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68000

68000² = (1² + 4)(2² + 4)(4² + 4)(8² + 4)(11² + 4)(26² + 4)
= (1² + 4)(4² + 4)(6² + 4)(8² + 4)(9² + 4)(14² + 4) = (1² + 4)(4² + 4)(6² + 4)(14² + 4)(76² + 4)
= (2² + 4)(4² + 4)(6² + 4)(8² + 4)(9² + 4)(11² + 4) = (2² + 4)(4² + 4)(6² + 4)(11² + 4)(76² + 4)
= (4² + 4)(6² + 4)(8² + 4)(11² + 4)(26² + 4).

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

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68019

68019²± 2 are primes.

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

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68026

68026²± 3 are primes.

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

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68040

333² + 68040 = 423², 333² - 68040 = 207²,
261² + 68040 = 369², 261² - 68040 = 9²,
346² + 68640 = 434², 346² - 68640 = 226²

68040² = (2² - 1)(161² - 1)(244² - 1).

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

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68073

68073²± 2 are primes.

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

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68103

68103² = (8² + 5)(18² + 5)(452² + 5).

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

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68112

68112² = (1² + 8)(2² + 8)(32² + 8)(204² + 8) = (2² + 8)(4² + 8)(16² + 8)(247² + 8)
= (2² + 8)(8² + 8)(11² + 8)(204² + 8) = (4² + 8)(5² + 8)(6² + 8)(11² + 8)(32² + 8)
= (4² + 8)(6² + 8)(2096² + 8) = (4² + 8)(6² + 8)(8² + 8)(247² + 8)
= (4² + 8)(11² + 8)(32² + 8)(38² + 8) = (6² + 8)(11² + 8)(28² + 8)(32² + 8)
= (10² + 8)(32² + 8)(204² + 8).

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

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68121

68121 = 261², a zigzag square.

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

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68122

68122² = 4640606884, a square with even digits.

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

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68187

68187² = 4649466969, 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

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68258

68258²± 3 are primes.

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

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68298

68298²± 5 are primes.

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

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68302

68302²± 3 are primes.

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

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68355

68355²± 2 are primes.

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

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68356

68356²± 3 are primes.

68356² = 6929² + 6930² + 6931² + ... + 7024².

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

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68412

68412²± 5 are primes.

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

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68450

68450² = (1² + 1)(6² + 1)(68² + 1)(117² + 1) = (2² + 1)(6² + 1)(43² + 1)(117² + 1).

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

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68456

68456² = (1² + 3)(13² + 3)(14² + 3)(185² + 3).

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

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68499

68499² = (11² + 8)(6031² + 8).

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

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68522

68522²± 3 are primes.

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

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68534

68534²± 3 are primes.

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

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68544

68544² = (8² - 1)(15² - 1)(577² - 1).

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

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68553

68553²± 2 are primes.

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

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68554

68554²± 3 are primes.

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

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68596

68596² = 899² + 900² + 901² + ... + 2457².

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

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68608

68608² = (1² + 7)(5² + 7)(11² + 7)(379² + 7) = (181² + 7)(379² + 7).

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

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68625

68625² = (4² + 9)(6² + 9)(2046² + 9).

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

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68628

68628² = (1² + 3)(2² + 3)(4² + 3)(30² + 3)(99² + 3) = (2² + 3)(4² + 3)(13² + 3)(15² + 3)(30² + 3)
= (3² + 3)(4² + 3)(4545² + 3) = (4² + 3)(5² + 3)(30² + 3)(99² + 3)
= (4² + 3)(12² + 3)(13² + 3)(99² + 3) = (4² + 3)(99² + 3)(159² + 3)
= (15² + 3)(4545² + 3) = (23² + 3)(30² + 3)(99² + 3).

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

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68632

68632² = (65² + 7)(1055² + 7).

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

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68638

68638²± 3 are primes.

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

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68640

68640² = (2² - 1)(12² - 1)(51² - 1)(65² - 1) = (2² - 1)(3² - 1)(12² - 1)(23² - 1)(51² - 1)
= (2² - 1)(3² - 1)(9² - 1)(12² - 1)(131² - 1) = (3² - 1)(4² - 1)(12² - 1)(21² - 1)(25² - 1)
= (3² - 1)(7² - 1)(12² - 1)(14² - 1)(21² - 1) = (5² - 1)(9² - 1)(12² - 1)(131² - 1)
= (5² - 1)(12² - 1)(23² - 1)(51² - 1) = (11² - 1)(12² - 1)(21² - 1)(25² - 1)
= (21² - 1)(25² - 1)(131² - 1).

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

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68644

68644 = 262², a square with even digits.

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

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68655

68655² = 1560² + 1561² + 1562² + ... + 2617².

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

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68663

68663² = 2263² + 2265² + 2267² + 2269² + ... + 3415².

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

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68670

68670² = (1² + 5)(10² + 5)(39² + 5)(70² + 5) = (4² + 5)(5² + 5)(39² + 5)(70² + 5)
= (5² + 5)(70² + 5)(179² + 5) = (25² + 5)(39² + 5)(70² + 5).

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

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68672

68672² = (5² + 7)(15² + 7)(797² + 7).

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

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68728

68728² = (2² + 7)(8² + 7)(31² + 7)(79² + 7) = (2² + 7)(9² + 7)(2209² + 7) = (31² + 7)(2209² + 7).

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

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68742

68742²± 5 are primes.

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

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68758

68758²± 3 are primes.

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

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68763

68763² = 4728350169, a square with different digits.

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

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68781

68781² = 4730825961, a square with different digits.

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

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68782

68782²± 3 are primes.

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

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68824

68824²± 3 are primes.

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

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68832

68832²± 5 are primes.

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

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68848

68848²± 3 are primes.

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

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68850

68850² = (3² + 9)(4² + 9)(6² + 9)(12² + 9)(39² + 9) = (3² + 9)(6² + 9)(21² + 9)(114² + 9)
= (6² + 9)(12² + 9)(21² + 9)(39² + 9).

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

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68880

29⁴ + 68880 = 881², 29⁴ - 68880 = 799².

68880² = (2² - 1)(6² - 1)(81² - 1)(83² - 1) = (2² - 1)(81² - 1)(491² - 1).

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

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68900

68900²± 3 are primes.

68900² = (1² + 1)(3² + 1)(8² + 1)(23² + 1)(83² + 1)
= (2² + 1)(3² + 1)(5² + 1)(23² + 1)(83² + 1) = (5² + 1)(7² + 1)(23² + 1)(83² + 1).

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

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68912

68912²± 3 are primes.

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

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68915

68915² = 841² + 842² + 843² + ... + 2457².

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

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68943

68943²± 2 are primes.

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

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68955

68955²± 2 are primes.

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

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68962

68962² = 4755757444, 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

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