9277 = (2 * 4638) + 1 ;
hence not 2 divides 9277 by NAT_4:9; :: thesis:
9277 = (3 * 3092) + 1 ;
hence not 3 divides 9277 by NAT_4:9; :: thesis:
9277 = (5 * 1855) + 2 ;
hence not 5 divides 9277 by NAT_4:9; :: thesis:
9277 = (7 * 1325) + 2 ;
hence not 7 divides 9277 by NAT_4:9; :: thesis:
9277 = (11 * 843) + 4 ;
hence not 11 divides 9277 by NAT_4:9; :: thesis:
9277 = (13 * 713) + 8 ;
hence not 13 divides 9277 by NAT_4:9; :: thesis:
9277 = (17 * 545) + 12 ;
hence not 17 divides 9277 by NAT_4:9; :: thesis:
9277 = (19 * 488) + 5 ;
hence not 19 divides 9277 by NAT_4:9; :: thesis:
9277 = (23 * 403) + 8 ;
hence not 23 divides 9277 by NAT_4:9; :: thesis:
9277 = (29 * 319) + 26 ;
hence not 29 divides 9277 by NAT_4:9; :: thesis:
9277 = (31 * 299) + 8 ;
hence not 31 divides 9277 by NAT_4:9; :: thesis:
9277 = (37 * 250) + 27 ;
hence not 37 divides 9277 by NAT_4:9; :: thesis:
9277 = (41 * 226) + 11 ;
hence not 41 divides 9277 by NAT_4:9; :: thesis:
9277 = (43 * 215) + 32 ;
hence not 43 divides 9277 by NAT_4:9; :: thesis:
9277 = (47 * 197) + 18 ;
hence not 47 divides 9277 by NAT_4:9; :: thesis:
9277 = (53 * 175) + 2 ;
hence not 53 divides 9277 by NAT_4:9; :: thesis:
9277 = (59 * 157) + 14 ;
hence not 59 divides 9277 by NAT_4:9; :: thesis:
9277 = (61 * 152) + 5 ;
hence not 61 divides 9277 by NAT_4:9; :: thesis:
9277 = (67 * 138) + 31 ;
hence not 67 divides 9277 by NAT_4:9; :: thesis:
9277 = (71 * 130) + 47 ;
hence not 71 divides 9277 by NAT_4:9; :: thesis:
9277 = (73 * 127) + 6 ;
hence not 73 divides 9277 by NAT_4:9; :: thesis:
9277 = (79 * 117) + 34 ;
hence not 79 divides 9277 by NAT_4:9; :: thesis:
9277 = (83 * 111) + 64 ;
hence not 83 divides 9277 by NAT_4:9; :: thesis:
9277 = (89 * 104) + 21 ;
hence not 89 divides 9277 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9277 & n is prime holds
not n divides 9277 by XPRIMET1:48;
hence 9277 is prime by NAT_4:14; :: thesis: