    9587 = 97*98 + 81; hence not 97 divides 9587 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9587 & n is prime
  holds not n divides 9587 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
