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<DIV><FONT face=Arial size=2>Dear SeqFan,</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Let a(n) = n!.2^n +1</FONT></DIV>
<DIV><FONT face=Arial size=2>a(n) is prime for n=1 and n=259 but there are no
other prime for n<3000</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>Can any one extend this sequence ?</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I think that there are no other prime,
</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>If A(n,b)=((n-1)!.b^(n-1) + 1)/n and n,b are
distinct prime </FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I think that the number of prime A(n,b) is
finite</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>A(n,2) is prime for n=3,37,61,??</FONT></DIV>
<DIV><FONT face=Arial size=2>A(n,3) is prime for n=2,5,??</FONT></DIV>
<DIV><FONT face=Arial size=2>A(n,5) is prime for n=2,3,7,13,19,??</FONT></DIV>
<DIV><FONT face=Arial size=2>A(n,7) is prime for n=11,17,??</FONT></DIV>
<DIV><FONT face=Arial size=2>A(n,11) is prime for n= (no prime n <800)
??</FONT></DIV>
<DIV><FONT face=Arial size=2>A(n,13) is prime for n=2,3,??</FONT></DIV>
<DIV><FONT face=Arial size=2>A(n,17) is prime for n=3,7,13,??</FONT></DIV>
<DIV><FONT face=Arial size=2>A(n,19) is prime for n=3,7,281, ??</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2> I remark that if p is prime then p divide
a(p-1)</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>we can prove this by wilson's theorem and Fermat's
Little Theorem</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>if p is prime and gcd(q,p)=1 then p divide
(p-1)!.q^(p-1) + 1</FONT></DIV>
<DIV><FONT face=Arial size=2>can any one help me if this theorem exist
?</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>if q=1 we have wilson's theorem</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Thanks</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>M.Bouayoun</FONT></DIV>
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