2383 = (2 * 1191) + 1 ;
hence not 2 divides 2383 by NAT_4:9; :: thesis:
2383 = (3 * 794) + 1 ;
hence not 3 divides 2383 by NAT_4:9; :: thesis:
2383 = (5 * 476) + 3 ;
hence not 5 divides 2383 by NAT_4:9; :: thesis:
2383 = (7 * 340) + 3 ;
hence not 7 divides 2383 by NAT_4:9; :: thesis:
2383 = (11 * 216) + 7 ;
hence not 11 divides 2383 by NAT_4:9; :: thesis:
2383 = (13 * 183) + 4 ;
hence not 13 divides 2383 by NAT_4:9; :: thesis:
2383 = (17 * 140) + 3 ;
hence not 17 divides 2383 by NAT_4:9; :: thesis:
2383 = (19 * 125) + 8 ;
hence not 19 divides 2383 by NAT_4:9; :: thesis:
2383 = (23 * 103) + 14 ;
hence not 23 divides 2383 by NAT_4:9; :: thesis:
2383 = (29 * 82) + 5 ;
hence not 29 divides 2383 by NAT_4:9; :: thesis:
2383 = (31 * 76) + 27 ;
hence not 31 divides 2383 by NAT_4:9; :: thesis:
2383 = (37 * 64) + 15 ;
hence not 37 divides 2383 by NAT_4:9; :: thesis:
2383 = (41 * 58) + 5 ;
hence not 41 divides 2383 by NAT_4:9; :: thesis:
2383 = (43 * 55) + 18 ;
hence not 43 divides 2383 by NAT_4:9; :: thesis:
2383 = (47 * 50) + 33 ;
hence not 47 divides 2383 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 2383 & n is prime holds
not n divides 2383 by XPRIMET1:30;
hence 2383 is prime by NAT_4:14; :: thesis: