SYMMETRIC MATRIX of FREQUENTIC PRIMES

frede SCHANDORF- 1 - søren MAGNE GUDIKSEN

“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.

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

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

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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 3 1 7 7 1 3 1 7

7 1 3 1 7 7 1 3 1 7 7 1 3 1 7 7 1 3 1 7 1 3 9 3 1 7 3 0 3 7 7 0 6 0 7 9 0 7 0 9 9 3 2 3 9 3 9 2 9 3 9 6 2 6 9 3 6 2 6 3 1 3 9 3 1 7 3 0 3 7 7 0 6 0 7 9 0 7 0 9 7 1 3 1 7 7 1 3 1 7 7 1 3 1 7 7 1 3 1 7

C o r n e r 7 1 3 1 7 7 1 3 1 7 7 1 3 1 7 f r a m e : 7 3 6 3 7 7 3 0 3 7 9 0 7 0 9 7 1 3 1 7 3 9 2 9 3 9 3 2 3 9 3 6 5 6 3 7 1 9 1 7 7 3 6 3 7 7 3 0 3 7 9 0 7 0 9 N u m b e r 7 1 3 1 7 7 1 3 1 7 7 1 3 1 7 o f p e r f e c t C o r n e r 7 1 3 1 7 7 1 3 1 7 s q u a r e s : f r a m e : 7 3 6 3 7 9 3 1 3 9 3 7 1 3 1 7 9 3 2 3 9 3 8 0 8 3 7 7 3 7 7 7 3 6 3 7 9 3 1 3 9 ------N u m b e r 7 1 3 1 7 7 1 3 1 7 o f p e r f e c t 7 1 3 1 7 7 1 3 1 7 s q u a r e s : 7 4 0 4 7 9 3 7 3 9 3 9 3 7 3 9 3 9 2 9 3 7 4 0 4 7 9 3 7 3 9 ------7 1 3 1 7 7 1 3 1 7

7 1 3 1 7 7 1 3 1 7 7 8 4 8 7 9 6 2 6 9 9 4 8 4 9 3 5 3 5 3 7 8 4 8 7 9 6 2 6 9 7 1 3 1 7 7 1 3 1 7

C o r n e r C o r n e r f r a m e : f r a m e : 7 1 3 1 7 7 1 3 1 7 7 7 9 7 7 7 9 3 9 7 N u m b e r N u m b e r o f o f p e r f e c t p e r f e c t s q u a r e s : s q u a r e s : 6 6

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7 1 3 1 7 7 1 9 1 7 7 1 9 1 7 7 1 9 1 7 9 0 7 0 9 7 0 6 0 7 7 0 6 0 7 9 0 7 0 9 9 3 2 3 9 3 6 2 6 3 9 3 2 3 9 3 3 5 3 3 9 0 7 0 9 7 0 6 0 7 7 0 6 0 7 9 0 7 0 9 7 1 3 1 7 7 1 9 1 7 7 1 9 1 7 7 1 9 1 7

7 1 3 1 7 7 1 9 1 7 7 1 9 1 7 7 1 9 1 7 9 0 7 0 9 7 3 6 3 7 7 3 6 3 7 9 0 7 0 9 9 6 2 6 9 3 9 2 9 3 9 3 2 3 9 3 6 5 6 3 9 0 7 0 9 7 3 6 3 7 7 3 6 3 7 9 0 7 0 9 7 1 3 1 7 7 1 9 1 7 7 1 9 1 7 7 1 9 1 7

7 1 3 1 7 7 1 9 1 7 7 1 9 1 7 7 1 9 1 7 9 3 7 3 9 7 8 4 8 7 7 4 0 4 7 9 3 1 3 9 9 3 2 3 9 3 4 8 4 3 9 3 7 3 9 3 8 0 8 3 9 3 7 3 9 7 8 4 8 7 7 4 0 4 7 9 3 1 3 9 7 1 3 1 7 7 1 9 1 7 7 1 9 1 7 7 1 9 1 7

7 1 3 1 7 7 1 9 1 7 7 1 9 1 7 9 4 0 4 9 7 1 9 1 7 7 8 7 8 7 9 6 4 6 9 9 3 7 3 9 7 8 7 8 7 9 4 8 4 9 3 5 3 5 3 9 4 0 4 9 3 4 8 4 3 7 8 7 8 7 9 6 4 6 9 7 1 3 1 7 7 8 7 8 7 7 1 9 1 7 7 1 9 1 7 7 1 9 1 7 7 1 3 1 7 C o r n e r 7 1 9 1 7 9 4 8 4 9 C o r n e r f r a m e : 9 6 7 6 9 9 3 7 3 9 f r a m e : 7 1 9 1 7 3 5 3 5 3 9 4 8 4 9 7 1 9 1 7 7 7 9 7 7 9 6 7 6 9 7 1 3 1 7 7 7 3 7 7 N u m b e r 7 1 9 1 7 N u m b e r o f 7 1 3 1 7 o f p e r f e c t C o r n e r 9 7 5 7 9 p e r f e c t s q u a r e s : f r a m e : 9 4 3 4 9 s q u a r e s : 4 7 1 9 1 7 9 7 5 7 9 4 7 9 3 9 7 7 1 3 1 7 ------N u m b e r ------o f C o r n e r p e r f e c t f r a m e : s q u a r e s : 7 1 3 1 7 5 7 9 9 9 7 N u m b e r ------o f p e r f e c t s q u a r e s : 6

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7 1 9 1 7 7 7 3 7 7 7 7 3 7 7 7 7 3 7 7 9 4 0 4 9 7 3 0 3 7 9 0 7 0 9 9 0 7 0 9 9 3 7 3 9 9 6 2 6 9 3 6 2 6 3 9 6 2 6 9 9 4 0 4 9 7 3 0 3 7 9 0 7 0 9 9 0 7 0 9 7 1 9 1 7 7 7 3 7 7 7 7 3 7 7 7 7 3 7 7

7 1 9 1 7 7 7 3 7 7 7 7 3 7 7 7 7 3 7 7 9 4 6 4 9 7 8 4 8 7 9 0 7 0 9 9 3 7 3 9 9 3 7 3 9 9 7 8 7 9 3 6 5 6 3 9 6 2 6 9 9 4 6 4 9 7 8 4 8 7 9 0 7 0 9 9 3 7 3 9 7 1 9 1 7 7 7 3 7 7 7 7 3 7 7 7 7 3 7 7

7 1 9 1 7 C o r n e r 7 7 3 7 7 7 7 3 7 7 9 7 5 7 9 f r a m e : 9 3 7 3 9 9 4 0 4 9 9 4 9 4 9 7 7 3 7 7 3 0 2 0 3 9 0 7 0 9 9 7 5 7 9 7 7 9 7 7 9 3 7 3 9 9 4 0 4 9 7 1 9 1 7 N u m b e r 7 7 3 7 7 7 7 3 7 7 o f 7 1 9 1 7 p e r f e c t 7 7 3 7 7 7 7 3 7 7 9 7 8 7 9 s q u a r e s : 9 3 7 3 9 9 4 8 4 9 9 4 3 4 9 2 3 6 2 6 3 9 0 7 0 9 9 7 8 7 9 9 3 7 3 9 9 4 8 4 9 7 1 9 1 7 ------7 7 3 7 7 7 7 3 7 7

C o r n e r 7 7 3 7 7 C o r n e r f r a m e : 9 4 8 4 9 f r a m e : 7 1 9 1 7 3 0 7 0 3 7 7 3 7 7 7 9 9 9 7 9 4 8 4 9 7 9 9 9 7 N u m b e r 7 7 3 7 7 N u m b e r o f o f p e r f e c t C o r n e r p e r f e c t s q u a r e s : f r a m e : s q u a r e s : 4 7 7 3 7 7 4 7 9 3 9 7 ------N u m b e r ------o f p e r f e c t s q u a r e s : 5

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7 7 9 7 7 7 7 9 7 7 7 9 3 9 7 N u m b e r 9 0 7 0 9 9 4 3 4 9 9 4 0 4 9 o f 3 6 5 6 3 9 0 7 0 9 9 3 7 3 9 p e r f e c t 9 0 7 0 9 9 4 3 4 9 9 4 0 4 9 s q u a r e s : 7 7 9 7 7 7 7 9 7 7 7 9 3 9 7 8

7 7 9 7 7 7 7 9 7 7 7 9 3 9 7 ------9 4 0 4 9 9 4 6 4 9 9 4 0 4 9 3 0 7 0 3 9 0 7 0 9 9 6 7 6 9 9 4 0 4 9 9 4 6 4 9 9 4 0 4 9 7 7 9 7 7 7 7 9 7 7 7 9 3 9 7

7 7 9 7 7 7 7 9 7 7 7 9 3 9 7 9 4 3 4 9 9 7 8 7 9 9 4 8 4 9 3 0 7 0 3 9 4 3 4 9 9 0 7 0 9 9 4 3 4 9 9 7 8 7 9 9 4 8 4 9 7 7 9 7 7 7 7 9 7 7 7 9 3 9 7

7 7 9 7 7 C o r n e r 7 9 3 9 7 9 4 6 4 9 f r a m e : 9 4 8 4 9 3 0 7 0 3 7 7 9 7 7 9 3 7 3 9 9 4 6 4 9 7 9 9 9 7 9 4 8 4 9 7 7 9 7 7 N u m b e r 7 9 3 9 7 o f 7 7 9 7 7 p e r f e c t 7 9 3 9 7 9 8 3 8 9 s q u a r e s : 9 4 8 4 9 3 8 7 8 3 3 9 6 7 6 9 9 8 3 8 9 9 4 8 4 9 7 7 9 7 7 ------7 9 3 9 7

7 7 9 7 7 7 9 3 9 7 9 8 6 8 9 9 6 2 6 9 3 8 7 8 3 9 4 3 4 9 9 8 6 8 9 9 6 2 6 9 7 7 9 7 7 7 9 3 9 7

C o r n e r 7 9 3 9 7 f r a m e : 9 6 2 6 9 7 7 9 7 7 9 7 3 7 9 7 9 3 9 7 9 6 2 6 9 N u m b e r 7 9 3 9 7 o f p e r f e c t 7 9 3 9 7 s q u a r e s : 9 7 5 7 9 6 9 8 3 8 9 9 7 5 7 9 ------7 9 3 9 7

C o r n e r f r a m e : 7 9 3 9 7 7 9 9 9 7

9 3 1 3 9 9 3 1 3 9 9 3 1 3 9 9 3 7 3 9 3 0 2 0 3 3 8 1 8 3 7 0 2 0 7 7 0 2 0 7 7 4 7 4 7 7 7 3 7 7 3 8 7 8 3 3 8 7 8 3 3 0 2 0 3 3 8 1 8 3 7 0 2 0 7 7 0 2 0 7 9 3 1 3 9 9 3 1 3 9 9 3 1 3 9 9 3 7 3 9

9 3 1 3 9 C o r n e r 9 3 1 3 9 9 3 7 3 9 3 0 2 0 3 f r a m e : 7 3 2 3 7 7 1 3 1 7 7 8 7 8 7 9 3 1 3 9 3 5 7 5 3 3 5 0 5 3 3 0 2 0 3 9 3 7 3 9 7 3 2 3 7 7 1 3 1 7 9 3 1 3 9 N u m b e r 9 3 1 3 9 9 3 7 3 9 o f 9 3 1 3 9 p e r f e c t 9 3 1 3 9 9 3 7 3 9 3 0 4 0 3 s q u a r e s : 7 4 0 4 7 7 4 7 4 7 7 2 7 2 7 1 0 3 5 3 5 3 3 5 3 5 3 3 0 4 0 3 7 4 0 4 7 7 4 7 4 7 9 3 1 3 9 ------9 3 1 3 9 9 3 7 3 9

9 3 1 3 9 C o r n e r C o r n e r 3 0 4 0 3 f r a m e : f r a m e : 7 8 7 8 7 9 3 1 3 9 9 3 7 3 9 3 0 4 0 3 9 7 3 7 9 9 7 3 7 9 9 3 1 3 9 N u m b e r N u m b e r o f o f 9 3 1 3 9 p e r f e c t p e r f e c t 3 5 3 5 3 s q u a r e s : s q u a r e s : 7 1 9 1 7 3 3 3 5 3 5 3 9 3 1 3 9 ------

9 3 1 3 9 3 5 3 5 3 7 7 9 7 7 3 5 3 5 3 9 3 1 3 9

9 3 1 3 9 3 5 7 5 3 7 1 9 1 7 3 5 7 5 3 9 3 1 3 9

9 3 1 3 9 3 8 0 8 3 7 1 3 1 7 3 8 0 8 3 9 3 1 3 9

This report was released by Chronomatics Institute Denmark on August 27, 2007.

This paper and all its contents © 2007, Søren Schandorf and Chronomatics Institute, DENMARK. All rights reserved. This work and all its content are, to the best knowledge of its author, original and solely of and by the author at the time of its creation. Permission is hereby granted for single copies to be made for personal, non-commercial use for students and teachers of schools, colleges, universities and other individuals sincerely interested in this subject provided that: either the entire paper, including figures and tables, is kept intact; or, any extracts of the text, or figures or tables (in part or whole), be properly and visibly cited as to authorship and source.