52000
520002 = (12 + 4)(22 + 4)(32 + 4)(42 + 4)(142 + 4)(362 + 4)
= (12 + 4)(22 + 4)(42 + 4)(102 + 4)(112 + 4)(162 + 4) = (12 + 4)(22 + 4)(42 + 4)(162 + 4)(1142 + 4)
= (12 + 4)(22 + 4)(142 + 4)(162 + 4)(362 + 4) = (12 + 4)(32 + 4)(42 + 4)(62 + 4)(142 + 4)(162 + 4)
= (12 + 4)(42 + 4)(102 + 4)(142 + 4)(362 + 4) = (22 + 4)(32 + 4)(42 + 4)(62 + 4)(112 + 4)(162 + 4)
= (22 + 4)(42 + 4)(102 + 4)(112 + 4)(362 + 4) = (22 + 4)(42 + 4)(362 + 4)(1142 + 4)
= (32 + 4)(42 + 4)(62 + 4)(142 + 4)(362 + 4) = (42 + 4)(62 + 4)(102 + 4)(112 + 4)(162 + 4)
= (42 + 4)(62 + 4)(162 + 4)(1142 + 4) = (62 + 4)(142 + 4)(162 + 4)(362 + 4).
by Yoshio Mimura, Kobe, Japan
52002
520022 = (12 + 2)(22 + 2)(52 + 2)(312 + 2)(762 + 2) = (42 + 2)(52 + 2)(312 + 2)(762 + 2)
= (222 + 2)(312 + 2)(762 + 2).
by Yoshio Mimura, Kobe, Japan
52051
531302 + 520512 = 5532103501 is a mosaic.
Page of Squares : First Upload September 1, 2012 ; Last Revised September 1, 2012by Yoshio Mimura, Kobe, Japan
52056
520562= 3232 x 3233 + 3233 x 3234 + 3234 x 3235 + ... + 3472 x 3473.
Page of Squares : First Upload September 1, 2012 ; Last Revised September 1, 2012by Yoshio Mimura, Kobe, Japan
52063
520632 = 90472 + 90482 + 90492 + ... + 90792.
Page of Squares : First Upload September 1, 2012 ; Last Revised September 1, 2012by Yoshio Mimura, Kobe, Japan
52065
520652 = (62 + 9)(762 + 9)(1022 + 9).
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52081
The sum of consecutive primes 3 + 5 + 7 + 11 + ... + 52081 is a square (114422).
Page of Squares : First Upload September 1, 2012 ; Last Revised September 1, 2012by Yoshio Mimura, Kobe, Japan
52090
520902 = 18202 + 18212 + 18222 + ... + 24192.
Page of Squares : First Upload September 1, 2012 ; Last Revised September 1, 2012by Yoshio Mimura, Kobe, Japan
52094
520942 = 30892 + 30912 + 30932 + 30952 + ... + 35752.
Page of Squares : First Upload September 1, 2012 ; Last Revised September 1, 2012by Yoshio Mimura, Kobe, Japan
52096
520962 = (12 + 7)(22 + 7)(52 + 7)(172 + 7)(572 + 7) = (12 + 7)(32 + 7)(132 + 7)(172 + 7)(202 + 7)
= (12 + 7)(52 + 7)(92 + 7)(172 + 7)(202 + 7) = (12 + 7)(172 + 7)(202 + 7)(532 + 7)
= (112 + 7)(132 + 7)(172 + 7)(202 + 7) = (172 + 7)(532 + 7)(572 + 7)
= (22 + 7)(32 + 7)(112 + 7)(172 + 7)(202 + 7) = (32 + 7)(112 + 7)(202 + 7)(572 + 7)
= (32 + 7)(132 + 7)(172 + 7)(572 + 7) = (32 + 7)(172 + 7)(7572 + 7)
= (52 + 7)(92 + 7)(172 + 7)(572 + 7).
by Yoshio Mimura, Kobe, Japan
52130
521302 = (32 + 4)(402 + 4)(3612 + 4).
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52136
521362 = (12 + 3)(22 + 3)(42 + 3)(372 + 3)(612 + 3) = (22 + 3)(42 + 3)(52 + 3)(232 + 3)(372 + 3)
= (42 + 3)(52 + 3)(372 + 3)(612 + 3) = (232 + 3)(372 + 3)(612 + 3).
by Yoshio Mimura, Kobe, Japan
52144
521442± 3 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52164
521642 = (12 + 5)(22 + 5)(32 + 5)(72 + 5)(82 + 5)(312 + 5)
= (12 + 5)(22 + 5)(32 + 5)(112 + 5)(1692 + 5) = (12 + 5)(22 + 5)(32 + 5)(312 + 5)(612 + 5)
= (12 + 5)(32 + 5)(42 + 5)(72 + 5)(1692 + 5) = (12 + 5)(32 + 5)(82 + 5)(112 + 5)(612 + 5)
= (12 + 5)(72 + 5)(82 + 5)(112 + 5)(312 + 5) = (12 + 5)(72 + 5)(172 + 5)(1692 + 5)
= (12 + 5)(112 + 5)(312 + 5)(612 + 5) = (32 + 5)(72 + 5)(112 + 5)(1692 + 5)
= (32 + 5)(72 + 5)(312 + 5)(612 + 5).
by Yoshio Mimura, Kobe, Japan
52221
522212± 2 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52233
522332± 2 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52271
522712 = 26372 + 26392 + 26412 + 26432 + ... + 32612.
Page of Squares : First Upload September 1, 2012 ; Last Revised September 1, 2012by Yoshio Mimura, Kobe, Japan
52272
522722 = (12 + 8)(42 + 8)(52 + 8)(162 + 8)(382 + 8) = (12 + 8)(52 + 8)(62 + 8)(162 + 8)(282 + 8)
= (12 + 8)(162 + 8)(282 + 8)(382 + 8) = (22 + 8)(52 + 8)(62 + 8)(102 + 8)(382 + 8)
= (42 + 8)(52 + 8)(62 + 8)(162 + 8)(172 + 8) = (42 + 8)(52 + 8)(62 + 8)(2802 + 8)
= (42 + 8)(162 + 8)(172 + 8)(382 + 8) = (42 + 8)(382 + 8)(2802 + 8)
= (52 + 8)(82 + 8)(282 + 8)(382 + 8) = (62 + 8)(162 + 8)(172 + 8)(282 + 8)
= (62 + 8)(282 + 8)(2802 + 8).
by Yoshio Mimura, Kobe, Japan
52275
522752 = (462 + 9)(11342 + 9).
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52298
522982± 3 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52326
523262 = (12 + 2)(52 + 2)(62 + 2)(72 + 2)(102 + 2)(132 + 2)
= (12 + 2)(52 + 2)(102 + 2)(132 + 2)(442 + 2) = (12 + 2)(72 + 2)(102 + 2)(132 + 2)(322 + 2)
= (22 + 2)(213622 + 2) = (22 + 2)(52 + 2)(72 + 2)(132 + 2)(442 + 2)
= (22 + 2)(62 + 2)(132 + 2)(2652 + 2) = (52 + 2)(72 + 2)(322 + 2)(442 + 2)
= (52 + 2)(132 + 2)(242 + 2)(322 + 2) = (62 + 2)(322 + 2)(2652 + 2).
by Yoshio Mimura, Kobe, Japan
52332
523322 = (12 + 5)(32 + 5)(172 + 5)(3332 + 5).
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52362
523622± 5 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52382
523822± 3 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52416
524162 = (22 - 1)(72 - 1)(132 - 1)(3372 - 1) = (32 - 1)(72 - 1)(82 - 1)(3372 - 1)
= (32 - 1)(132 - 1)(272 - 1)(532 - 1) = (32 - 1)(552 - 1)(3372 - 1).
by Yoshio Mimura, Kobe, Japan
52428
524282± 5 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52448
524482 = (22 + 7)(692 + 7)(2292 + 7).
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52490
524902 = (12 + 1)(122 + 1)(192 + 1)(1622 + 1) = (172 + 1)(192 + 1)(1622 + 1).
Page of Squares : First Upload November 16, 2013 ; Last Revised November 16, 2013by Yoshio Mimura, Kobe, Japan
52500
525002 = (22 + 6)(82 + 6)(122 + 6)(1622 + 6).
A cubic polynomial:
(X + 1052)(X + 1402)(X + 2882) = X3 + 3372X2 + 525002X + 42336002.
by Yoshio Mimura, Kobe, Japan
52514
525142 = (12 + 6)(42 + 6)(52 + 6)(262 + 6)(292 + 6).
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52520
525202 = (12 + 4)(32 + 4)(62 + 4)(10302 + 4) = (32 + 4)(142 + 4)(10302 + 4).
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52521
525212± 2 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52538
525382± 3 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52548
525482± 5 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52560
525602 = (22 - 1)(32 - 1)(742 - 1)(1452 - 1) = (52 - 1)(742 - 1)(1452 - 1).
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52593
525932± 2 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52606
526062± 3 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52622
526222± 3 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52632
526322 = (12 + 8)(112 + 8)(322 + 8)(482 + 8).
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52650
526502 = (22 + 9)(32 + 9)(62 + 9)(92 + 9)(542 + 9) = (22 + 9)(32 + 9)(62 + 9)(212 + 9)(242 + 9)
= (32 + 9)(42 + 9)(62 + 9)(152 + 9)(242 + 9) = (32 + 9)(92 + 9)(242 + 9)(542 + 9)
= (62 + 9)(92 + 9)(152 + 9)(542 + 9) = (62 + 9)(152 + 9)(212 + 9)(242 + 9).
by Yoshio Mimura, Kobe, Japan
52660
526602± 3 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52668
526682 = (102 - 1)(202 - 1)(2652 - 1) = (22 - 1)(102 - 1)(202 - 1)(1532 - 1).
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52725
527252± 2 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52730
527302± 3 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52808
528082 = 2034 x 2035 + 2036 x 2037 + 2038 x 2039 + 2040 x 2041 + ... + 2928 x 2929.
Page of Squares : First Upload September 1, 2012 ; Last Revised September 1, 2012by Yoshio Mimura, Kobe, Japan
52824
528242± 5 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52842
528422± 5 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52856
528562± 3 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52866
528662± 5 are primes.
528662 = (12 + 2)(32 + 2)(52 + 2)(82 + 2)(2182 + 2) = (12 + 2)(1402 + 2)(2182 + 2)
= (22 + 2)(52 + 2)(192 + 2)(2182 + 2) = (32 + 2)(52 + 2)(142 + 2)(2182 + 2)
= (32 + 2)(82 + 2)(402 + 2)(492 + 2).
by Yoshio Mimura, Kobe, Japan
52920
529202 = (32 - 1)(62 - 1)(132 - 1)(2442 - 1).
2732 + 52920 = 3572, 2732 - 52920 = 1472.
Page of Squares : First Upload September 1, 2012 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52924
The quadratic polynomial 52924X2 - 279756X + 473841 takes the values 4972, 3552, 3332, 4492, 6312, 8372 at X = 1, 2,..., 6
529242± 3 are primes.
Page of Squares : First Upload September 1, 2012 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52953
529532± 2 are primes.
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52962
529622 = (22 + 3)(62 + 3)(192 + 3)(1682 + 3) = (22 + 3)(62 + 3)(262 + 3)(1232 + 3).
Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014by Yoshio Mimura, Kobe, Japan
52978
529782 = 2806668484 is a square with even digits.
Page of Squares : First Upload September 1, 2012 ; Last Revised September 1, 2012by Yoshio Mimura, Kobe, Japan
52992
523 + 52992 = 4402, 523 - 52992 = 2962.