Squares:63000s

63000

265² + 63000 = 365², 265² - 63000 = 85².

63000² = (4² - 1)(6² - 1)(11² - 1)(251² - 1).

Page of Squares : First Upload October 6, 2012 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63002

63002² = 3969252004, and 39693969 = 63², 252004 = 502².

Page of Squares : First Upload October 6, 2012 ; Last Revised October 6, 2012
by Yoshio Mimura, Kobe, Japan

63042

63042²± 5 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63050

63050² = (1² + 9)(4² + 9)(31² + 9)(128² + 9).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63051

63051² = 3975428601, a square with different digits.

Page of Squares : First Upload October 6, 2012 ; Last Revised October 6, 2012
by Yoshio Mimura, Kobe, Japan

63054

63054²± 5 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63099

63099² = (1² + 8)(7² + 8)(19² + 8)(145² + 8).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63129

63129² = 3985270641, a square with different digits.

Page of Squares : First Upload October 6, 2012 ; Last Revised October 6, 2012
by Yoshio Mimura, Kobe, Japan

63130

63130²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63168

63168² = (3² - 1)(5² - 1)(48² - 1)(95² - 1).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63172

63172²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63242

63242²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63252

63252²± 5 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63262

63262² = 4002080644, a square with even digits.

Page of Squares : First Upload October 6, 2012 ; Last Revised October 6, 2012
by Yoshio Mimura, Kobe, Japan

63296

63296² = (1² + 7)(4² + 7)(6² + 7)(19² + 7)(37² + 7) = (3² + 7)(6² + 7)(37² + 7)(65² + 7).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63351

63351²± 2 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63360

404² + 63360 = 476², 404² - 63360 = 316².

63360² = (2² - 1)(3² - 1)(4² - 1)(7² - 1)(21² - 1)(23² - 1) = (2² - 1)(3² - 1)(5² - 1)(11² - 1)(241² - 1)
= (2² - 1)(3² - 1)(7² - 1)(21² - 1)(89² - 1) = (2² - 1)(3² - 1)(7² - 1)(9² - 1)(10² - 1)(21² - 1)
= (2² - 1)(3² - 1)(65² - 1)(199² - 1) = (2² - 1)(4² - 1)(7² - 1)(21² - 1)(65² - 1)
= (2² - 1)(5² - 1)(31² - 1)(241² - 1) = (2² - 1)(7² - 1)(11² - 1)(21² - 1)(23² - 1)
= (2² - 1)(9² - 1)(17² - 1)(241² - 1) = (3² - 1)(4² - 1)(9² - 1)(10² - 1)(65² - 1)
= (3² - 1)(4² - 1)(65² - 1)(89² - 1) = (3² - 1)(5² - 1)(19² - 1)(241² - 1)
= (3² - 1)(5² - 1)(23² - 1)(199² - 1) = (3² - 1)(9² - 1)(10² - 1)(11² - 1)(23² - 1)
= (3² - 1)(9² - 1)(23² - 1)(109² - 1) = (3² - 1)(11² - 1)(23² - 1)(89² - 1)
= (4² - 1)(5² - 1)(7² - 1)(21² - 1)(23² - 1) = (4² - 1)(11² - 1)(23² - 1)(65² - 1)
= (5² - 1)(7² - 1)(9² - 1)(10² - 1)(21² - 1) = (5² - 1)(7² - 1)(21² - 1)(89² - 1)
= (5² - 1)(65² - 1)(199² - 1) = (7² - 1)(19² - 1)(21² - 1)(23² - 1) = (9² - 1)(10² - 1)(11² - 1)(65² - 1)
= (9² - 1)(10² - 1)(23² - 1)(31² - 1) = (9² - 1)(65² - 1)(109² - 1) = (11² - 1)(65² - 1)(89² - 1)
= (23² - 1)(31² - 1)(89² - 1).

Page of Squares : First Upload October 6, 2012 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63364

63364²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63412

63412² = 4493² + 4494² + 4495² + ... + 4683².

Page of Squares : First Upload October 6, 2012 ; Last Revised October 6, 2012
by Yoshio Mimura, Kobe, Japan

63432

63432² = (1² + 8)(4² + 8)(4316² + 8).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63480

299² + 63480 = 391², 299² - 63480 = 161².

Page of Squares : First Upload October 6, 2012 ; Last Revised October 6, 2012
by Yoshio Mimura, Kobe, Japan

63504

63504 = 252², a zigzag square with different digits.

Page of Squares : First Upload October 6, 2012 ; Last Revised October 6, 2012
by Yoshio Mimura, Kobe, Japan

63510

63510² = (1² + 9)(8² + 9)(36² + 9)(65² + 9).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63525

63525² = (1² + 6)(3² + 6)(29² + 6)(213² + 6) = (1² + 6)(7² + 6)(15² + 6)(213² + 6)
= (3² + 6)(15² + 6)(29² + 6)(37² + 6).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63558

63558² = (3² + 2)(8² + 2)(31² + 2)(76² + 2).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63572

63572² = 701² + 703² + 705² + 707² + ... + 2907².

Page of Squares : First Upload October 6, 2012 ; Last Revised October 6, 2012
by Yoshio Mimura, Kobe, Japan

63616

63616² = (1² + 7)(5² + 7)(7² + 7)(8² + 7)(63² + 7) = (5² + 7)(8² + 7)(21² + 7)(63² + 7).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63630

63630² = (1² + 5)(10² + 5)(46² + 5)(55² + 5) = (4² + 5)(5² + 5)(46² + 5)(55² + 5)
= (25² + 5)(46² + 5)(55² + 5).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63636

63636² = 4049540496.

Page of Squares : First Upload October 6, 2012 ; Last Revised October 6, 2012
by Yoshio Mimura, Kobe, Japan

63650

63650² = 12981² + 12982² + 12983² + ... + 13004².

Page of Squares : First Upload October 6, 2012 ; Last Revised October 6, 2012
by Yoshio Mimura, Kobe, Japan

63666

63666² = (1² + 2)(2² + 2)(5² + 2)(28² + 2)(103² + 2) = (4² + 2)(5² + 2)(28² + 2)(103² + 2)
= (22² + 2)(28² + 2)(103² + 2).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63684

63684²± 5 are primes.

63684² = (1² + 5)(13² + 5)(19² + 5)(103² + 5).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63724

63724²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63747

63747²± 2 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63750

63750² = (4² + 9)(9² + 9)(29² + 9)(46² + 9).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63770

63770² = 4645 x 4646 + 4647 x 4648 + 4649 x 4650 + 4651 x 4652 + ... + 4993 x 4994.

Page of Squares : First Upload October 6, 2012 ; Last Revised October 6, 2012
by Yoshio Mimura, Kobe, Japan

63788

63788²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63798

63798² = (1² + 6)(5² + 6)(36² + 6)(120² + 6).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63839

63839 is the 5th prime for which the Legendre symbol (a/63839) = 1 for 1, 2, 3,..., 28.

Page of Squares : First Upload October 6, 2012 ; Last Revised October 6, 2012
by Yoshio Mimura, Kobe, Japan

63840

63840² = (3² - 1)(5² - 1)(6² - 1)(20² - 1)(39² - 1) = (3² - 1)(6² - 1)(20² - 1)(191² - 1)
= (3² - 1)(20² - 1)(29² - 1)(39² - 1) = (6² - 1)(15² - 1)(721² - 1).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63855

63855²± 2 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63880

63880² = (2² + 4)(6² + 4)(3571² + 4).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63894

63894²± 5 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63910

63910² = (1² + 6)(2² + 6)(7² + 6)(1030² + 6) = (4² + 6)(13² + 6)(1030² + 6)
= (7² + 6)(8² + 6)(1030² + 6) = (62² + 6)(1030² + 6).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63922

63922² = 4086022084, a square with even digits.

Page of Squares : First Upload October 6, 2012 ; Last Revised October 6, 2012
by Yoshio Mimura, Kobe, Japan

63937

63937² = (3² + 8)(15507² + 8).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63954

63954² = 19² + 21² + 23² + 25² + 27² + 29² + ... + 2905².

63954² = (1² + 2)(2² + 2)(3² + 2)(7² + 2)(10² + 2)(63² + 2) = (1² + 2)(2² + 2)(25² + 2)(602² + 2)
= (1² + 2)(3² + 2)(6² + 2)(41² + 2)(44² + 2) = (1² + 2)(3² + 2)(6² + 2)(7² + 2)(10² + 2)(25² + 2)
= (1² + 2)(3² + 2)(10² + 2)(25² + 2)(44² + 2) = (1² + 2)(6² + 2)(7² + 2)(19² + 2)(44² + 2)
= (1² + 2)(6² + 2)(13² + 2)(19² + 2)(24² + 2) = (1² + 2)(6² + 2)(41² + 2)(146² + 2)
= (1² + 2)(7² + 2)(8² + 2)(10² + 2)(63² + 2) = (1² + 2)(10² + 2)(25² + 2)(146² + 2)
= (1² + 2)(10² + 2)(58² + 2)(63² + 2) = (2² + 2)(10² + 2)(41² + 2)(63² + 2)
= (2² + 2)(3² + 2)(5² + 2)(24² + 2)(63² + 2) = (2² + 2)(3² + 2)(7² + 2)(25² + 2)(44² + 2)
= (2² + 2)(3² + 2)(13² + 2)(24² + 2)(25² + 2) = (2² + 2)(3² + 2)(13² + 2)(602² + 2)
= (2² + 2)(7² + 2)(25² + 2)(146² + 2) = (2² + 2)(7² + 2)(58² + 2)(63² + 2)
= (3² + 2)(10² + 2)(13² + 2)(146² + 2) = (3² + 2)(24² + 2)(25² + 2)(32² + 2)
= (3² + 2)(32² + 2)(602² + 2) = (3² + 2)(4² + 2)(7² + 2)(10² + 2)(63² + 2)
= (3² + 2)(5² + 2)(6² + 2)(24² + 2)(25² + 2) = (3² + 2)(5² + 2)(6² + 2)(602² + 2)
= (4² + 2)(25² + 2)(602² + 2) = (5² + 2)(8² + 2)(24² + 2)(63² + 2)
= (6² + 2)(7² + 2)(25² + 2)(58² + 2) = (6² + 2)(10² + 2)(25² + 2)(41² + 2)
= (7² + 2)(8² + 2)(25² + 2)(44² + 2) = (7² + 2)(10² + 2)(14² + 2)(63² + 2)
= (8² + 2)(13² + 2)(24² + 2)(25² + 2) = (8² + 2)(13² + 2)(602² + 2) = (25² + 2)(44² + 2)(58² + 2).

Page of Squares : First Upload October 6, 2012 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63974

63974²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

63975

63975²± 2 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan