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65000

65000² = (1² + 4)(3² + 4)(6² + 4)(11² + 4)(114² + 4) = (1² + 4)(4² + 4)(11² + 4)(16² + 4)(36² + 4)
= (1² + 4)(6² + 4)(11² + 4)(14² + 4)(29² + 4) = (3² + 4)(11² + 4)(14² + 4)(114² + 4).

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

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65008

65008² = 4226040064, a square with even digits.

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

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65025

65025² = (12² + 9)(46² + 9)(114² + 9).

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

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65026

65026² = (5² + 1)(50² + 1)(255² + 1).

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

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65054

65054²± 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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65078

65078²± 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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65096

65096²± 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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65100

65100² = (1² + 6)(2² + 6)(6² + 6)(12² + 6)(98² + 6) = (2² + 6)(3² + 6)(6² + 6)(8² + 6)(98² + 6)
= (2² + 6)(5² + 6)(8² + 6)(12² + 6)(36² + 6) = (2² + 6)(6² + 6)(36² + 6)(88² + 6)
= (6² + 6)(8² + 6)(12² + 6)(98² + 6).

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

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65157

65157² = 4245434649, a square pegged by 4.

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

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65162

65162² = 4246086244, a square with even digits.

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

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65168

65168² = 4246868224, a square with even digits.

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

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65184

65184² = (2² - 1)(193² - 1)(195² - 1).

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

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65199

65199²± 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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65205

65205² = (2² + 5)(8² + 5)(20² + 5)(130² + 5) = (8² + 5)(10² + 5)(20² + 5)(38² + 5).

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

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65234

65234²± 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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65241

65241² = (5² + 8)(11357² + 8).

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

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65250

65250² = (6² + 9)(79² + 9)(123² + 9).

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

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65280

514² + 65280 = 574², 514² - 65280 = 446².

65280² = (3² - 1)(5² - 1)(9² - 1)(16² - 1)(33² - 1) = (3² - 1)(7² - 1)(33² - 1)(101² - 1)
= (4² - 1)(33² - 1)(511² - 1).

Page of Squares : First Upload October 13, 2012 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

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65296

65296² = (24² + 7)(35² + 7)(77² + 7).

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

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65300

65300²± 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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65416

65416² = (25² + 4)(42² + 4)(62² + 4).

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

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65441

65441² = 72⁴ + 175⁴ + 240⁴, the 4th primitive sum of three 4-th powers.

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

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65472

65472² = 496³ + 497³ + 498³ + 499² + 500² + ... + 527³.

65472² = (32² - 1)(2047² - 1).

Page of Squares : First Upload October 13, 2012 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

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65520

65520² = (2² - 1)(3² - 1)(14² - 1)(15² - 1)(64² - 1) = (2² - 1)(3² - 1)(64² - 1)(209² - 1)
= (2² - 1)(4² - 1)(5² - 1)(6² - 1)(337² - 1) = (2² - 1)(4² - 1)(25² - 1)(391² - 1)
= (2² - 1)(4² - 1)(29² - 1)(337² - 1) = (2² - 1)(6² - 1)(14² - 1)(17² - 1)(27² - 1)
= (2² - 1)(6² - 1)(19² - 1)(337² - 1) = (2² - 1)(7² - 1)(14² - 1)(391² - 1)
= (2² - 1)(13² - 1)(14² - 1)(209² - 1) = (2² - 1)(14² - 1)(15² - 1)(181² - 1)
= (2² - 1)(181² - 1)(209² - 1) = (3² - 1)(8² - 1)(14² - 1)(209² - 1)
= (4² - 1)(8² - 1)(27² - 1)(79² - 1) = (5² - 1)(14² - 1)(15² - 1)(64² - 1)
= (5² - 1)(64² - 1)(209² - 1) = (6² - 1)(7² - 1)(25² - 1)(64² - 1)
= (6² - 1)(14² - 1)(15² - 1)(53² - 1) = (6² - 1)(53² - 1)(209² - 1)
= (8² - 1)(64² - 1)(129² - 1) = (13² - 1)(64² - 1)(79² - 1)
= (25² - 1)(41² - 1)(64² - 1).

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

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65526

65526² = (18² + 2)(20² + 2)(181² + 2).

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

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65532

65532²± 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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65536

65536 = 256², a square with 3 kinds of digits.

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

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65562

65562² = (2² + 3)(3² + 3)(12² + 3)(590² + 3) = (9² + 3)(12² + 3)(590² + 3).

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

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65585

65585² = (2² + 9)(4² + 9)(3638² + 9).

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

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65590

65590²± 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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65627

65627² = 1083² + 1085² + 1087² + 1089² + ... + 3003².

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

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65634

65634² = 4307821956, a square with different digits.

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

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65637

65637² = 4308215769, a square with different digits.

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

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65648

65648² = (2² + 7)(64² + 7)(309² + 7).

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

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65650

65650² = (2² + 1)(3² + 1)(18² + 1)(515² + 1) = (2² + 1)(57² + 1)(515² + 1)
= (2² + 1)(7² + 1)(8² + 1)(515² + 1) = (7² + 1)(18² + 1)(515² + 1)
= (3² + 4)(11² + 4)(20² + 4)(81² + 4).

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

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65664

65664² = (2² - 1)(37² - 1)(1025² - 1).

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

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65676

65676² = (3² + 3)(41² + 3)(462² + 3).

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

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65682

65682² = (1² + 2)(2² + 2)(71² + 2)(218² + 2) = (4² + 2)(71² + 2)(218² + 2).

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

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65702

65702² = (4² + 3)(110² + 3)(137² + 3).

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

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65772

65772² = (1² + 5)(2² + 5)(3² + 5)(4² + 5)(7² + 5)(71² + 5)
= (1² + 5)(2² + 5)(3² + 5)(11² + 5)(13² + 5)(16² + 5) = (1² + 5)(2² + 5)(7² + 5)(17² + 5)(71² + 5)
= (1² + 5)(3² + 5)(4² + 5)(7² + 5)(13² + 5)(16² + 5) = (1² + 5)(3² + 5)(7² + 5)(13² + 5)(74² + 5)
= (1² + 5)(3² + 5)(71² + 5)(101² + 5) = (1² + 5)(4² + 5)(7² + 5)(11² + 5)(71² + 5)
= (1² + 5)(7² + 5)(13² + 5)(16² + 5)(17² + 5) = (1² + 5)(7² + 5)(13² + 5)(277² + 5)
= (2² + 5)(3² + 5)(7² + 5)(11² + 5)(71² + 5) = (3² + 5)(7² + 5)(11² + 5)(13² + 5)(16² + 5).

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

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65778

65778² = (6² + 2)(13² + 2)(816² + 2).

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

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65835

65835² = (2² - 1)(20² - 1)(34² - 1)(56² - 1) = (4² - 1)(6² - 1)(8² - 1)(362² - 1)
= (6² - 1)(10² - 1)(20² - 1)(56² - 1).

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

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65848

65848²± 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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65856

350² + 65856 = 434², 350² - 65856 = 238².

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

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65866

65866²± 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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65892

65892²± 5 are primes.

65892² = (6² + 2)(10² + 2)(24² + 2)(44² + 2).

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

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65908

65908²± 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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65944

65944²± 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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