
theorem
  9613 is prime
proof
  now
    9613 = 2*4806 + 1; hence not 2 divides 9613 by NAT_4:9;
    9613 = 3*3204 + 1; hence not 3 divides 9613 by NAT_4:9;
    9613 = 5*1922 + 3; hence not 5 divides 9613 by NAT_4:9;
    9613 = 7*1373 + 2; hence not 7 divides 9613 by NAT_4:9;
    9613 = 11*873 + 10; hence not 11 divides 9613 by NAT_4:9;
    9613 = 13*739 + 6; hence not 13 divides 9613 by NAT_4:9;
    9613 = 17*565 + 8; hence not 17 divides 9613 by NAT_4:9;
    9613 = 19*505 + 18; hence not 19 divides 9613 by NAT_4:9;
    9613 = 23*417 + 22; hence not 23 divides 9613 by NAT_4:9;
    9613 = 29*331 + 14; hence not 29 divides 9613 by NAT_4:9;
    9613 = 31*310 + 3; hence not 31 divides 9613 by NAT_4:9;
    9613 = 37*259 + 30; hence not 37 divides 9613 by NAT_4:9;
    9613 = 41*234 + 19; hence not 41 divides 9613 by NAT_4:9;
    9613 = 43*223 + 24; hence not 43 divides 9613 by NAT_4:9;
    9613 = 47*204 + 25; hence not 47 divides 9613 by NAT_4:9;
    9613 = 53*181 + 20; hence not 53 divides 9613 by NAT_4:9;
    9613 = 59*162 + 55; hence not 59 divides 9613 by NAT_4:9;
    9613 = 61*157 + 36; hence not 61 divides 9613 by NAT_4:9;
    9613 = 67*143 + 32; hence not 67 divides 9613 by NAT_4:9;
    9613 = 71*135 + 28; hence not 71 divides 9613 by NAT_4:9;
    9613 = 73*131 + 50; hence not 73 divides 9613 by NAT_4:9;
    9613 = 79*121 + 54; hence not 79 divides 9613 by NAT_4:9;
    9613 = 83*115 + 68; hence not 83 divides 9613 by NAT_4:9;
    9613 = 89*108 + 1; hence not 89 divides 9613 by NAT_4:9;
    9613 = 97*99 + 10; hence not 97 divides 9613 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9613 & n is prime
  holds not n divides 9613 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
