9619 = (2 * 4809) + 1 ;
hence not 2 divides 9619 by NAT_4:9; :: thesis:
9619 = (3 * 3206) + 1 ;
hence not 3 divides 9619 by NAT_4:9; :: thesis:
9619 = (5 * 1923) + 4 ;
hence not 5 divides 9619 by NAT_4:9; :: thesis:
9619 = (7 * 1374) + 1 ;
hence not 7 divides 9619 by NAT_4:9; :: thesis:
9619 = (11 * 874) + 5 ;
hence not 11 divides 9619 by NAT_4:9; :: thesis:
9619 = (13 * 739) + 12 ;
hence not 13 divides 9619 by NAT_4:9; :: thesis:
9619 = (17 * 565) + 14 ;
hence not 17 divides 9619 by NAT_4:9; :: thesis:
9619 = (19 * 506) + 5 ;
hence not 19 divides 9619 by NAT_4:9; :: thesis:
9619 = (23 * 418) + 5 ;
hence not 23 divides 9619 by NAT_4:9; :: thesis:
9619 = (29 * 331) + 20 ;
hence not 29 divides 9619 by NAT_4:9; :: thesis:
9619 = (31 * 310) + 9 ;
hence not 31 divides 9619 by NAT_4:9; :: thesis:
9619 = (37 * 259) + 36 ;
hence not 37 divides 9619 by NAT_4:9; :: thesis:
9619 = (41 * 234) + 25 ;
hence not 41 divides 9619 by NAT_4:9; :: thesis:
9619 = (43 * 223) + 30 ;
hence not 43 divides 9619 by NAT_4:9; :: thesis:
9619 = (47 * 204) + 31 ;
hence not 47 divides 9619 by NAT_4:9; :: thesis:
9619 = (53 * 181) + 26 ;
hence not 53 divides 9619 by NAT_4:9; :: thesis:
9619 = (59 * 163) + 2 ;
hence not 59 divides 9619 by NAT_4:9; :: thesis:
9619 = (61 * 157) + 42 ;
hence not 61 divides 9619 by NAT_4:9; :: thesis:
9619 = (67 * 143) + 38 ;
hence not 67 divides 9619 by NAT_4:9; :: thesis:
9619 = (71 * 135) + 34 ;
hence not 71 divides 9619 by NAT_4:9; :: thesis:
9619 = (73 * 131) + 56 ;
hence not 73 divides 9619 by NAT_4:9; :: thesis:
9619 = (79 * 121) + 60 ;
hence not 79 divides 9619 by NAT_4:9; :: thesis:
9619 = (83 * 115) + 74 ;
hence not 83 divides 9619 by NAT_4:9; :: thesis:
9619 = (89 * 108) + 7 ;
hence not 89 divides 9619 by NAT_4:9; :: thesis:
9619 = (97 * 99) + 16 ;
hence not 97 divides 9619 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 9619 & n is prime holds
not n divides 9619 by XPRIMET1:50;
hence 9619 is prime by NAT_4:14; :: thesis: