Squares:67000s

67004

67004²± 3 are primes.

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

67014

67014² = (1² + 2)(5² + 2)(10² + 2)(12² + 2)(61² + 2) = (2² + 2)(5² + 2)(7² + 2)(12² + 2)(61² + 2).

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

67032

67032² = (2² - 1)(3² - 1)(20² - 1)(685² - 1) = (5² - 1)(20² - 1)(685² - 1)
= (2² + 3)(3² + 3)(4² + 3)(9² + 3)(12² + 3)(15² + 3).

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

67046

67046²± 3 are primes.

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

67050

67050² = (6² + 9)(17² + 9)(579² + 9).

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

67068

67068²± 5 are primes.

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

67081

67081 = 259², a zigzag square with different digits.

Page of Squares : First Upload October 20, 2012 ; Last Revised October 20, 2012
by Yoshio Mimura, Kobe, Japan

67089

67089² = (5² + 8)(45² + 8)(259² + 8).

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

67091

67091² = 2649² + 2650² + 2651² + ... + 3177².

Page of Squares : First Upload October 20, 2012 ; Last Revised October 20, 2012
by Yoshio Mimura, Kobe, Japan

67101

67101²± 2 are primes.

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

67158

67158²± 5 are primes.

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

67179

67179²± 2 are primes.

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

67187

The sum of consecutive primes 2, 3, 5, 7, 11, ..., 67187 is a square 14573².

Page of Squares : First Upload October 20, 2012 ; Last Revised October 20, 2012
by Yoshio Mimura, Kobe, Japan

67200

67200² = (2² - 1)(6² - 1)(9² - 1)(15² - 1)(49² - 1) = (3² - 1)(4² - 1)(7² - 1)(9² - 1)(99² - 1)
= (3² - 1)(5² - 1)(49² - 1)(99² - 1) = (3² - 1)(6² - 1)(9² - 1)(11² - 1)(41² - 1)
= (3² - 1)(6² - 1)(9² - 1)(449² - 1) = (6² - 1)(9² - 1)(31² - 1)(41² - 1)
= (7² - 1)(9² - 1)(11² - 1)(99² - 1).

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

67215

67215²± 2 are primes.

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

67225

56722567225 = 238165².

Page of Squares : First Upload October 20, 2012 ; Last Revised October 20, 2012
by Yoshio Mimura, Kobe, Japan

67229

67229² = 2379² + 2381² + 2383² + 2385² + ... + 3435².

Page of Squares : First Upload October 20, 2012 ; Last Revised October 20, 2012
by Yoshio Mimura, Kobe, Japan

67232

67232² = (1² + 7)(3² + 7)(39² + 7)(152² + 7) = (11² + 7)(39² + 7)(152² + 7).

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

67240

41³ + 67240 = 369², 41³ - 67240 = 41².

Page of Squares : First Upload October 20, 2012 ; Last Revised October 20, 2012
by Yoshio Mimura, Kobe, Japan

67242

67242²± 5 are primes.

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

67275

67275² = (2² - 1)(14² - 1)(24² - 1)(116² - 1).

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

67280

67280² = (1² + 4)(2² + 4)(5² + 4)(24² + 4)(82² + 4) = (4² + 4)(5² + 4)(34² + 4)(82² + 4)
= (5² + 4)(6² + 4)(24² + 4)(82² + 4) = (24² + 4)(34² + 4)(82² + 4).

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

67284

67284² = (1² + 5)(2² + 5)(3² + 5)(7² + 5)(333² + 5) = (1² + 5)(7² + 5)(11² + 5)(333² + 5).

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

67298

67298²± 3 are primes.

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

67320

67320² = (10² - 1)(67² - 1)(101² - 1).

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

67338

67338² = (2² + 5)(9² + 5)(34² + 5)(71² + 5) = (9² + 5)(13² + 5)(16² + 5)(34² + 5).

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

67364

67364²± 3 are primes.

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

67410

67410² = (1² + 5)(10² + 5)(40² + 5)(67² + 5) = (4² + 5)(5² + 5)(40² + 5)(67² + 5)
= (25² + 5)(40² + 5)(67² + 5).

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

67416

265² + 67416 = 371², 265² - 67416 = 53².

Page of Squares : First Upload October 20, 2012 ; Last Revised October 20, 2012
by Yoshio Mimura, Kobe, Japan

67419

67419²± 2 are primes.

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

67430

67430²= 1923 x 1924 + 1924 x 1925 + 1925 x 1926 +...+ 2747 x 2748.

Page of Squares : First Upload October 20, 2012 ; Last Revised October 20, 2012
by Yoshio Mimura, Kobe, Japan

67470

67470² = (2² + 9)(67² + 9)(279² + 9) = (9² + 9)(67² + 9)(106² + 9).

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

67482

67482²± 5 are primes.

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

67485

67485² = 4554225225, a sqaure with 3 kinds of digits.

Page of Squares : First Upload October 20, 2012 ; Last Revised October 20, 2012
by Yoshio Mimura, Kobe, Japan

67500

67500² = (1² + 9)(3² + 9)(6² + 9)(9² + 9)(79² + 9) = (3² + 9)(9² + 9)(21² + 9)(79² + 9).

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

67532

67532²± 3 are primes.

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

67563

67563²± 2 are primes.

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

67570

67570² = (5² + 4)(24² + 4)(521² + 4).

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

67575

67575² = (16² + 9)(46² + 9)(90² + 9).

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

67600

65³ + 67600 = 585², 65³ - 67600 = 455².

67600² = (1² + 4)(2² + 4)(3² + 4)(6² + 4)(16² + 4)(29² + 4)
= (1² + 4)(2² + 4)(10² + 4)(29² + 4)(36² + 4) = (1² + 4)(3² + 4)(4² + 4)(6² + 4)(10² + 4)(29² + 4)
= (1² + 4)(4² + 4)(14² + 4)(478² + 4) = (1² + 4)(6² + 4)(10² + 4)(16² + 4)(29² + 4)
= (10² + 4)(14² + 4)(16² + 4)(29² + 4) = (2² + 4)(3² + 4)(6² + 4)(29² + 4)(36² + 4)
= (2² + 4)(3² + 4)(14² + 4)(16² + 4)(29² + 4) = (2² + 4)(4² + 4)(11² + 4)(478² + 4)
= (3² + 4)(4² + 4)(10² + 4)(14² + 4)(29² + 4) = (3² + 4)(10² + 4)(16² + 4)(114² + 4)
= (6² + 4)(10² + 4)(29² + 4)(36² + 4).

Page of Squares : First Upload October 20, 2012 ; Last Revised March 26, 2014
by Yoshio Mimura, Kobe, Japan

67608

67608²± 5 are primes.

67608² = (4² + 8)(53² + 8)(260² + 8).

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

67620

67620² = (9² - 1)(22² - 1)(344² - 1).

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

67626

67626²± 5 are primes.

67626² = (3² + 9)(15² + 9)(1042² + 9).

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

67628

67628²± 3 are primes.

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

67635

67635²± 2 are primes.

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

67677

67677² = 4580176329, a square with different digits.

Page of Squares : First Upload October 20, 2012 ; Last Revised October 20, 2012
by Yoshio Mimura, Kobe, Japan

67680

67680² = (2² - 1)(9² - 1)(46² - 1)(95² - 1).

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

67695

67695²± 2 are primes.

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

67704

67704² = (1² + 3)(2² + 3)(3² + 3)(6² + 3)(7² + 3)(82² + 3)
= (1² + 3)(2² + 3)(3² + 3)(45² + 3)(82² + 3) = (1² + 3)(2² + 3)(6² + 3)(9² + 3)(11² + 3)(20² + 3)
= (1² + 3)(3² + 3)(6² + 3)(19² + 3)(82² + 3) = (1² + 3)(5² + 3)(6² + 3)(20² + 3)(51² + 3)
= (1² + 3)(6² + 3)(7² + 3)(9² + 3)(82² + 3) = (1² + 3)(9² + 3)(45² + 3)(82² + 3)
= (1² + 3)(20² + 3)(33² + 3)(51² + 3) = (2² + 3)(3² + 3)(5² + 3)(6² + 3)(11² + 3)(20² + 3)
= (2² + 3)(3² + 3)(7² + 3)(20² + 3)(51² + 3) = (2² + 3)(3² + 3)(11² + 3)(20² + 3)(33² + 3)
= (2² + 3)(6² + 3)(7² + 3)(11² + 3)(51² + 3) = (2² + 3)(11² + 3)(45² + 3)(51² + 3)
= (3² + 3)(5² + 3)(6² + 3)(7² + 3)(82² + 3) = (3² + 3)(5² + 3)(45² + 3)(82² + 3)
= (3² + 3)(19² + 3)(20² + 3)(51² + 3) = (3² + 3)(51² + 3)(383² + 3)
= (3² + 3)(7² + 3)(11² + 3)(12² + 3)(20² + 3) = (3² + 3)(7² + 3)(20² + 3)(135² + 3)
= (3² + 3)(7² + 3)(33² + 3)(82² + 3) = (5² + 3)(6² + 3)(9² + 3)(11² + 3)(20² + 3)
= (6² + 3)(7² + 3)(11² + 3)(135² + 3) = (6² + 3)(11² + 3)(19² + 3)(51² + 3)
= (7² + 3)(9² + 3)(20² + 3)(51² + 3) = (9² + 3)(11² + 3)(20² + 3)(33² + 3)
= (11² + 3)(45² + 3)(135² + 3).

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

67712

67712² = (1² + 7)(3² + 7)(4² + 7)(19² + 7)(65² + 7) = (4² + 7)(11² + 7)(19² + 7)(65² + 7).

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

67714

67714²± 3 are primes.

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

67716

67716² = (1² + 2)(2² + 2)(3² + 2)(4² + 2)(6² + 2)(13² + 2)(14² + 2)
= (1² + 2)(2² + 2)(3² + 2)(4² + 2)(6² + 2)(184² + 2)
= (1² + 2)(2² + 2)(4² + 2)(6² + 2)(19² + 2)(32² + 2) = (1² + 2)(2² + 2)(6² + 2)(14² + 2)(184² + 2)
= (1² + 2)(3² + 2)(4² + 2)(6² + 2)(14² + 2)(32² + 2)
= (1² + 2)(4² + 2)(6² + 2)(8² + 2)(13² + 2)(14² + 2) = (1² + 2)(4² + 2)(6² + 2)(8² + 2)(184² + 2)
= (2² + 2)(3² + 2)(5² + 2)(6² + 2)(8² + 2)(32² + 2)
= (2² + 2)(4² + 2)(5² + 2)(6² + 2)(8² + 2)(25² + 2) = (2² + 2)(4² + 2)(8² + 2)(25² + 2)(32² + 2)
= (2² + 2)(6² + 2)(8² + 2)(22² + 2)(25² + 2) = (4² + 2)(6² + 2)(14² + 2)(184² + 2)
= (2² + 2)(6² + 2)(32² + 2)(140² + 2) = (1² + 8)(2² + 8)(7² + 8)(10² + 8)(83² + 8)
= (1² + 8)(2² + 8)(7² + 8)(17² + 8)(50² + 8) = (1² + 8)(5² + 8)(7² + 8)(10² + 8)(50² + 8)
= (1² + 8)(6² + 8)(7² + 8)(17² + 8)(26² + 8) = (1² + 8)(10² + 8)(17² + 8)(126² + 8)
= (1² + 8)(10² + 8)(26² + 8)(83² + 8) = (1² + 8)(17² + 8)(26² + 8)(50² + 8)
= (2² + 8)(5² + 8)(7² + 8)(17² + 8)(26² + 8) = (7² + 8)(10² + 8)(17² + 8)(50² + 8).

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

67728

67728² = (3² + 8)(4² + 8)(18² + 8)(184² + 8) = (18² + 8)(20² + 8)(184² + 8).

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

67731

67731²± 2 are primes.

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

67804

67804² = (4² + 7)(90² + 7)(157² + 7).

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

67850

67850²± 3 are primes.

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

67852

67852²± 3 are primes.

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

67860

67860² = (1² + 9)(2² + 9)(3² + 9)(11² + 9)(123² + 9) = (1² + 9)(2² + 9)(7² + 9)(15² + 9)(51² + 9)
= (1² + 9)(3² + 9)(41² + 9)(123² + 9) = (1² + 9)(7² + 9)(9² + 9)(297² + 9)
= (1² + 9)(11² + 9)(15² + 9)(123² + 9) = (2² + 9)(3² + 9)(7² + 9)(11² + 9)(51² + 9)
= (3² + 9)(7² + 9)(41² + 9)(51² + 9) = (7² + 9)(11² + 9)(15² + 9)(51² + 9).

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

67862

67862²± 3 are primes.

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

67863

67863²± 2 are primes.

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

67900

67900²± 3 are primes.

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

67923

67923²± 2 are primes.

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

67924

67924²± 3 are primes.

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

67936

67936² = (2² + 7)(5² + 7)(3621² + 7).

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

67941

67941²± 2 are primes.

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

67963

67963² = 5552² + 5553² + 5554² + ... + 5697².

Page of Squares : First Upload October 20, 2012 ; Last Revised October 20, 2012
by Yoshio Mimura, Kobe, Japan

67986

67986²± 5 are primes.

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