Squares:35000s

35000

35000² = 1225000000, with 1² = 1 and 225000000 = 15000².

50³ + 35000 = 400², 50³ - 35000 = 300².

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35019

35019²± 2 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35037

35037²± 2 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35046

35046² = (2² + 2)(3² + 2)(5² + 2)(23² + 2)(36² + 2) = (5² + 2)(8² + 2)(23² + 2)(36² + 2).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35056

35056²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35058

35058²± 5 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35076

35076²± 5 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35088

35088² = (3² + 8)(4² + 8)(32² + 8)(54² + 8) = (20² + 8)(32² + 8)(54² + 8).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35100

35100² = (1² + 9)(2² + 9)(3² + 9)(4² + 9)(9² + 9)(15² + 9)
= (1² + 9)(2² + 9)(3² + 9)(6² + 9)(9² + 9)(11² + 9) = (1² + 9)(2² + 9)(9² + 9)(15² + 9)(21² + 9)
= (1² + 9)(3² + 9)(6² + 9)(9² + 9)(41² + 9) = (1² + 9)(3² + 9)(9² + 9)(11² + 9)(24² + 9)
= (1² + 9)(3² + 9)(15² + 9)(171² + 9) = (1² + 9)(6² + 9)(9² + 9)(11² + 9)(15² + 9)
= (2² + 9)(3² + 9)(9² + 9)(11² + 9)(21² + 9) = (3² + 9)(4² + 9)(9² + 9)(11² + 9)(15² + 9)
= (3² + 9)(9² + 9)(21² + 9)(41² + 9) = (4² - 1)(14² - 1)(25² - 1)(26² - 1)
= (4² - 1)(14² - 1)(649² - 1) = (9² + 9)(11² + 9)(15² + 9)(21² + 9) = (26² - 1)(1351² - 1).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35112

35112² = (97² - 1)(362² - 1).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35121

35121²± 2 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35140

35140² = 3849 x 3850 + 3851 x 3852 + 3853 x 3854 + 3855 x 3856 + ... + 4007 x 4008.

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35164

35164²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35172

35172² = 1237069584, a square with different digits.

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35176

35176²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35202

35202²± 5 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35208

35208² = (4² + 8)(36² + 8)(199² + 8).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35211

35211² = 500² + 501² + 502² + ... + 1566².

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35223

35223²± 2 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35244

35244² = (5² + 8)(6² + 8)(9² + 8)(98² + 8).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35253

35253²± 2 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35262

35262² = 651³ + 729³ + 834³.

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35279

35279 is the third prime number for which the Legendre symbol (a/35279) = 1 for a = 1, 2,..., 28.
35279 is the fifth prime number for which the Legendre symbol (a/35279) = 1 for a = 1,2,...,22.

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35280

35280² = (2² - 1)(6² - 1)(8² - 1)(15² - 1)(29² - 1) = (4² - 1)(6² - 1)(8² - 1)(13² - 1)(15² - 1).

287² + 35280 = 343², 287² - 35280 = 217².

Page of Squares : First Upload June 16 2012 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35308

35308² = (19² + 3)(26² + 3)(71² + 3) = (2² + 3)(7² + 3)(26² + 3)(71² + 3).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35310

35310² = (3² + 6)(4² + 6)(23² + 6)(84² + 6) = (18² + 6)(23² + 6)(84² + 6).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35337

35337² = 1248703569, a square with different digits.

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35344

35344 = 188², a square with 3 kinds of digits.

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35350

35350² = (13² + 6)(14² + 6)(188² + 6).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35358

35358² = 1191² + 1192² + 1193² + ... + 1758².

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35360

35360² = (1² + 4)(2² + 4)(3² + 4)(4² + 4)(8² + 4)(42² + 4)
= (1² + 4)(2² + 4)(8² + 4)(16² + 4)(42² + 4) = (1² + 4)(4² + 4)(8² + 4)(10² + 4)(42² + 4)
= (2² + 4)(3² + 4)(4² + 4)(8² + 4)(9² + 4)(10² + 4) = (2² + 4)(3² + 4)(4² + 4)(8² + 4)(94² + 4)
= (2² + 4)(3² + 4)(4² + 4)(10² + 4)(76² + 4) = (2² + 4)(3² + 4)(8² + 4)(16² + 4)(26² + 4)
= (2² + 4)(8² + 4)(9² + 4)(10² + 4)(16² + 4) = (2² + 4)(8² + 4)(16² + 4)(94² + 4)
= (2² + 4)(8² + 4)(36² + 4)(42² + 4) = (2² + 4)(10² + 4)(16² + 4)(76² + 4)
= (3² + 4)(4² + 4)(6² + 4)(8² + 4)(42² + 4) = (3² + 4)(4² + 4)(8² + 4)(10² + 4)(26² + 4)
= (4² + 4)(8² + 4)(10² + 4)(94² + 4) = (6² + 4)(8² + 4)(16² + 4)(42² + 4)
= (8² + 4)(10² + 4)(16² + 4)(26² + 4).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35376

35376² = (4² + 8)(6² + 8)(27² + 8)(40² + 8).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35380

35380² = (1² + 1)(11² + 1)(17² + 1)(133² + 1).

Page of Squares : First Upload November 9, 2013 ; Last Revised November 9, 2013
by Yoshio Mimura, Kobe, Japan

35397

35397² = 516² + 517² + 518² + ... + 1573².

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35425

35425² = (1² + 4)(3² + 4)(11² + 4)(393² + 4).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35475

35475²± 2 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35532

35532² = (1² + 5)(3² + 5)(7² + 5)(18² + 5)(29² + 5).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35540

35540²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35568

35568²± 5 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35574

35574² = (1² + 6)(4² + 6)(6² + 6)(15² + 6)(29² + 6).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35584

35584²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35595

35595²± 2 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35596

35596²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35600

35600² = (1² + 4)(2² + 4)(4² + 4)(6² + 4)(199² + 4) = (2² + 4)(4² + 4)(14² + 4)(199² + 4).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35606

35606²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35607

35607² = 1763² + 1765² + 1767² + 1769² + ... + 2355².

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35616

The quadratic polynomial 35616X² - 60984X + 408529 takes the values 619², 655², 739², 857², 997², 1151² at X = 1, 2,..., 6,

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35640

303² + 35640 = 357², 303² - 35640 = 237².

35640² = (2² - 1)(4² - 1)(5² - 1)(10² - 1)(109² - 1) = (2² - 1)(4² - 1)(11² - 1)(485² - 1)
= (2² - 1)(10² - 1)(19² - 1)(109² - 1) = (4² - 1)(19² - 1)(485² - 1) = (3² - 1)(26² - 1)(485² - 1).

Page of Squares : First Upload June 16 2012 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35662

35662²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35696

35696²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35721

35721 = 189², a square with different digits.

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35728

35728² = (2² + 7)(3² + 7)(14² + 7)(189² + 7) = (2² + 7)(7² + 7)(14² + 7)(101² + 7)
= (13² + 7)(14² + 7)(189² + 7).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35739

35739² = (1² + 2)(13² + 2)(25² + 2)(63² + 2).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35755

35755² = 5032² + 5033² + 5034² + ... + 5081².

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35757

35757² = 1278563049, a square with different digits.

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35776

35776²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35805

35805² = (3² + 6)(5² + 6)(29² + 6)(57² + 6) = (5² + 6)(7² + 6)(15² + 6)(57² + 6).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35815

35815² = 956² + 957² + 958² + ... + 1677².

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35816

35816² = (2² + 7)(9² + 7)(20² + 7)(57² + 7) = (2² + 7)(17² + 7)(20² + 7)(31² + 7)
= (20² + 7)(31² + 7)(57² + 7).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35846

35846²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35853

35853² = 1285437609, a square with different digits.

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35880

269² + 35880 = 329², 269² - 35880 = 191².

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35904

545² + 35904 = 577², 545² - 35904 = 511².

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35939

35939² = 2025² + 2027² + 2029² + 2031² + ... + 2521².

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan

35943

35943²± 2 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35974

35974²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

35945

35945² = 301² + 302² + 303² + ... + 1574².

Page of Squares : First Upload June 16 2012 ; Last Revised June 16, 2012
by Yoshio Mimura, Kobe, Japan