38 MÉMOIRES. 
3. Soit : 
œ = 3.5.7.2x^,4 + 2.5.7.3^24 -(-2.3.7.5.1^34 + 2.3.5.7.1^^44 . 
;mod 2.3.5.7 
On a : î^,„=:1; donc i;i,4 = l 
2^2 (mod3) ^^22 =: 2 
5^2 (mod3) 2.5^1 (mod 3) 1^23=! 
7 = 1 mod 3 2.5.7=1 mod 3 j^ua — H 
2 = 2 mod 5 
3 = 3 mod 5 2.3 = 1 (mod 5) 1^^33 = 1 
7 = 2 mod 5 2.3.7 = 2 (mod 5) 1^^34 = 3 
2 = 2, 3 = 3, 5 = 5 mod 7, 30 = 2 mod 7, 1:^44 = 4 
a; = 3.5.7.2 + 2.5.7.3 + 2.3.7.5.3 + 2.3.5.7.4 
mod (2.3.5.7) 
ou: ^=105.2 + 70.3 + 126.5 + 120.7 (mod 210) 
15 18 24 ^ = 1,121,241 = 31,151,271 = 61,181 105 
7 __7 _^ 127, 247 = 37, 157, 277 = 67, 187, 307 = 97 70 
105 126 120 ^^^ = ^^' ^^^' ^^^ = ^^' ^^^' ^^^ = ^^^' ^^^ = ^^ 1^^ 
169, 289 = 79, 199, 319 = 109, 229 = 19, 139 120 
71, 191, 101, 221 = 11, 131, 251 = 41 431 
197, 107, 227 = 17, 137, 257 = 47, 167 
113, 233 = 23, 143, 263 = 53, 173, 83 
239 = 29, 149, 269 = 59, 179, 89, 209 
d'où les nouveaux nombres premiers : 
11, 13, 17, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 
73, 79, 83, 89, 97, 101, 103, 107, 109, 113. 
