
theorem
  9601 is prime
proof
  now
    9601 = 2*4800 + 1; hence not 2 divides 9601 by NAT_4:9;
    9601 = 3*3200 + 1; hence not 3 divides 9601 by NAT_4:9;
    9601 = 5*1920 + 1; hence not 5 divides 9601 by NAT_4:9;
    9601 = 7*1371 + 4; hence not 7 divides 9601 by NAT_4:9;
    9601 = 11*872 + 9; hence not 11 divides 9601 by NAT_4:9;
    9601 = 13*738 + 7; hence not 13 divides 9601 by NAT_4:9;
    9601 = 17*564 + 13; hence not 17 divides 9601 by NAT_4:9;
    9601 = 19*505 + 6; hence not 19 divides 9601 by NAT_4:9;
    9601 = 23*417 + 10; hence not 23 divides 9601 by NAT_4:9;
    9601 = 29*331 + 2; hence not 29 divides 9601 by NAT_4:9;
    9601 = 31*309 + 22; hence not 31 divides 9601 by NAT_4:9;
    9601 = 37*259 + 18; hence not 37 divides 9601 by NAT_4:9;
    9601 = 41*234 + 7; hence not 41 divides 9601 by NAT_4:9;
    9601 = 43*223 + 12; hence not 43 divides 9601 by NAT_4:9;
    9601 = 47*204 + 13; hence not 47 divides 9601 by NAT_4:9;
    9601 = 53*181 + 8; hence not 53 divides 9601 by NAT_4:9;
    9601 = 59*162 + 43; hence not 59 divides 9601 by NAT_4:9;
    9601 = 61*157 + 24; hence not 61 divides 9601 by NAT_4:9;
    9601 = 67*143 + 20; hence not 67 divides 9601 by NAT_4:9;
    9601 = 71*135 + 16; hence not 71 divides 9601 by NAT_4:9;
    9601 = 73*131 + 38; hence not 73 divides 9601 by NAT_4:9;
    9601 = 79*121 + 42; hence not 79 divides 9601 by NAT_4:9;
    9601 = 83*115 + 56; hence not 83 divides 9601 by NAT_4:9;
    9601 = 89*107 + 78; hence not 89 divides 9601 by NAT_4:9;
    9601 = 97*98 + 95; hence not 97 divides 9601 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9601 & n is prime
  holds not n divides 9601 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
