frede SCHANDORF- 1 - søren MAGNE GUDIKSEN SYMMETRIC MATRIX of FREQUENTIC PRIMES “Super Perfect Palindromic Prime Squares” Chronomatics© Chronomatics InstituteInstitute 2007 2007 - 2 - SYMMETRIC MATRIX of FREQUENTIC PRIMES ...is the title of the investigation into the phenomenon “super perfect palindromic prime squares” - SPPPS. In the following survey we have listed the complete collection of super perfect order-5 prime squares. They are listed according to their so called “corner number”. Within each corner number list the squares are ordered according to the different sets of “corner frames”. For a square to be “super perfect” it must contain 7 unique palindromic prime numbers. On the following page the principles and codex for SPPPS are explained. Enjoy your trip into the fascinating world of the SYMMETRIC MATRIX of FREQUENTIC PRIMES*. Best regards! Søren and Frede Schandorf and Magne Gudiksen Chronomatics Institute DENMARK August 2007 *) The deeper explanation of the title will be released later this year. © Chronomatics Institute 2007 - 3 - © Chronomatics Institute 2007 - 4 - Total number of 5th order palindromic primes: 93 Wing Wing Wing Wing no.: 1 no.: 3 no.: 7 no.: 9 10301 30103 70207 90709 10501 30203 70507 91019 10601 30403 70607 93139* 11311* 30703 71317* 93239 11411 30803 71917* 93739* 12421 31013 72227 94049 12721 31513 72727 94349 12821 32323 73037 94649 13331* 32423 73237 94849 13831 33533 73637 94949 13931* 34543 74047 95959 14341 34843 74747 96269 14741 35053 75557 96469 15451 35153 76367 96769 15551 35353 76667 97379* 16061 35753 77377* 97579 16361 36263 77477 97879 16561 36563 77977* 98389 16661 37273 78487 98689 17471 37573 78787 17971* 38083 78887 18181 38183 79397* 18481 38783 79697 19391* 39293 79997* 19891 19991* *) Frame numbers © Chronomatics Institute 2007 - 5 - © Chronomatics Institute 2007 - 6 - 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 3 0 1 0 3 3 5 7 5 3 3 2 4 2 3 7 3 2 3 7 3 3 5 3 3 3 4 5 4 3 9 4 8 4 9 9 8 3 8 9 3 0 1 0 3 3 5 7 5 3 3 2 4 2 3 7 3 2 3 7 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 3 0 1 0 3 3 6 2 6 3 3 2 4 2 3 7 4 0 4 7 3 6 5 6 3 3 5 3 5 3 9 7 8 7 9 9 3 7 3 9 3 0 1 0 3 3 6 2 6 3 3 2 4 2 3 7 4 0 4 7 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 C o r n e r 1 1 3 1 1 C o r n e r 3 0 2 0 3 f r a m e : 3 3 5 3 3 f r a m e : 3 5 3 5 3 1 1 3 1 1 9 8 3 8 9 1 1 3 1 1 3 0 2 0 3 1 3 3 3 1 3 3 5 3 3 1 7 9 7 1 1 1 3 1 1 N u m b e r 1 1 3 1 1 N u m b e r o f o f 1 1 3 1 1 p e r f e c t 1 1 3 1 1 p e r f e c t 3 0 4 0 3 s q u a r e s : 3 4 5 4 3 s q u a r e s : 3 3 5 3 3 1 1 9 3 7 3 9 2 3 0 4 0 3 3 4 5 4 3 1 1 3 1 1 ------- 1 1 3 1 1 ------- 1 1 3 1 1 1 1 3 1 1 3 0 4 0 3 3 4 5 4 3 3 6 5 6 3 9 7 3 7 9 3 0 4 0 3 3 4 5 4 3 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 3 0 7 0 3 3 4 8 4 3 3 3 5 3 3 9 3 7 3 9 3 0 7 0 3 3 4 8 4 3 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 3 0 7 0 3 3 9 2 9 3 3 6 5 6 3 9 8 3 8 9 3 0 7 0 3 3 9 2 9 3 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 C o r n e r 3 5 1 5 3 f r a m e : 3 4 5 4 3 1 1 3 1 1 3 5 1 5 3 1 3 9 3 1 1 1 3 1 1 N u m b e r o f 1 1 3 1 1 p e r f e c t 3 5 3 5 3 s q u a r e s : 3 4 5 4 3 7 3 5 3 5 3 1 1 3 1 1 ------- © Chronomatics Institute 2007 - 7 - 1 1 3 1 1 1 1 3 1 1 1 3 3 3 1 N u m b e r 9 0 7 0 9 9 3 2 3 9 3 0 1 0 3 o f 3 3 5 3 3 9 8 3 8 9 9 7 5 7 9 p e r f e c t 9 0 7 0 9 9 3 2 3 9 3 0 1 0 3 s q u a r e s : 1 1 3 1 1 1 1 3 1 1 1 3 3 3 1 8 1 1 3 1 1 1 1 3 1 1 1 3 3 3 1 ------- 9 0 7 0 9 9 4 0 4 9 3 0 2 0 3 3 6 5 6 3 9 3 7 3 9 9 4 3 4 9 9 0 7 0 9 9 4 0 4 9 3 0 2 0 3 1 1 3 1 1 1 1 3 1 1 1 3 3 3 1 1 1 3 1 1 1 1 3 1 1 1 3 3 3 1 9 6 2 6 9 9 4 8 4 9 3 0 2 0 3 3 5 3 5 3 9 3 7 3 9 9 7 3 7 9 9 6 2 6 9 9 4 8 4 9 3 0 2 0 3 1 1 3 1 1 1 1 3 1 1 1 3 3 3 1 1 1 3 1 1 C o r n e r 1 3 3 3 1 9 6 4 6 9 f r a m e : 3 0 2 0 3 3 3 5 3 3 1 1 3 1 1 9 8 3 8 9 9 6 4 6 9 1 9 9 9 1 3 0 2 0 3 1 1 3 1 1 N u m b e r 1 3 3 3 1 o f 1 1 3 1 1 p e r f e c t 1 3 3 3 1 9 6 4 6 9 s q u a r e s : 3 0 4 0 3 3 6 5 6 3 3 9 7 5 7 9 9 6 4 6 9 3 0 4 0 3 1 1 3 1 1 ------- 1 3 3 3 1 1 1 3 1 1 1 3 3 3 1 9 6 7 6 9 3 4 5 4 3 3 3 5 3 3 9 8 3 8 9 9 6 7 6 9 3 4 5 4 3 1 1 3 1 1 1 3 3 3 1 1 1 3 1 1 1 3 3 3 1 9 6 7 6 9 3 5 1 5 3 3 6 5 6 3 9 7 5 7 9 9 6 7 6 9 3 5 1 5 3 1 1 3 1 1 1 3 3 3 1 C o r n e r 1 3 3 3 1 f r a m e : 3 5 3 5 3 1 1 3 1 1 9 7 5 7 9 1 9 3 9 1 3 5 3 5 3 N u m b e r 1 3 3 3 1 o f p e r f e c t C o r n e r s q u a r e s : f r a m e : 7 1 3 3 3 1 1 3 9 3 1 ------- © Chronomatics Institute 2007 - 8 - 1 3 3 3 1 1 3 3 3 1 1 3 3 3 1 1 3 9 3 1 7 0 2 0 7 9 0 7 0 9 9 0 7 0 9 7 2 7 2 7 9 4 3 4 9 3 1 5 1 3 9 7 5 7 9 9 4 8 4 9 7 0 2 0 7 9 0 7 0 9 9 0 7 0 9 7 2 7 2 7 1 3 3 3 1 1 3 3 3 1 1 3 3 3 1 1 3 9 3 1 1 3 3 3 1 1 3 3 3 1 C o r n e r 1 3 9 3 1 7 0 2 0 7 9 0 7 0 9 f r a m e : 7 4 7 4 7 9 7 3 7 9 3 4 5 4 3 1 3 3 3 1 9 8 3 8 9 7 0 2 0 7 9 0 7 0 9 1 9 9 9 1 7 4 7 4 7 1 3 3 3 1 1 3 3 3 1 N u m b e r 1 3 9 3 1 o f 1 3 3 3 1 1 3 3 3 1 p e r f e c t C o r n e r 7 0 2 0 7 9 4 0 4 9 s q u a r e s : f r a m e : 9 8 3 8 9 3 5 7 5 3 1 1 3 9 3 1 7 0 2 0 7 9 4 0 4 9 1 7 9 7 1 1 3 3 3 1 1 3 3 3 1 ------- N u m b e r o f 1 3 3 3 1 1 3 3 3 1 p e r f e c t 7 0 5 0 7 9 4 0 4 9 s q u a r e s : 9 4 3 4 9 3 8 7 8 3 2 7 0 5 0 7 9 4 0 4 9 1 3 3 3 1 1 3 3 3 1 ------- 1 3 3 3 1 7 0 5 0 7 1 3 3 3 1 9 7 3 7 9 9 4 8 4 9 7 0 5 0 7 3 5 7 5 3 1 3 3 3 1 9 4 8 4 9 1 3 3 3 1 1 3 3 3 1 7 0 5 0 7 1 3 3 3 1 9 8 3 8 9 9 6 2 6 9 7 0 5 0 7 3 5 3 5 3 1 3 3 3 1 9 6 2 6 9 1 3 3 3 1 1 3 3 3 1 7 0 6 0 7 C o r n e r 9 7 5 7 9 f r a m e : 7 0 6 0 7 1 3 3 3 1 1 3 3 3 1 1 9 3 9 1 N u m b e r C o r n e r o f f r a m e : p e r f e c t 1 3 3 3 1 s q u a r e s : 1 7 9 7 1 6 N u m b e r o f ------- p e r f e c t s q u a r e s : 7 ------- © Chronomatics Institute 2007 - 9 - 1 3 9 3 1 1 3 9 3 1 1 3 9 3 1 1 3 9 3 1 9 0 7 0 9 9 4 6 4 9 9 8 6 8 9 9 0 7 0 9 3 1 5 1 3 3 5 7 5 3 3 0 4 0 3 9 4 3 4 9 9 0 7 0 9 9 4 6 4 9 9 8 6 8 9 9 0 7 0 9 1 3 9 3 1 1 3 9 3 1 1 3 9 3 1 1 3 9 3 1 1 3 9 3 1 1 3 9 3 1 C o r n e r 1 3 9 3 1 9 0 7 0 9 9 4 6 4 9 f r a m e : 9 0 7 0 9 3 2 3 2 3 3 8 7 8 3 1 3 9 3 1 9 8 3 8 9 9 0 7 0 9 9 4 6 4 9 1 9 3 9 1 9 0 7 0 9 1 3 9 3 1 1 3 9 3 1 N u m b e r 1 3 9 3 1 o f 1 3 9 3 1 1 3 9 3 1 p e r f e c t C o r n e r 9 0 7 0 9 9 4 8 4 9 s q u a r e s : f r a m e : 3 4 5 4 3 3 5 3 5 3 1 9 1 3 9 3 1 9 0 7 0 9 9 4 8 4 9 1 9 9 9 1 1 3 9 3 1 1 3 9 3 1 ------- N u m b e r o f 1 3 9 3 1 1 3 9 3 1 p e r f e c t 9 0 7 0 9 9 6 4 6 9 s q u a r e s : 3 7 5 7 3 3 2 3 2 3 2 9 0 7 0 9 9 6 4 6 9 1 3 9 3 1 1 3 9 3 1 ------- 1 3 9 3 1 1 3 9 3 1 9 3 7 3 9 9 6 4 6 9 3 5 3 5 3 3 5 0 5 3 9 3 7 3 9 9 6 4 6 9 1 3 9 3 1 1 3 9 3 1 1 3 9 3 1 1 3 9 3 1 9 4 0 4 9 9 6 4 6 9 3 5 7 5 3 3 5 3 5 3 9 4 0 4 9 9 6 4 6 9 1 3 9 3 1 1 3 9 3 1 1 3 9 3 1 1 3 9 3 1 9 4 0 4 9 9 6 7 6 9 3 8 7 8 3 3 2 3 2 3 9 4 0 4 9 9 6 7 6 9 1 3 9 3 1 1 3 9 3 1 1 3 9 3 1 1 3 9 3 1 9 4 3 4 9 9 6 7 6 9 3 5 7 5 3 3 5 3 5 3 9 4 3 4 9 9 6 7 6 9 1 3 9 3 1 1 3 9 3 1 1 3 9 3 1 1 3 9 3 1 9 4 3 4 9 9 8 3 8 9 3 8 7 8 3 3 0 1 0 3 9 4 3 4 9 9 8 3 8 9 1 3 9 3 1 1 3 9 3 1 © Chronomatics Institute 2007 - 10 - 1 7 9 7 1 1 7 9 7 1 1 7 9 7 1 1 9 3 9 1 9 0 7 0 9 9 6 7 6 9 9 4 3 4 9 9 3 2 3 9 3 2 3 2 3 3 6 5 6 3 9 0 7 0 9 9 7 3 7 9 9 0 7 0 9 9 6 7 6 9 9 4 3 4 9 9 3 2 3 9 1 7 9 7 1 1 7 9 7 1 1 7 9 7 1 1 9 3 9 1 1 7 9 7 1 1 7 9 7 1 1 7 9 7 1 1 9 3 9 1 9 0 7 0 9 9 8 3 8 9 9 4 6 4 9 9 4 0 4 9 3 5 3 5 3 3 8 1 8 3 9 0 7 0 9 9 3 7 3 9 9 0 7 0 9 9 8 3 8 9 9 4 6 4 9 9 4 0 4 9 1 7 9 7 1 1 7 9 7 1 1 7 9 7 1 1 9 3 9 1 1 7 9 7 1 C o r n e r 1 7 9 7 1 1 9 3 9 1 9 0 7 0 9 f r a m e : 9 4 8 4 9 9 4 0 4 9 3 6 5 6 3 1 7 9 7 1 9 7 3 7 9 9 6 7 6 9 9 0 7 0 9 1 9 3 9 1 9 4 8 4 9 9 4 0 4 9 1 7 9 7 1 N u m b e r 1 7 9 7 1 1 9 3 9 1 o f 1 7 9 7 1 p e r f e c t C o r n e r 1 9 3 9 1 9 3 7 3 9 s q u a r e s : f r a m e : 9 4 8 4 9 3 0 8 0 3 1 1 1 7 9 7 1 9 0 7 0 9 9 3 7 3 9 1 9 9 9 1 9 4 8 4 9 1 7 9 7 1 ------- N u m b e r 1 9 3 9 1 o f 1 7 9 7 1 p e r f e c t 1 9 3 9 1 9 3 7 3 9 s q u a r e s : 9 4 8 4 9 3 2 3 2 3 3 9 3 7 3 9 9 3 7 3 9 9 4 8 4 9 1 7 9 7 1 ------- 1 9 3 9 1 1 7 9 7 1 1 9 3 9 1 9 4 0 4 9 9 4 8 4 9 3 0 7 0 3 9 6 7 6 9 9 4 0 4 9 9 4 8 4 9 1 7 9 7 1 1 9 3 9 1 1 7 9 7 1 1 9 3 9 1 9 4 3 4 9 9 6 2 6 9 3 0 7 0 3 9 4 3 4 9 9 4 3 4 9 9 6 2 6 9 1 7 9 7 1 1 9 3 9 1 1 7 9 7 1 1 9 3 9 1 9 4 6 4 9 9 6 2 6 9 3 0 7 0 3 9 7 3 7 9 9 4 6 4 9 9 6 2 6 9 1 7 9 7 1 1 9 3 9 1 1 7 9 7 1 9 6 7 6 9 3 3 5 3 3 9 6 7 6 9 1 7 9 7 1 © Chronomatics Institute 2007 - 11 - 1 9 3 9 1 9 6 4 6 9 9 7 5 7 9 9 6 4 6 9 1 9 3 9 1 C o r n e r f r a m e : 1 9 3 9 1 1 9 9 9 1 N u m b e r o f p e r f e c t s q u a r e s : 9 ------- © Chronomatics Institute 2007 - 12 - © Chronomatics Institute 2007 - 13 - 7 1 3 1 7 7 1 3 1 7 7 1 3 1 7 7 1 3 1 7 1 0 6 0 1 7 0 6 0 7 7 0 6 0 7 9 0 7 0 9 9 3 2 3 9 3 3 5 3 3 9 3 2 3 9 3 3 5 3 3 1 0 6 0 1 7 0 6 0 7 7 0 6 0 7 9 0 7 0 9 7 1 3 1 7 7 1 3 1 7 7 1.