Squares:73000s

73000

73000² = (1² + 4)(2² + 4)(11² + 4)(19² + 4)(54² + 4) = (6² + 4)(11² + 4)(19² + 4)(54² + 4).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73006

73006²± 3 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73032

73032² = (3² + 8)(4² + 8)(23² + 8)(156² + 8) = (20² + 8)(23² + 8)(156² + 8).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73056

73056² = 5337179136, 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

73058

73058²± 3 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73062

73062² = (1² + 2)(2² + 2)(3² + 2)(5² + 2)(14² + 2)(71² + 2)
= (1² + 2)(3² + 2)(4² + 2)(5² + 2)(8² + 2)(71² + 2)
= (1² + 2)(3² + 2)(4² + 2)(5² + 2)(11² + 2)(52² + 2) = (1² + 2)(3² + 2)(8² + 2)(22² + 2)(71² + 2)
= (1² + 2)(3² + 2)(11² + 2)(22² + 2)(52² + 2) = (1² + 2)(4² + 2)(71² + 2)(140² + 2)
= (1² + 2)(5² + 2)(8² + 2)(14² + 2)(71² + 2) = (1² + 2)(5² + 2)(11² + 2)(14² + 2)(52² + 2)
= (2² + 2)(4² + 2)(5² + 2)(19² + 2)(71² + 2) = (2² + 2)(19² + 2)(22² + 2)(71² + 2)
= (3² + 2)(4² + 2)(5² + 2)(14² + 2)(71² + 2) = (3² + 2)(14² + 2)(22² + 2)(71² + 2).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73074

73074²± 5 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73076

73076²± 3 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73080

73080² = (2² - 1)(5² - 1)(59² - 1)(146² - 1) = (2² - 1)(146² - 1)(289² - 1).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73112

73112² = (1² + 3)(4² + 3)(7² + 3)(1163² + 3).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73164

73164²± 5 are primes.

73164² = (1² + 3)(6² + 3)(8² + 3)(12² + 3)(59² + 3) = (2² + 3)(6² + 3)(7² + 3)(8² + 3)(75² + 3)
= (2² + 3)(6² + 3)(8² + 3)(9² + 3)(59² + 3) = (2² + 3)(6² + 3)(59² + 3)(75² + 3)
= (2² + 3)(8² + 3)(45² + 3)(75² + 3) = (6² + 3)(8² + 3)(19² + 3)(75² + 3).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73188

73188² = (2² + 8)(7² + 8)(45² + 8)(62² + 8) = (26² + 8)(45² + 8)(62² + 8).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73206

73206² = (2² + 5)(3² + 5)(4² + 5)(24² + 5)(59² + 5) = (2² + 5)(17² + 5)(24² + 5)(59² + 5)
= (4² + 5)(11² + 5)(24² + 5)(59² + 5).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73224

73224² = (4² + 8)(52² + 8)(287² + 8).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73242

73242² = 592² + 593² + 594² + ... + 2535².

Page of Squares : First Upload November 10, 2012 ; Last Revised November 10, 2012
by Yoshio Mimura, Kobe, Japan

73248

73248²± 5 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73346

73346² = (2² + 3)(11² + 3)(20² + 3)(124² + 3) = (7² + 3)(82² + 3)(124² + 3).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73360

73360²± 3 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73416

445² + 73416 = 521², 445² - 73416 = 353².

73461² = 323² + 324² + 325² + ... + 2531².

Page of Squares : First Upload November 10, 2012 ; Last Revised November 10, 2012
by Yoshio Mimura, Kobe, Japan

73440

73440² = (2² - 1)(3² - 1)(4² - 1)(7² - 1)(16² - 1)(35² - 1) = (2² - 1)(3² - 1)(26² - 1)(577² - 1)
= (2² - 1)(4² - 1)(19² - 1)(577² - 1) = (2² - 1)(7² - 1)(11² - 1)(16² - 1)(35² - 1)
= (4² - 1)(5² - 1)(7² - 1)(16² - 1)(35² - 1) = (5² - 1)(26² - 1)(577² - 1)
= (7² - 1)(16² - 1)(19² - 1)(35² - 1) = (16² - 1)(17² - 1)(271² - 1).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73444

73444² = (2² + 3)(5² + 3)(13² + 3)(400² + 3).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73447

73447, 73448, 73449, 73450, 73451 and 73452 are consecutive integers having square factors (the 7th case).

Page of Squares : First Upload December 14, 2013 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

73480

73480² = 3784 x 3785 + 3786 x 3787 + 3788 x 3789 + 3790 x 3791 + ... + 4422 x 4423.

Page of Squares : First Upload November 10, 2012 ; Last Revised November 10, 2012
by Yoshio Mimura, Kobe, Japan

73488

73488²± 5 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73500

73500² = (1² + 6)(2² + 6)(3² + 6)(8² + 6)(12² + 6)(22² + 6)
= (1² + 6)(2² + 6)(6² + 6)(8² + 6)(12² + 6)(13² + 6) = (1² + 6)(2² + 6)(6² + 6)(8² + 6)(162² + 6)
= (2² + 6)(6² + 6)(12² + 6)(13² + 6)(22² + 6) = (2² + 6)(6² + 6)(22² + 6)(162² + 6).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73510

73510²± 3 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73512

73512²± 5 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73556

73556²± 3 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73584

73584² = (2² - 1)(145² - 1)(293² - 1).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73592

73592²± 3 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73594

73594²± 3 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73619

73619² = 1393² + 1394² + 1395² + ... + 2666².

Page of Squares : First Upload November 10, 2012 ; Last Revised November 10, 2012
by Yoshio Mimura, Kobe, Japan

73632

73632²± 5 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73635

73635²± 2 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73677

73677²± 2 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73722

73722²± 5 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73730

73730² = (1² + 1)(10² + 1)(27² + 1)(192² + 1).

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

73767

73767²± 2 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73790

73790²± 3 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73832

73832²± 3 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73842

73842²± 5 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73856

73856²± 3 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73863

73863² = (2² + 5)(16² + 5)(1524² + 5).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73872

73872² = (1² + 8)(4² + 8)(7² + 8)(10² + 8)(64² + 8) = (2² + 8)(7² + 8)(44² + 8)(64² + 8)
= (7² + 8)(8² + 8)(26² + 8)(44² + 8) = (26² + 8)(44² + 8)(64² + 8).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73888

73888²= 1778 x 1779 + 1779 x 1780 + 1780 x 1781 +...+ 2801 x 2802.

Page of Squares : First Upload November 10, 2012 ; Last Revised November 10, 2012
by Yoshio Mimura, Kobe, Japan

73920

281² + 73920 = 391², 281² - 73920 = 71²,
274² + 73920 = 386², 274² - 73920 = 34².

73920² = (2² - 1)(3² - 1)(6² - 1)(23² - 1)(111² - 1) = (2² - 1)(3² - 1)(43² - 1)(351² - 1)
= (2² - 1)(6² - 1)(15² - 1)(21² - 1)(23² - 1) = (2² - 1)(6² - 1)(65² - 1)(111² - 1)
= (2² - 1)(9² - 1)(43² - 1)(111² - 1) = (3² - 1)(5² - 1)(6² - 1)(21² - 1)(43² - 1)
= (3² - 1)(7² - 1)(34² - 1)(111² - 1) = (3² - 1)(15² - 1)(23² - 1)(76² - 1)
= (3² - 1)(21² - 1)(29² - 1)(43² - 1) = (3² - 1)(34² - 1)(769² - 1)
= (5² - 1)(6² - 1)(23² - 1)(111² - 1) = (5² - 1)(43² - 1)(351² - 1)
= (7² - 1)(15² - 1)(21² - 1)(34² - 1) = (15² - 1)(65² - 1)(76² - 1)
= (23² - 1)(29² - 1)(111² - 1).

Page of Squares : First Upload November 10, 2012 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73950

73950² = (1² + 9)(4² + 9)(5² + 9)(22² + 9)(36² + 9) = (1² + 9)(22² + 9)(29² + 9)(36² + 9)
= (4² + 9)(9² + 9)(1559² + 9) = (5² + 9)(7² + 9)(36² + 9)(46² + 9)
= (7² + 9)(9² + 9)(22² + 9)(46² + 9).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73984

73984 = 272², a square with different digits.

Page of Squares : First Upload November 10, 2012 ; Last Revised November 10, 2012
by Yoshio Mimura, Kobe, Japan

73986

73986² = (3² + 2)(82² + 2)(272² + 2) = (25² + 2)(36² + 2)(82² + 2).

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan

73998

73998²± 5 are primes.

Page of Squares : First Upload March 29, 2014 ; Last Revised March 29, 2014
by Yoshio Mimura, Kobe, Japan