Wroblewski's method described here: http://www.math.uni.wroc.pl/~jwr/AP26/AP26v2.pdf Christian. -----Message d'origine----- De : math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] De la part de Christian Boyer Envoyé : lundi 19 mai 2008 18:46 À : 'math-fun' Objet : [math-fun] First known AP25 New longest known arithmetic progression of primes! Here is the first known AP25, found 2 days ago: 6171054912832631 + 366384*23#*n, for n=0 to 24 (Raanan Chermoni & Jaroslaw Wroblewski, May 17 2008) With such an AP, we can directly get a 5x5 pandiagonal magic square of primes. Pandiagonal means that the broken diagonals are also magic, here 20 different lines having the same sum 35759534049087955: 6171054912832631 6743218519407191 7315382125981751 7478857442145911 8051021048720471 7070169151735511 7642332758310071 7805808074474231 6334530228996791 6906693835571351 7969283390638391 6498005545160951 6661480861325111 7233644467899671 7397119784063831 6824956177489271 6988431493653431 7560595100227991 8132758706802551 6252792570914711 7724070416392151 7887545732556311 6416267887078871 6579743203243031 7151906809817591 6171054912832631 6171054912832631 6171054912832631 6171054912832631 6171054912832631 This square should have the biggest magic sum of any known magic square of primes, for ANY order >= 5. On the orders 3 and 4, we can construct magic squares of primes having bigger magic sums, using the Oakes's AP9 and Anderson-Lee's AP16 http://en.wikipedia.org/wiki/Primes_in_arithmetic_progression Christian. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun