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69000 - 69999

69003

690032 = (12 + 2)(72 + 2)(112 + 2)(5032 + 2) = (32 + 2)(72 + 2)(412 + 2)(712 + 2).

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69042

690422± 5 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69048

690482± 5 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69056

690562± 3 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69120

3122 + 69120 = 4082, 3122 - 69120 = 1682.

691202 = (22 - 1)(32 - 1)(42 - 1)(72 - 1)(172 - 1)(312 - 1)
= (22 - 1)(32 - 1)(52 - 1)(92 - 1)(172 - 1)(192 - 1) = (22 - 1)(72 - 1)(112 - 1)(172 - 1)(312 - 1)
= (32 - 1)(42 - 1)(52 - 1)(72 - 1)(112 - 1)(172 - 1) = (32 - 1)(52 - 1)(312 - 1)(1612 - 1)
= (32 - 1)(72 - 1)(112 - 1)(172 - 1)(192 - 1) = (32 - 1)(92 - 1)(172 - 1)(1612 - 1)
= (42 - 1)(52 - 1)(72 - 1)(172 - 1)(312 - 1) = (72 - 1)(172 - 1)(192 - 1)(312 - 1).

Page of Squares : First Upload October 27, 2012 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69121

691212 = 1204 + 1364 + 2554, the 5th primitive sum of three 4-th powers.

Page of Squares : First Upload October 27, 2012 ; Last Revised October 27, 2012
by Yoshio Mimura, Kobe, Japan

69136

691362 = (152 + 7)(45392 + 7).

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69141

691412± 2 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69160

691602± 3 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69169

69169 = 2632, a square with 3 kinds of digits.

Page of Squares : First Upload October 27, 2012 ; Last Revised October 27, 2012
by Yoshio Mimura, Kobe, Japan

69174

691742 = (22 + 5)(42 + 5)(192 + 5)(2632 + 5) = (22 + 5)(72 + 5)(192 + 5)(1642 + 5).

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69200

692002 = (12 + 4)(22 + 4)(42 + 4)(132 + 4)(1862 + 4) = (42 + 4)(62 + 4)(132 + 4)(1862 + 4).

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69264

692642 = (252 - 1)(382 - 1)(732 - 1).

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69290

692902 = (92 + 1)(322 + 1)(2392 + 1).

Page of Squares : First Upload November 16, 2013 ; Last Revised November 16, 2013
by Yoshio Mimura, Kobe, Japan

69300

693002 = (12 + 6)(32 + 6)(42 + 6)(62 + 6)(122 + 6)(182 + 6)
= (22 + 6)(32 + 6)(42 + 6)(62 + 6)(122 + 6)(152 + 6) = (22 + 6)(32 + 6)(62 + 6)(182 + 6)(482 + 6)
= (22 + 6)(62 + 6)(122 + 6)(152 + 6)(182 + 6) = (32 + 6)(42 + 6)(62 + 6)(122 + 6)(482 + 6)
= (62 + 6)(122 + 6)(182 + 6)(482 + 6) = (22 - 1)(42 - 1)(62 - 1)(232 - 1)(762 - 1)
= (22 - 1)(62 - 1)(92 - 1)(102 - 1)(762 - 1) = (22 - 1)(62 - 1)(342 - 1)(1992 - 1)
= (22 - 1)(62 - 1)(762 - 1)(892 - 1) = (42 - 1)(62 - 1)(92 - 1)(102 - 1)(342 - 1)
= (42 - 1)(62 - 1)(342 - 1)(892 - 1) = (42 - 1)(72 - 1)(342 - 1)(762 - 1).

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69306

693062± 5 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69344

693442 = (22 + 7)(32 + 7)(52272 + 7) = (132 + 7)(52272 + 7).

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69360

174 + 69360 = 3912, 174 - 69360 = 1192.

Page of Squares : First Upload October 27, 2012 ; Last Revised October 27, 2012
by Yoshio Mimura, Kobe, Japan

69376

693762± 3 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69393

693932± 2 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69432

694322 = 4820802624, a square with even digits.

Page of Squares : First Upload October 27, 2012 ; Last Revised October 27, 2012
by Yoshio Mimura, Kobe, Japan

69483

694832± 2 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69496

694962± 3 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69513

695132 = 4832057169, a square with different digits.

Page of Squares : First Upload October 27, 2012 ; Last Revised October 27, 2012
by Yoshio Mimura, Kobe, Japan

69552

695522 = (22 - 1)(52 - 1)(82 - 1)(222 - 1)(472 - 1).

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69568

695682 = (12 + 7)(32 + 7)(61492 + 7) = (112 + 7)(61492 + 7).

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69575

695752 = 4840680625, and 484 = 222, 680625 = 8252.

Page of Squares : First Upload October 27, 2012 ; Last Revised October 27, 2012
by Yoshio Mimura, Kobe, Japan

69626

696262± 3 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69696

69696 = 2642, a palindromic zigzag square with 2 kinds of digits.

696962 = (22 + 8)(42 + 8)(62 + 8)(162 + 8)(382 + 8).

Page of Squares : First Upload October 27, 2012 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69700

697002 = (12 + 1)(32 + 1)(42 + 1)(92 + 1)(132 + 1)(322 + 1)
= (12 + 1)(32 + 1)(92 + 1)(132 + 1)(1322 + 1) = (12 + 4)(42 + 4)(92 + 4)(7562 + 4)
= (12 + 4)(82 + 4)(592 + 4)(642 + 4) = (42 + 4)(592 + 4)(2642 + 4) = (82 + 4)(112 + 4)(7562 + 4).

Page of Squares : First Upload November 16, 2013 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69708

697082± 5 are primes.

697082 = (212 + 3)(252 + 3)(1322 + 3).

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69748

697482± 3 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69753

697532± 2 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69762

697622 = (12 + 6)(302 + 6)(8762 + 6) = (42 + 6)(62 + 6)(22952 + 6).

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69768

697682± 5 are primes.

697682 = (12 + 8)(32 + 8)(72 + 8)(82 + 8)(882 + 8) = (12 + 8)(32 + 8)(642 + 8)(882 + 8)
= (12 + 8)(42 + 8)(72 + 8)(202 + 8)(312 + 8) = (12 + 8)(42 + 8)(202 + 8)(2352 + 8)
= (12 + 8)(72 + 8)(482 + 8)(642 + 8) = (12 + 8)(82 + 8)(312 + 8)(882 + 8)
= (32 + 8)(42 + 8)(72 + 8)(122 + 8)(372 + 8) = (32 + 8)(82 + 8)(312 + 8)(642 + 8)
= (32 + 8)(122 + 8)(312 + 8)(442 + 8) = (42 + 8)(122 + 8)(312 + 8)(372 + 8)
= (72 + 8)(122 + 8)(202 + 8)(372 + 8).

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69794

697942± 3 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69796

697962± 3 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69826

698262± 3 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69832

698322 = (62 + 7)(142 + 7)(152 + 7)(492 + 7) = (62 + 7)(492 + 7)(2172 + 7).

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69855

698552± 2 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69860

698602± 3 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69864

698642 = (32 - 1)(52 - 1)(50422 - 1).

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69874

698742± 3 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69888

698882 = (32 - 1)(52 - 1)(152 - 1)(3372 - 1) = (72 - 1)(152 - 1)(252 - 1)(272 - 1).

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69936

699362± 5 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69964

699642± 3 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69968

699682± 3 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69981

699812± 2 are primes.

Page of Squares : First Upload March 26, 2014 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

69984

699842± 5 are primes.

2702 + 69984 = 3782, 2702 - 69984 = 542.

Page of Squares : First Upload October 27, 2012 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan