%I #16 Nov 29 2013 21:17:12

%S 113,613,5,24421,101,2042221,13,41,60731221,102975601,6653,253102501,

%T 327449641,17,14957,722798221,37,35597,797,233,2284271641,7937,337,73,

%U 29,53,46414646521,57358506301,2521,89,89249322541,61,281,56597

%N Unique encountered factors from ( (prime(n)*prime(n+1))^2 + 1 )/2.

%C Write down the prime factors of ( (prime(n)*prime(n+1))^2 + 1 )/2 for n >=2, omitting any that have been observed earlier.

%D C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory. Dover. New York: 1988.

%H Chris Nash, <a href="http://pages.prodigy.net/chris_nash/primeform.html">PrimeForm - Probable Prime and Classical Primality Testing for 32-bit Windows</a>. [?Broken link]

%H George F. Woltman, <a href="http://www.mersenne.org">GIMPS - The Great Internet Mersenne Prime Search</a>.

%e Primeform reports 2281 as the factor from ( (P(38321)*P(38322))2+1)/2; this is M17.

%t PrimeFactors[n_] := Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]; a = {}; Do[l = PrimeFactors[((Prime[n]*Prime[n + 1])^2 + 1)/2]; If[ Position[a, l[[1]]] == {}, AppendTo[a, l[[1]]]], {n, 2, 127}]; a

%o (Gnumeric) cell B2 =pfactor(((A1*A2)^2+1)/2) # supposes the prime list is in col A; Ai, Bi include the cell indices. The output may contain duplicates. - _Bill McEachen_, Dec 10 2010

%K nonn

%O 2,1

%A _Bill McEachen_, Aug 22 2003

%E Edited by _Robert G. Wilson v_, Sep 27 2003