Squares:85000s

85000

85000² = (1² + 4)(9² + 4)(11² + 4)(14² + 4)(26² + 4).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85021

85021² = 1! + 5! + 6! + 10! + 11! + 12! + 12! + 13!.

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

85029

85029²± 2 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85050

85050² = (2² + 5)(5² + 5)(10² + 5)(20² + 5)(25² + 5).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85064

85064² = (1² + 3)(2² + 3)(5² + 3)(37² + 3)(82² + 3).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85138

85138²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85142

85142²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85158

85158² = (1² + 2)(2² + 2)(5² + 2)(9² + 2)(424² + 2) = (4² + 2)(5² + 2)(9² + 2)(424² + 2)
= (9² + 2)(22² + 2)(424² + 2).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85164

85164²± 5 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85176

85176² = (2² + 3)(3² + 3)(6² + 3)(33² + 3)(45² + 3) = (3² + 3)(6² + 3)(7² + 3)(12² + 3)(45² + 3)
= (6² + 3)(9² + 3)(33² + 3)(45² + 3).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85185

85185²± 2 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85204

85204²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85214

85214²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85250

85250² = (2² + 6)(7² + 6)(37² + 6)(98² + 6) = (4² + 6)(5² + 6)(37² + 6)(88² + 6)
= (26² + 6)(37² + 6)(88² + 6).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85260

85260² = (2² - 1)(6² - 1)(57² - 1)(146² - 1) = (1² + 6)(2² + 6)(6² + 6)(8² + 6)(9² + 6)(20² + 6)
= (1² + 6)(2² + 6)(6² + 6)(20² + 6)(78² + 6) = (2² + 6)(6² + 6)(9² + 6)(20² + 6)(22² + 6)
= (6² + 6)(8² + 6)(20² + 6)(78² + 6).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85264

85264 = 292², a square with different digits.

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

85272

85272² = (3² + 8)(5² + 8)(12² + 8)(292² + 8) = (3² + 8)(12² + 8)(20² + 8)(83² + 8)
= (5² + 8)(12² + 8)(1204² + 8).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85280

85280²± 3 are primes.

85280² = (2² + 4)(4² + 4)(16² + 4)(18² + 4)(23² + 4).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85293

85293²± 2 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85308

85308² = 2460² + 2461² + 2462² + ... + 3323².

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

85320

85320² = (2² - 1)(4² - 1)(80² - 1)(159² - 1).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85353

85353² = 7285134609, a square with different digits.

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

85372

85372²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85376

85376² = (1² + 7)(4² + 7)(5² + 7)(15² + 7)(73² + 7) = (1² + 7)(15² + 7)(27² + 7)(73² + 7)
= (27² + 7)(3147² + 7) = (27² + 7)(43² + 7)(73² + 7) = (3² + 7)(15² + 7)(19² + 7)(73² + 7)
= (4² + 7)(5² + 7)(43² + 7)(73² + 7) = (4² + 7)(5² + 7)(3147² + 7)
= (4² + 7)(15² + 7)(27² + 7)(43² + 7).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85410

85410² = (3² + 9)(6² + 9)(3001² + 9) = (3² + 9)(8² + 9)(15² + 9)(154² + 9).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85436

85436²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85460

85460²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85490

85490²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85536

85536² = (1² + 8)(2² + 8)(4² + 8)(5² + 8)(6² + 8)(44² + 8)
= (1² + 8)(2² + 8)(4² + 8)(5² + 8)(10² + 8)(28² + 8) = (1² + 8)(2² + 8)(4² + 8)(38² + 8)(44² + 8)
= (1² + 8)(2² + 8)(5² + 8)(8² + 8)(10² + 8)(16² + 8) = (1² + 8)(2² + 8)(6² + 8)(28² + 8)(44² + 8)
= (2² + 8)(4² + 8)(6² + 8)(17² + 8)(44² + 8) = (2² + 8)(4² + 8)(10² + 8)(17² + 8)(28² + 8)
= (2² + 8)(8² + 8)(10² + 8)(16² + 8)(17² + 8) = (2² + 8)(8² + 8)(10² + 8)(280² + 8)
= (4² + 8)(5² + 8)(6² + 8)(10² + 8)(44² + 8) = (4² + 8)(10² + 8)(38² + 8)(44² + 8)
= (6² + 8)(10² + 8)(28² + 8)(44² + 8).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85543

1² + 2² + 3² + 4² + ... + 85543² = 208660282682684, a square with even digits.

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

85544

85544² = 7317775936, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

85608

85608² = 2522² + 2523² + 2524² + ... + 3362².

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

85628

85628²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85680

85680² = (2² - 1)(6² - 1)(15² - 1)(16² - 1)(35² - 1) = (2² - 1)(6² - 1)(35² - 1)(239² - 1)
= (2² - 1)(7² - 1)(9² - 1)(16² - 1)(50² - 1) = (2² - 1)(13² - 1)(16² - 1)(239² - 1)
= (3² - 1)(15² - 1)(2024² - 1) = (3² - 1)(8² - 1)(16² - 1)(239² - 1) = (17² - 1)(50² - 1)(101² - 1)
= (35² - 1)(49² - 1)(50² - 1) = (35² - 1)(2449² - 1).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85692

85692²± 5 are primes.

85692² = (21² + 3)(24² + 3)(169² + 3).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85695

85695²± 2 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85698

85698² = (8² + 5)(61² + 5)(169² + 5).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85730

85730²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85736

85736²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85743

85743² = 7351862049, a square with different digits.

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

85750

85750² = (1² + 6)(2² + 6)(22² + 6)(463² + 6) = (8² + 6)(22² + 6)(463² + 6).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85786

85786²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85800

85800² = (2² - 1)(4² - 1)(12² - 1)(21² - 1)(51² - 1).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85803

85803² = 7362154809, a square with different digits.

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

85806

85806²± 5 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85840

85840² = (2² + 4)(5² + 4)(24² + 4)(234² + 4) = (4² + 4)(82² + 4)(234² + 4)
= (12² + 4)(82² + 4)(86² + 4).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85849

85849 = 293², a zigzag square.

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

85850

85850² = (2² + 1)(10² + 1)(13² + 1)(293² + 1)
= (2² + 1)(3² + 1)(4² + 1)(10² + 1)(293² + 1) = (4² + 1)(7² + 1)(10² + 1)(293² + 1).

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

85870

85870²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85875

85875²± 2 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85917

85917²± 2 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85956

18595685956 = 136366².

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

85974

85974² = (8² + 5)(31² + 5)(333² + 5).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85986

85986²± 5 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

85996

85996²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan