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51018

51018²± 5 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51030

51030² = (1² + 5)(2² + 5)(4² + 5)(7² + 5)(10² + 5)(20² + 5) = (1² + 5)(4² + 5)(5² + 5)(830² + 5)
= (1² + 5)(10² + 5)(20² + 5)(101² + 5) = (1² + 5)(25² + 5)(830² + 5)
= (2² + 5)(3² + 5)(5² + 5)(830² + 5) = (2² + 5)(4² + 5)(7² + 5)(20² + 5)(25² + 5)
= (2² + 5)(7² + 5)(10² + 5)(11² + 5)(20² + 5) = (2² + 5)(7² + 5)(20² + 5)(115² + 5)
= (4² + 5)(5² + 5)(20² + 5)(101² + 5) = (5² + 5)(11² + 5)(830² + 5) = (20² + 5)(25² + 5)(101² + 5).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51051

51051²± 2 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51076

51076 = 226² is a square with different digits.

Page of Squares : First Upload August 25, 2012 ; Last Revised August 25, 2012
by Yoshio Mimura, Kobe, Japan

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51083

51083² = 1012² + 1013² + 1014² + ... + 2069².

Page of Squares : First Upload August 25, 2012 ; Last Revised August 25, 2012
by Yoshio Mimura, Kobe, Japan

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51084

51084² = (1² + 8)(6² + 8)(10² + 8)(247² + 8) = (1² + 8)(6² + 8)(11² + 8)(226² + 8)
= (2² + 8)(5² + 8)(10² + 8)(247² + 8) = (2² + 8)(5² + 8)(11² + 8)(226² + 8)
= (5² + 8)(6² + 8)(11² + 8)(118² + 8) = (11² + 8)(38² + 8)(118² + 8).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51135

51135² = (3² + 6)(13203² + 6).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51138

51138² = (1² + 5)(2² + 5)(6959² + 5) = (7² + 5)(6959² + 5).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51150

51150² = (3² + 6)(5² + 6)(7² + 6)(12² + 6)(26² + 6) = (3² + 6)(7² + 6)(18² + 6)(98² + 6)
= (3² + 6)(88² + 6)(150² + 6).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51156

51156² = (1² + 5)(3² + 5)(4² + 5)(17² + 5)(71² + 5) = (3² + 5)(11² + 5)(17² + 5)(71² + 5).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51192

51192² = 2620620864 is a square with even digits.

Page of Squares : First Upload August 25, 2012 ; Last Revised August 25, 2012
by Yoshio Mimura, Kobe, Japan

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51208

51208²± 3 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51220

51220² = (1² + 4)(28² + 4)(816² + 4).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51225

51225²± 2 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51294

51294²± 5 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51357

51357²± 2 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51394

51394²± 3 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51399

51399²± 2 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51402

51402²± 5 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51408

51408² = (2² - 1)(17² - 1)(35² - 1)(50² - 1).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51414

51414² = (1² + 2)(3² + 2)(30² + 2)(298² + 2) = (2² + 2)(11² + 2)(30² + 2)(63² + 2)
= (3² + 2)(52² + 2)(298² + 2) = (6² + 2)(11² + 2)(25² + 2)(30² + 2).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51422

51422² = 2644222084 is a square with even digits.

Page of Squares : First Upload August 25, 2012 ; Last Revised August 25, 2012
by Yoshio Mimura, Kobe, Japan

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51429

51429²± 2 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51438

51438²± 5 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51450

51450² = (1² + 6)(2² + 6)(3² + 6)(13² + 6)(120² + 6) = (1² + 6)(3² + 6)(8² + 6)(22² + 6)(27² + 6)
= (1² + 6)(6² + 6)(8² + 6)(13² + 6)(27² + 6) = (1² + 6)(12² + 6)(13² + 6)(120² + 6)
= (1² + 6)(120² + 6)(162² + 6) = (3² + 6)(8² + 6)(13² + 6)(120² + 6)
= (6² + 6)(13² + 6)(22² + 6)(27² + 6).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51470

51470²± 3 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51480

51480² = (2² - 1)(4² - 1)(5² - 1)(12² - 1)(131² - 1) = (2² - 1)(5² - 1)(10² - 1)(12² - 1)(51² - 1)
= (2² - 1)(12² - 1)(19² - 1)(131² - 1) = (3² - 1)(10² - 1)(11² - 1)(12² - 1)(14² - 1)
= (3² - 1)(10² - 1)(14² - 1)(131² - 1) = (3² - 1)(12² - 1)(14² - 1)(109² - 1)
= (4² - 1)(12² - 1)(21² - 1)(53² - 1) = (10² - 1)(12² - 1)(14² - 1)(31² - 1).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51500

51500² = 23027 x 23028 + 23029 x 23030 + 23031 x 23032 + ... + 23035 x 23036.

Page of Squares : First Upload August 25, 2012 ; Last Revised August 25, 2012
by Yoshio Mimura, Kobe, Japan

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51514

51514²± 3 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51529

51529 = 227² is a zigzag square.

Page of Squares : First Upload August 25, 2012 ; Last Revised August 25, 2012
by Yoshio Mimura, Kobe, Japan

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51604

51604² = 2534² + 2535² + 2536² + ... + 2894².

Page of Squares : First Upload August 25, 2012 ; Last Revised August 25, 2012
by Yoshio Mimura, Kobe, Japan

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51612

51612² = (1³ + 2³ + 3³ + ... + 22³)(23³ + 24³ + 25³).

Page of Squares : First Upload February 9, 2013 ; Last Revised February 9, 2013
by Yoshio Mimura, Kobe, Japan

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51651

51651²± 2 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51660

51660² = (1² + 5)(3² + 5)(4² + 5)(5² + 5)(6² + 5)(35² + 5)
= (1² + 5)(3² + 5)(6² + 5)(25² + 5)(35² + 5) = (1² + 5)(5² + 5)(6² + 5)(17² + 5)(35² + 5)
= (3² + 5)(5² + 5)(6² + 5)(11² + 5)(35² + 5).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51661

51661² = 2351² + 2353² + 2355² + 2357² + ... + 3071².

Page of Squares : First Upload August 25, 2012 ; Last Revised August 25, 2012
by Yoshio Mimura, Kobe, Japan

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51672

51672²± 5 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51714

51714² = (5² + 9)(12² + 9)(717² + 9).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51729

51729²± 2 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51754

51754² = (15² + 4)(3420² + 4).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51758

51758²± 3 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51776

51776²± 3 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51795

51795²± 2 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51808

51808² = 2684068864 is a square with even digits.

Page of Squares : First Upload August 25, 2012 ; Last Revised August 25, 2012
by Yoshio Mimura, Kobe, Japan

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51840

51840² = (17² - 1)(19² - 1)(161² - 1) = (2² - 1)(3² - 1)(4² - 1)(17² - 1)(161² - 1)
= (2² - 1)(11² - 1)(17² - 1)(161² - 1) = (4² - 1)(5² - 1)(17² - 1)(161² - 1).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51850

51850² = (1² + 1)(4² + 1)(13² + 1)(682² + 1) = (2² + 1)(4² + 1)(7² + 1)(11² + 1)(72² + 1)
= (1² + 4)(144² + 4)(161² + 4) = (8² + 4)(39² + 4)(161² + 4) = (9² + 4)(39² + 4)(144² + 4).

Page of Squares : First Upload November 16, 2013 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51948

51948²± 5 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51968

51968² = (1² + 7)(3² + 7)(7² + 7)(14² + 7)(43² + 7) = (1² + 7)(3² + 7)(14² + 7)(15² + 7)(21² + 7)
= (1² + 7)(3² + 7)(21² + 7)(217² + 7) = (1² + 7)(7² + 7)(11² + 7)(14² + 7)(15² + 7)
= (1² + 7)(7² + 7)(11² + 7)(217² + 7) = (3² + 7)(14² + 7)(21² + 7)(43² + 7)
= (7² + 7)(11² + 7)(14² + 7)(43² + 7) = (11² + 7)(14² + 7)(15² + 7)(21² + 7)
= (11² + 7)(21² + 7)(217² + 7).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51975

51975² = (6² - 1)(10² - 1)(26² - 1)(34² - 1).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51981

51981²± 2 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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51984

51984 = 228² is a square with different digits.

Page of Squares : First Upload August 25, 2012 ; Last Revised August 25, 2012
by Yoshio Mimura, Kobe, Japan

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51986

51986²± 3 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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