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83007

83007²± 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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83019

83019²± 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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83061

83061²± 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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83076

83076² = (3² + 5)(9² + 5)(31² + 5)(77² + 5).

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

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83079

83079² = 168³ + 169³ + 170³ + 171³ + ... + 410³.

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

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83088

83088² = (1² + 8)(2² + 8)(4² + 8)(1632² + 8) = (4² + 8)(10² + 8)(1632² + 8).

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

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83106

83106² = (1² + 2)(5² + 2)(13² + 2)(22² + 2)(32² + 2).

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

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83160

663² + 83160 = 723², 663² - 83160 = 597².

83160² = (2² - 1)(3² - 1)(4² - 1)(10² - 1)(13² - 1)(34² - 1)
= (2² - 1)(4² - 1)(5² - 1)(6² - 1)(10² - 1)(43² - 1) = (2² - 1)(4² - 1)(10² - 1)(29² - 1)(43² - 1)
= (2² - 1)(5² - 1)(6² - 1)(8² - 1)(10² - 1)(21² - 1) = (2² - 1)(5² - 1)(10² - 1)(13² - 1)(76² - 1)
= (2² - 1)(5² - 1)(10² - 1)(29² - 1)(34² - 1) = (2² - 1)(6² - 1)(10² - 1)(19² - 1)(43² - 1)
= (2² - 1)(8² - 1)(10² - 1)(21² - 1)(29² - 1) = (2² - 1)(8² - 1)(6049² - 1)
= (2² - 1)(10² - 1)(11² - 1)(13² - 1)(34² - 1) = (2² - 1)(13² - 1)(34² - 1)(109² - 1)
= (2² - 1)(99² - 1)(485² - 1) = (3² - 1)(5² - 1)(8² - 1)(10² - 1)(76² - 1)
= (3² - 1)(8² - 1)(10² - 1)(11² - 1)(34² - 1) = (3² - 1)(8² - 1)(34² - 1)(109² - 1)
= (4² - 1)(5² - 1)(10² - 1)(13² - 1)(34² - 1) = (4² - 1)(8² - 1)(10² - 1)(13² - 1)(21² - 1)
= (4² - 1)(10² - 1)(11² - 1)(197² - 1) = (4² - 1)(109² - 1)(197² - 1)
= (6² - 1)(10² - 1)(13² - 1)(109² - 1) = (6² - 1)(29² - 1)(485² - 1)
= (8² - 1)(10² - 1)(31² - 1)(34² - 1) = (10² - 1)(13² - 1)(19² - 1)(34² - 1).

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

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83171

83171² = (3² + 2)(25077² + 2).

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

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83210

83210² = (23² + 1)(28² + 1)(129² + 1).

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

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83232

83232² = (2² + 8)(3² + 8)(8² + 8)(14² + 8)(48² + 8).

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

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83248

83248² = (2² + 7)(6² + 7)(31² + 7)(123² + 7).

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

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83250

83250² = (1² + 9)(6² + 9)(19² + 9)(204² + 9) = (1² + 9)(129² + 9)(204² + 9)
= (3² + 9)(4² + 9)(19² + 9)(204² + 9) = (4² + 9)(6² + 9)(19² + 9)(129² + 9)
= (19² + 9)(21² + 9)(204² + 9).

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

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83334

83334² = (6² + 2)(7² + 2)(27² + 2)(70² + 2) = (6² + 2)(27² + 2)(500² + 2)
= (27² + 2)(44² + 2)(70² + 2).

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

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83349

83349²± 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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83394

83394² = (27² + 9)(45² + 9)(68² + 9).

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

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83398

83398²± 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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83416

83416²± 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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83423

83423² = 6959396929, a square pegged by 9.

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

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83458

83458²± 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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83504

83504²± 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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83520

83520² = (2² - 1)(3² - 1)(59² - 1)(289² - 1) = (5² - 1)(59² - 1)(289² - 1).

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

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83521

83521 = 289², 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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83524

83524² = (2² + 3)(4² + 3)(25² + 3)(289² + 3).

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

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83525

83525² = (2² + 1)(18² + 1)(2072² + 1).

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

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83544

295² + 83544 = 413², 295² - 83544 = 59².

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

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83548

83548²± 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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83590

83590²± 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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83600

83600²± 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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83665

83665² = (12² + 1)(6948² + 1).

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

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83666

83666² = 6999999556, a square with 3 kinds of digits.

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

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83694

83694² = (2² + 9)(7² + 9)(18² + 9)(167² + 9).

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

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83810

83810² = (4² + 1)(13² + 1)(38² + 1)(41² + 1).

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

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83811

83811²± 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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83862

83862²± 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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83919

83919² = 7042398561, 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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83980

83980² = 256³ + 257³ + 258³ + 259³ + ... + 424³.

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

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83990

83990² = 3125² + 3126² + 3127² + ... + 3724².

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

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