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82000

82000² = (1² + 4)(2² + 4)(11² + 4)(18² + 4)(64² + 4) = (6² + 4)(11² + 4)(18² + 4)(64² + 4).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82008

82008² = (3² + 8)(4² + 8)(4060² + 8) = (3² + 8)(40² + 8)(496² + 8) = (8² + 8)(40² + 8)(241² + 8) = (20² + 8)(4060² + 8).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82012

82012²± 3 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82016

82016² = (2² + 7)(61² + 7)(405² + 7).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82080

82080² = (2² - 1)(4² - 1)(17² - 1)(721² - 1).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82119

82119²± 2 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82137

82137² = 6746486769, and 674648676 = 25974², 9 = 3².

Page of Squares : First Upload December 1, 2012 ; Last Revised December 1, 2012
by Yoshio Mimura, Kobe, Japan

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82150

82150² = (98² + 6)(838² + 6).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82202

82202²± 3 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82224

82224²± 5 are primes.

82224² = (4² + 8)(8² + 8)(1978² + 8).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82225

82225² = (12² - 1)(6876² - 1).

82225² = 6760950625, and 676 = 26², 950625 = 975².

Page of Squares : First Upload December 1, 2012 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82227

82227²± 2 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82347

82347²± 2 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82350

82350² = (3² + 9)(9² + 9)(2046² + 9).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82353

82353²± 2 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82354

82354²± 3 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82368

82368² = (2² - 1)(3² - 1)(5² - 1)(12² - 1)(287² - 1) = (2² - 1)(7² - 1)(12² - 1)(23² - 1)(25² - 1).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82369

82369 = 287², a square with different digits.

Page of Squares : First Upload December 1, 2012 ; Last Revised December 1, 2012
by Yoshio Mimura, Kobe, Japan

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82390

82390² = (1² + 6)(8² + 6)(3722² + 6) = (22² + 6)(3722² + 6).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82398

82398²± 5 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82418

82418² = (1² + 6)(20² + 6)(1546² + 6).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82422

82422² = (1² + 2)(6² + 2)(38² + 2)(203² + 2).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82432

82432² = (1² + 7)(3² + 7)(4² + 7)(7² + 7)(203² + 7) = (1² + 7)(7² + 7)(19² + 7)(203² + 7)
= (3² + 7)(4² + 7)(7² + 7)(21² + 7)(27² + 7) = (3² + 7)(4² + 7)(21² + 7)(203² + 7)
= (4² + 7)(5² + 7)(7² + 7)(19² + 7)(21² + 7) = (4² + 7)(7² + 7)(11² + 7)(203² + 7)
= (7² + 7)(19² + 7)(21² + 7)(27² + 7) = (19² + 7)(21² + 7)(203² + 7).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82445

82445² = 1336² + 1337² + 1338² + ... + 2834².

Page of Squares : First Upload December 1, 2012 ; Last Revised December 1, 2012
by Yoshio Mimura, Kobe, Japan

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82450

82450² = (5² + 9)(31² + 9)(454² + 9).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82467

82467² = (2² - 1)(8² - 1)(50² - 1)(120² - 1).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82476

82476² = 75³ + 264³ + 1893³.

Page of Squares : First Upload December 1, 2012 ; Last Revised December 1, 2012
by Yoshio Mimura, Kobe, Japan

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82478

82478² = 6802620484, a square with even digits.

Page of Squares : First Upload December 1, 2012 ; Last Revised December 1, 2012
by Yoshio Mimura, Kobe, Japan

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82490

82490² = (2² + 1)(3² + 1)(15² + 1)(776² + 1) = (7² + 1)(15² + 1)(776² + 1).

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

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82496

82496²± 3 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82516

82516² = (1² + 3)(2² + 3)(41² + 3)(380² + 3) = (5² + 3)(41² + 3)(380² + 3).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82534

82534²± 3 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82536

82536² = (1² + 3)(4² + 3)(15² + 3)(627² + 3).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82558

82558²± 3 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82656

82656²± 5 are primes.

82656² = (2² - 1)(83² - 1)(575² - 1).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82664

82664²± 3 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82706

82706²± 3 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82720

82720²± 3 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82764

82764² = (1² + 8)(2² + 8)(6² + 8)(7² + 8)(159² + 8) = (1² + 8)(2² + 8)(50² + 8)(159² + 8)
= (1² + 8)(5² + 8)(38² + 8)(126² + 8) = (1² + 8)(6² + 8)(26² + 8)(159² + 8)
= (1² + 8)(6² + 8)(50² + 8)(83² + 8) = (2² + 8)(5² + 8)(6² + 8)(7² + 8)(83² + 8)
= (2² + 8)(5² + 8)(26² + 8)(159² + 8) = (2² + 8)(5² + 8)(50² + 8)(83² + 8)
= (2² + 8)(7² + 8)(38² + 8)(83² + 8) = (5² + 8)(6² + 8)(17² + 8)(126² + 8)
= (5² + 8)(6² + 8)(26² + 8)(83² + 8) = (5² + 8)(7² + 8)(38² + 8)(50² + 8)
= (6² + 8)(7² + 8)(10² + 8)(159² + 8) = (10² + 8)(50² + 8)(159² + 8)
= (17² + 8)(38² + 8)(126² + 8) = (26² + 8)(38² + 8)(83² + 8) = (10² - 1)(23² - 1)(362² - 1).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82788

82788²± 5 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82796

82796²± 3 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82800

82800² = (2² - 1)(4² - 1)(11² - 1)(24² - 1)(47² - 1) = (3² - 1)(24² - 1)(26² - 1)(47² - 1)
= (4² - 1)(19² - 1)(24² - 1)(47² - 1).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82818

82818²± 5 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82820

82820² = (1² + 1)(2² + 1)(3² + 1)(9² + 1)(10² + 1)(91² + 1) = (1² + 1)(7² + 1)(9² + 1)(10² + 1)(91² + 1).

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

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82823

82823² = 4640² + 4641² + 4642² + ... + 4938².

Page of Squares : First Upload December 1, 2012 ; Last Revised December 1, 2012
by Yoshio Mimura, Kobe, Japan

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82857

82857²± 2 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82908

82908² = (1² + 5)(3² + 5)(17² + 5)(18² + 5)(29² + 5) = (1² + 5)(3² + 5)(29² + 5)(311² + 5).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82950

82950² = (1² + 6)(2² + 6)(3² + 6)(12² + 6)(209² + 6) = (1² + 6)(3² + 6)(28² + 6)(288² + 6)
= (3² + 6)(8² + 6)(12² + 6)(209² + 6) = (3² + 6)(28² + 6)(762² + 6).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82960

82960² = (2² + 4)(8² + 4)(22² + 4)(161² + 4) = (2² + 4)(9² + 4)(22² + 4)(144² + 4)
= (22² + 4)(26² + 4)(144² + 4).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82992

82992² = (1² + 3)(2² + 3)(3² + 3)(4² + 3)(6² + 3)(7² + 3)(23² + 3)
= (1² + 3)(2² + 3)(3² + 3)(4² + 3)(23² + 3)(45² + 3)
= (1² + 3)(2² + 3)(3² + 3)(5² + 3)(6² + 3)(137² + 3) = (1² + 3)(2² + 3)(3² + 3)(33² + 3)(137² + 3)
= (1² + 3)(2² + 3)(4² + 3)(5² + 3)(6² + 3)(7² + 3)(15² + 3)
= (1² + 3)(2² + 3)(4² + 3)(5² + 3)(15² + 3)(45² + 3)
= (1² + 3)(2² + 3)(4² + 3)(7² + 3)(15² + 3)(33² + 3)
= (1² + 3)(2² + 3)(6² + 3)(7² + 3)(15² + 3)(23² + 3) = (1² + 3)(2² + 3)(15² + 3)(23² + 3)(45² + 3)
= (1² + 3)(3² + 3)(4² + 3)(5² + 3)(7² + 3)(72² + 3)
= (1² + 3)(3² + 3)(4² + 3)(6² + 3)(7² + 3)(61² + 3)
= (1² + 3)(3² + 3)(4² + 3)(6² + 3)(19² + 3)(23² + 3) = (1² + 3)(3² + 3)(4² + 3)(45² + 3)(61² + 3)
= (1² + 3)(3² + 3)(7² + 3)(12² + 3)(137² + 3) = (1² + 3)(3² + 3)(7² + 3)(15² + 3)(110² + 3)
= (1² + 3)(3² + 3)(7² + 3)(23² + 3)(72² + 3) = (1² + 3)(3² + 3)(9² + 3)(1307² + 3)
= (1² + 3)(4² + 3)(5² + 3)(6² + 3)(15² + 3)(19² + 3)
= (1² + 3)(4² + 3)(6² + 3)(7² + 3)(9² + 3)(23² + 3) = (1² + 3)(4² + 3)(9² + 3)(23² + 3)(45² + 3)
= (1² + 3)(4² + 3)(15² + 3)(19² + 3)(33² + 3) = (1² + 3)(5² + 3)(6² + 3)(9² + 3)(137² + 3)
= (1² + 3)(5² + 3)(7² + 3)(15² + 3)(72² + 3) = (1² + 3)(6² + 3)(7² + 3)(15² + 3)(61² + 3)
= (1² + 3)(6² + 3)(15² + 3)(19² + 3)(23² + 3) = (1² + 3)(9² + 3)(33² + 3)(137² + 3)
= (1² + 3)(15² + 3)(45² + 3)(61² + 3) = (2² + 3)(3² + 3)(4² + 3)(7² + 3)(15² + 3)(19² + 3)
= (2² + 3)(3² + 3)(7² + 3)(9² + 3)(137² + 3) = (3² + 3)(4² + 3)(5² + 3)(6² + 3)(7² + 3)(23² + 3)
= (3² + 3)(4² + 3)(5² + 3)(23² + 3)(45² + 3) = (3² + 3)(4² + 3)(7² + 3)(23² + 3)(33² + 3)
= (3² + 3)(5² + 3)(33² + 3)(137² + 3) = (3² + 3)(9² + 3)(19² + 3)(137² + 3)
= (4² + 3)(5² + 3)(7² + 3)(15² + 3)(33² + 3) = (4² + 3)(7² + 3)(9² + 3)(15² + 3)(19² + 3)
= (5² + 3)(6² + 3)(7² + 3)(15² + 3)(23² + 3) = (5² + 3)(15² + 3)(23² + 3)(45² + 3)
= (7² + 3)(15² + 3)(23² + 3)(33² + 3).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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82998

82998²± 5 are primes.

82998² = 6888668004, a square with even digits.

Page of Squares : First Upload December 1, 2012 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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