Squares:64000s

64009

64009 = 253², and 64 = 8², 9 = 3².

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

64010

64010² = (1² + 1)(2² + 1)(80² + 1)(253² + 1)
= (1² + 1)(6² + 1)(80² + 1)(93² + 1) = (3² + 1)(80² + 1)(253² + 1).

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

64015

64015² = (1² + 6)(5² + 6)(17² + 6)(253² + 6).

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

64030

64030²= 1026 x 1027 + 1027 x 1028 + 1028 x 1029 +...+ 2373 x 2374.

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

64090

64090² = (1² + 1)(12² + 1)(38² + 1)(99² + 1)
= (1² + 1)(17² + 1)(38² + 1)(70² + 1) = (1² + 1)(4² + 1)(12² + 1)(13² + 1)(70² + 1)
= (1² + 1)(4² + 1)(41² + 1)(268² + 1) = (1² + 1)(4² + 1)(70² + 1)(157² + 1)
= (17² + 1)(38² + 1)(99² + 1) = (2² + 1)(4² + 1)(8² + 1)(21² + 1)(41² + 1)
= (4² + 1)(12² + 1)(13² + 1)(99² + 1) = (4² + 1)(13² + 1)(17² + 1)(70² + 1)
= (4² + 1)(18² + 1)(21² + 1)(41² + 1) = (4² + 1)(8² + 1)(41² + 1)(47² + 1)
= (4² + 1)(99² + 1)(157² + 1) = (5² + 1)(8² + 1)(38² + 1)(41² + 1)
= (1² + 4)(3² + 4)(5² + 4)(8² + 4)(179² + 4) = (1² + 9)(2² + 9)(5² + 9)(964² + 9)
= (1² + 9)(11² + 9)(22² + 9)(80² + 9) = (2² + 9)(4² + 9)(5² + 9)(7² + 9)(80² + 9)
= (2² + 9)(7² + 9)(29² + 9)(80² + 9) = (2² + 9)(11² + 9)(1559² + 9) = (5² + 9)(11² + 9)(964² + 9)
= (7² + 9)(22² + 9)(379² + 9) = (41² + 9)(1559² + 9).

Page of Squares : First Upload November 16, 2013 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

64092

64092² = (1² + 3)(2² + 3)(12² + 3)(999² + 3) = (5² + 3)(12² + 3)(999² + 3)
= (1² + 5)(3² + 5)(39² + 5)(179² + 5).

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

64130

64130²± 3 are primes.

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

64152

64152² = (1² + 8)(4² + 8)(5² + 8)(17² + 8)(44² + 8) = (1² + 8)(17² + 8)(28² + 8)(44² + 8).

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

64161

64161²± 2 are primes.

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

64166

64166²± 3 are primes.

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

64182

64182²± 5 are primes.

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

64206

64206² = (2² + 5)(6² + 5)(47² + 5)(71² + 5) = (6² + 5)(13² + 5)(16² + 5)(47² + 5).

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

64207

64207² = 11161² + 11162² + 11163² + ... + 11193².

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

64232

64232² = (1² + 3)(2² + 3)(5² + 3)(11² + 3)(206² + 3).

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

64270

64270²± 3 are primes.

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

64285

64285² = 1187² + 1189² + 1191² + 1193² + ... + 2979².

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

64343

64343² = 590² + 591² + 592² + ... + 2328²,
64343² = 181² + 183² + 185² + 187² + 189² + ... + 2917²

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

64348

64348²± 3 are primes.

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

64372

64372² = 1471² + 1473² + 1475² +1477² + ... + 3037².

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

64390

64390²± 3 are primes.

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

64428

64428²± 5 are primes.

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

64512

64512² = (2² - 1)(3² - 1)(7² - 1)(15² - 1)(127² - 1) = (3² - 1)(7² - 1)(13² - 1)(15² - 1)(17² - 1)
= (5² - 1)(7² - 1)(15² - 1)(127² - 1).

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

64516

64516 = 254², a zigzag square.

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

64524

64524²± 5 are primes.

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

64536

The quadratic polynomial -64536X² + 670872X - 546311 takes the values 245², 733², 941², 1051², 1093², 1075² at X = 1, 2,..., 6.

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

64548

64548² = (2² + 2)(4² + 2)(18² + 2)(344² + 2).

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

64626

64626²± 5 are primes.

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

64674

64674²± 5 are primes.

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

64680

427² + 64680 = 497², 427² - 64680 = 343².

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

64726

64726²± 3 are primes.

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

64744

The quadratic polynomial 64744X² - 312312X + 369369 takes the values 349², 61², 123², 395², 653², 909² at X = 1, 2,..., 6.

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

64758

64758²± 5 are primes.

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

64768

64768² = (1² + 7)(2² + 7)(3² + 7)(4² + 7)(13² + 7)(27² + 7)
= (1² + 7)(2² + 7)(4² + 7)(5² + 7)(9² + 7)(27² + 7)
= (1² + 7)(2² + 7)(4² + 7)(5² + 7)(13² + 7)(19² + 7) = (1² + 7)(2² + 7)(4² + 7)(19² + 7)(75² + 7)
= (1² + 7)(2² + 7)(4² + 7)(27² + 7)(53² + 7) = (1² + 7)(2² + 7)(9² + 7)(11² + 7)(65² + 7)
= (1² + 7)(2² + 7)(13² + 7)(19² + 7)(27² + 7) = (1² + 7)(3² + 7)(4² + 7)(5² + 7)(211² + 7)
= (1² + 7)(3² + 7)(27² + 7)(211² + 7) = (1² + 7)(4² + 7)(5² + 7)(27² + 7)(31² + 7)
= (1² + 7)(5² + 7)(19² + 7)(211² + 7) = (1² + 7)(11² + 7)(31² + 7)(65² + 7)
= (2² + 7)(3² + 7)(4² + 7)(5² + 7)(9² + 7)(19² + 7) = (2² + 7)(3² + 7)(4² + 7)(19² + 7)(53² + 7)
= (2² + 7)(3² + 7)(5² + 7)(13² + 7)(65² + 7) = (2² + 7)(3² + 7)(9² + 7)(19² + 7)(27² + 7)
= (2² + 7)(3² + 7)(65² + 7)(75² + 7) = (2² + 7)(4² + 7)(11² + 7)(13² + 7)(27² + 7)
= (2² + 7)(5² + 7)(53² + 7)(65² + 7) = (3² + 7)(4² + 7)(5² + 7)(19² + 7)(31² + 7)
= (3² + 7)(4² + 7)(9² + 7)(13² + 7)(27² + 7) = (3² + 7)(19² + 7)(27² + 7)(31² + 7)
= (4² + 7)(5² + 7)(11² + 7)(211² + 7) = (4² + 7)(5² + 7)(9² + 7)(13² + 7)(19² + 7)
= (4² + 7)(9² + 7)(19² + 7)(75² + 7) = (4² + 7)(9² + 7)(27² + 7)(53² + 7)
= (4² + 7)(13² + 7)(19² + 7)(53² + 7) = (9² + 7)(13² + 7)(19² + 7)(27² + 7)
= (11² + 7)(27² + 7)(211² + 7) = (13² + 7)(65² + 7)(75² + 7).

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

64800

64800² = (2² - 1)(3² - 1)(4² - 1)(7² - 1)(19² - 1)(26² - 1)
= (2² - 1)(4² - 1)(5² - 1)(7² - 1)(11² - 1)(26² - 1) = (2² - 1)(7² - 1)(11² - 1)(19² - 1)(26² - 1)
= (2² - 1)(9² - 1)(26² - 1)(161² - 1) = (4² - 1)(5² - 1)(7² - 1)(19² - 1)(26² - 1).

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

64824

64824² = (1² + 3)(17² + 3)(21² + 3)(90² + 3).

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

64854

64854²± 5 are primes.

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

64856

64856² = (2² + 7)(9² + 7)(23² + 7)(90² + 7) = (23² + 7)(31² + 7)(90² + 7).

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

64868

64868²± 3 are primes.

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

64890

64890² = (1² + 5)(5² + 5)(10² + 5)(472² + 5) = (1² + 5)(10² + 5)(43² + 5)(60² + 5)
= (4² + 5)(5² + 5)(43² + 5)(60² + 5) = (5² + 5)(25² + 5)(472² + 5) = (25² + 5)(43² + 5)(60² + 5).

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

64896

260² + 64896 = 364², 260² - 64896 = 52².

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

64898

64898²± 3 are primes.

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

64902

64902²± 5 are primes.

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

64910

64910²± 3 are primes.

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

64914

64914²= 992 x 993 + 993 x 994 + 994 x 995 +...+ 2387 x 2388.

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan

64944

64944² = (1² + 8)(2² + 8)(60² + 8)(104² + 8) = (1² + 8)(16² + 8)(22² + 8)(60² + 8)
= (2² + 8)(16² + 8)(19² + 8)(60² + 8) = (4² + 8)(5² + 8)(16² + 8)(142² + 8)
= (4² + 8)(5² + 8)(22² + 8)(104² + 8) = (4² + 8)(6² + 8)(19² + 8)(104² + 8)
= (5² + 8)(8² + 8)(22² + 8)(60² + 8) = (6² + 8)(8² + 8)(19² + 8)(60² + 8)
= (10² + 8)(60² + 8)(104² + 8) = (16² + 8)(28² + 8)(142² + 8) = (22² + 8)(28² + 8)(104² + 8).

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

64950

64950² = (2² + 6)(12² + 6)(1677² + 6).

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

64960

64960² = 1210² + 1211² + 1212² + ... + 2434².

Page of Squares : First Upload October 13, 2012 ; Last Revised October 13, 2012
by Yoshio Mimura, Kobe, Japan