---

11000

11000²± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11001

11001² = 121022001 is a square consisting of 3 kinds of digits (0,1,2).

11001² = 121022001 is a reversible square (100220121 = 10011²).

11001² = 121022001, and 1 / 2 * 10 * 2200 + 1 = 11001.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11002

11002² = 121044004 is a reversible square (400440121 = 20011²).

11002² = 121044004, and 1 * 2 + 10 * 4400 / 4 = 11002.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11003

11003² = 121066009 is a reversible square (900660121 = 30011²).

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11005

11005² = 121110025, and 1 - 2 - 1 + 11002 + 5 = 11005.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11008

11008² = (3² + 7)(6² + 7)(11² + 7)(37² + 7).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11011

11011² = 121242121 is a palindromic square consisting of 3 kinds of digits (1,2,4).

11011² = 121242121 is a square pegged by 2.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11012

11012²± 3 are primes.

11012² = 121264144 is a reversible square (441462121 = 21011²).

Page of Squares : First Upload December 20, 2011 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11013

11013² = 121286169 is a reversible square (961682121 = 31011²).

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11016

11016² = (1² + 8)(3² + 8)(20² + 8)(44² + 8) = (1² + 8)(4² + 8)(20² + 8)(37² + 8).

11016² = 121352256, and 1 * 213 * 52 - 2 * 5 * 6 = 11016.

Page of Squares : First Upload December 20, 2011 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11021

11021² = 121462441 is a reversible square (144264121 = 12011²).

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11022

11022² = 121484484 is a reversible square (484484121 = 22011²).

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11024

11024² = 21³ + 22³ + 23³ + ... + 148³.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11028

11028² = 121616784, and 121 * 6 * 16 - 7 * 84 = 11028.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11031

11031² = 121682961 is a reversible square (169286121 = 13011²).

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11034

11034² = 121749156, and 121 - 7 + 4 * 91 * 5 * 6 = 11034.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11037

11037²± 2 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11043

11043² = 3³ + 6³ + 12³ + 87³ + 495³.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11046

11046²± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11050

11050² = 91 * 92 + 92 * 93 + 93 * 94 + 94 * 95 + ... + 715 * 716.

11050² = (1² + 1)(2² + 1)(13² + 1)(268² + 1) = (1² + 1)(2² + 1)(3² + 1)(4² + 1)(268² + 1)
= (1² + 1)(2² + 1)(4² + 1)(18² + 1)(47² + 1) = (1² + 1)(2² + 1)(5² + 1)(18² + 1)(38² + 1)
= (1² + 1)(4² + 1)(7² + 1)(268² + 1) = (1² + 1)(4² + 1)(8² + 1)(13² + 1)(18² + 1)
= (2² + 1)(13² + 1)(18² + 1)(21² + 1) = (2² + 1)(3² + 1)(4² + 1)(18² + 1)(21² + 1)
= (2² + 1)(3² + 1)(4² + 1)(8² + 1)(47² + 1) = (2² + 1)(3² + 1)(5² + 1)(8² + 1)(38² + 1)
= (2² + 1)(4² + 1)(21² + 1)(57² + 1) = (2² + 1)(4² + 1)(5² + 1)(13² + 1)(18² + 1)
= (2² + 1)(4² + 1)(7² + 1)(8² + 1)(21² + 1) = (2² + 1)(8² + 1)(13² + 1)(47² + 1)
= (3² + 1)(13² + 1)(268² + 1) = (3² + 1)(4² + 1)(18² + 1)(47² + 1)
= (3² + 1)(5² + 1)(18² + 1)(38² + 1) = (4² + 1)(47² + 1)(57² + 1)
= (4² + 1)(7² + 1)(18² + 1)(21² + 1) = (4² + 1)(7² + 1)(8² + 1)(47² + 1)
= (5² + 1)(38² + 1)(57² + 1) = (5² + 1)(7² + 1)(8² + 1)(38² + 1)
= (13² + 1)(18² + 1)(47² + 1) = (1² + 4)(9² + 4)(536² + 4)
= (2² + 9)(5² + 9)(11² + 9)(46² + 9) = (29² + 9)(379² + 9) = (4² + 9)(5² + 9)(379² + 9)
= (5² + 9)(41² + 9)(46² + 9).

Page of Squares : First Upload December 20, 2011 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11051

11051² = 122124601, and 12 + 2 * 12 * 460 - 1 = 11051.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11052

11052²± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11055

11055² = 122213025, and 1 / 2 * 22130 - 2 * 5 = 11055.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11058

11058² = (4² + 3)(15² + 3)(168² + 3).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11070

11070² = (1² + 5)(6² + 5)(20² + 5)(35² + 5) = (3² + 9)(27² + 9)(96² + 9)
= (3² + 9)(6² + 9)(14² + 9)(27² + 9).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11073

11073² = 122611329, and 12261 - 132 * 9 = 11073.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11082

11082²± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11088

11088² = 122943744, and 1 * 2 * 294 * 3 / 7 * 44 = 11088.

11088² = (2² - 1)(10² - 1)(15² - 1)(43² - 1).

11088² = (1³)(2³ + 3³ + 4³ + 5³)(6³ + 6³ + 7³ + ... + 38³).

Page of Squares : First Upload December 20, 2011 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11095

11095² = 123099025, and 1 * 230 * 9 + 9025 = 1230 * 9 +- 9 * 0 + 25 = 11095.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11096

11096² = 123121216, and 12312 - 1216 = 11096.

11096² = (12² + 8)(900² + 8).

Page of Squares : First Upload December 20, 2011 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11097

11097² = 123143409, and 1 * 231 * 4 * 3 * 4 +- 0 + 9 = 11097.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11099

11099² = S2(311) + S2(697), where S2(n) = 1² + ... + n².

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11101

11101² = 123232201 is a reversible square (102232321 = 10111²).

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11102

11102² = 123254404 is a reversible square (404452321 = 20111²).

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11103

11103² = 123276609 is a reversible square (906672321 = 30111²).

11103²± 2 are primes.

Page of Squares : First Upload December 20, 2011 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11104

11104² = 123298816, and 1232 * 9 + 8 - 8 + 16 = 1232 * 9 + 8 / 8 * 16 = 1232 * 9 - 8 + 8 + 16 = 1232 * 9 * 8 / 8 + 16 = 1232 * 9 / 8 * 8 + 16.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11108

11108² = 123387664, and 1 + 23 + 3 * 8 * 7 * 66 - 4 = 11108.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11111

11111² = 123454321 is a palindromic square.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11112

11112² = 123476544 is a reversible square (445674321 = 21111²).

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11113

11113² = 123498769 is a reversible square (967894321 = 31111²).

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11116

11116² = 123565456, and 1235 / 6 * 54 - 5 + 6 = 11116.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11121

11121² = 123676641 is a reversible square (146676321 = 12111²).

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11122

11122² = 123698884 is a reversible square (488896321 = 22111²).

11122² = 123698884, and 1236 * 9 + 8 - 8 - 8 / 4 = 1236 * 9 - 8 + 8 - 8 / 4 = 1236 * 9 - 8 * 8 / 8 / 4 = 1236 * 9 - 8 / 8 * 8 / 4 = 1236 * 9 * 8 / 8 - 8 / 4 = 1236 * 9 / 8 * 8 - 8 / 4 = 11122.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11124

11124² = 123743376, and 123 * 74 + 337 * 6 = 11124.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11125

11125² = 123765625, and 1 = 1², 23765625 = 4875².

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11130

11130² = (1² + 6)(6² + 6)(10² + 6)(63² + 6) = (3² + 6)(6² + 6)(10² + 6)(43² + 6).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11144

11144²± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11164

11164²± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11172

11172² = (12² + 3)(15² + 3)(61² + 3) = (2² + 3)(12² + 3)(15² + 3)(23² + 3)
= (2² + 3)(3² + 3)(4² + 3)(12² + 3)(23² + 3) = (2² + 3)(4² + 3)(5² + 3)(12² + 3)(15² + 3)
= (3² + 3)(4² + 3)(12² + 3)(61² + 3) = (4² + 3)(9² + 3)(12² + 3)(23² + 3).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11178

11178² = (2² + 5)(7² + 5)(8² + 5)(61² + 5).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11191

11191² = S2(249) + S2(711), where S2(n) = 1² + ... + n².

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11201

11201² = 125462401 is a reversible square (104264521 = 10211²).

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11202

11202² = 125484804 is a reversible square (408484521 = 20211²).

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11205

11205²± 2 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11211

11211² = 125686521 is a palindromic square.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11214

11214² = (1² + 5)(2² + 5)(23² + 5)(66² + 5) = (1² + 5)(2² + 5)(4² + 5)(333² + 5)
= (2² + 5)(11² + 5)(333² + 5) = (4² + 5)(7² + 5)(333² + 5) = (7² + 5)(23² + 5)(66² + 5).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11226

11226²± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11232

11232² = (2² - 1)(5² - 1)(25² - 1)(53² - 1).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11234

11234²± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11236

11236 is a square with non-decreasing digits (11236 = 106²).

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11242

11242² = (1² + 6)(40² + 6)(106² + 6).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11250

11250² = (3² + 9)(4² + 9)(6² + 9)(79² + 9) = (6² + 9)(21² + 9)(79² + 9).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11256

11256² = (1² + 3)(2² + 3)(3² + 3)(8² + 3)(75² + 3) = (1² + 3)(8² + 3)(9² + 3)(75² + 3)
= (3² + 3)(5² + 3)(8² + 3)(75² + 3).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11260

11260² = 474 * 475 + 476 * 477 + 478 * 479 + 480 * 481 + ... + 952 * 953.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11264

11264² = (1² + 7)(2² + 7)(3² + 7)(5² + 7)(53² + 7) = (1² + 7)(3² + 7)(13² + 7)(75² + 7)
= (1² + 7)(5² + 7)(13² + 7)(53² + 7) = (1² + 7)(5² + 7)(9² + 7)(75² + 7)
= (1² + 7)(53² + 7)(75² + 7) = (11² + 7)(13² + 7)(75² + 7) = (2² + 7)(3² + 7)(11² + 7)(75² + 7)
= (2² + 7)(3² + 7)(5² + 7)(11² + 7)(13² + 7) = (2² + 7)(5² + 7)(11² + 7)(53² + 7)
= (3² + 7)(5² + 7)(9² + 7)(53² + 7).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11269

11269² = 1438² + 1439² + 1440² + ... + 1496².

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11271

11271²± 2 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11284

11284² = (2² + 3)(11² + 3)(19² + 3)(20² + 3) = (2² + 3)(11² + 3)(383² + 3)
= (7² + 3)(19² + 3)(82² + 3).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11286

11286²± 5 are primes.

11286² = (1² + 2)(2² + 2)(3² + 2)(25² + 2)(32² + 2)
= (1² + 2)(2² + 2)(3² + 2)(5² + 2)(6² + 2)(25² + 2) = (1² + 2)(2² + 2)(5² + 2)(8² + 2)(63² + 2)
= (1² + 2)(2² + 2)(8² + 2)(13² + 2)(25² + 2) = (1² + 2)(4² + 2)(6² + 2)(13² + 2)(19² + 2)
= (1² + 2)(5² + 2)(6² + 2)(8² + 2)(25² + 2) = (1² + 2)(8² + 2)(25² + 2)(32² + 2)
= (14² + 2)(25² + 2)(32² + 2) = (2² + 2)(13² + 2)(14² + 2)(25² + 2) = (2² + 2)(25² + 2)(184² + 2)
= (2² + 2)(3² + 2)(22² + 2)(63² + 2) = (2² + 2)(3² + 2)(4² + 2)(13² + 2)(25² + 2)
= (2² + 2)(3² + 2)(4² + 2)(5² + 2)(63² + 2) = (2² + 2)(5² + 2)(14² + 2)(63² + 2)
= (3² + 2)(4² + 2)(25² + 2)(32² + 2) = (3² + 2)(4² + 2)(5² + 2)(6² + 2)(25² + 2)
= (3² + 2)(5² + 2)(6² + 2)(8² + 2)(13² + 2) = (3² + 2)(6² + 2)(22² + 2)(25² + 2)
= (3² + 2)(8² + 2)(13² + 2)(32² + 2) = (4² + 2)(5² + 2)(8² + 2)(63² + 2)
= (4² + 2)(8² + 2)(13² + 2)(25² + 2) = (5² + 2)(6² + 2)(14² + 2)(25² + 2)
= (6² + 2)(13² + 2)(140² + 2) = (8² + 2)(22² + 2)(63² + 2).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11308

11308²± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11310

11310² = (2² + 9)(7² + 9)(11² + 9)(36² + 9) = (4² + 9)(7² + 9)(297² + 9)
= (7² + 9)(36² + 9)(41² + 9).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11322

11322, 11323, 11324 and 11325 are four consecutive integers having square factors (the 9th case).

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

---

11326

11326² = (3² + 5)(3027² + 5).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11336

11336² = (2² + 4)(10² + 4)(393² + 4).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11340

11340² = (1² + 5)(2² + 5)(3² + 5)(5² + 5)(7² + 5)(10² + 5)
= (1² + 5)(2² + 5)(5² + 5)(11² + 5)(25² + 5) = (1² + 5)(3² + 5)(5² + 5)(11² + 5)(20² + 5)
= (1² + 5)(4² + 5)(5² + 5)(7² + 5)(25² + 5) = (1² + 5)(5² + 5)(7² + 5)(10² + 5)(11² + 5)
= (1² + 5)(5² + 5)(7² + 5)(115² + 5) = (2² + 5)(3² + 5)(5² + 5)(7² + 5)(25² + 5)
= (2² - 1)(4² - 1)(7² - 1)(244² - 1) = (5² + 5)(7² + 5)(11² + 5)(25² + 5)
= (8² - 1)(26² - 1)(55² - 1).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

1148

11348²± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11350

11350²± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11352

11352² = (4² + 8)(11² + 8)(204² + 8).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11361

11361²± 2 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11372

11372²± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11385

11385² = 129618225, and 1296 = 36², 18225 = 135².

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11391

11391²± 2 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11416

11416²± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11424

11424² = (7² - 1)(33² - 1)(50² - 1).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11433

11433²± 2 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

---

11442

11442² is a sum of odd consecutive primes (3 + 5 + 7 + 11 + ... + 52081).

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11449

11449 is a square with non-decreasing digits (11449 = 107²).

11449 is a square consisting of 3 kinds of digits (1,4,9).

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11470

11470² = 652 * 653 + 654 * 655 + 656 * 657 + 658 * 659 + ... + 1020 * 1021.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11481

1² + 3² + 5² + 7² + 9² + ... + 11481² is a square (46611179²).

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

---

11482

11482² = (1² + 1)(8119² + 1).

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

---

11495

11495² = 1985² + 1986² + 1987² + ... + 2017².

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

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11496

11496²± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11520

11520² = (2² - 1)(3² - 1)(7² - 1)(11² - 1)(31² - 1) = (3² - 1)(4² - 1)(5² - 1)(7² - 1)(31² - 1)
= (3² - 1)(4² - 1)(7² - 1)(9² - 1)(17² - 1) = (3² - 1)(5² - 1)(17² - 1)(49² - 1)
= (3² - 1)(7² - 1)(19² - 1)(31² - 1) = (5² - 1)(7² - 1)(11² - 1)(31² - 1)
= (7² - 1)(9² - 1)(11² - 1)(17² - 1).

164² + 11520 = 196², 164² - 11520 = 124².

Page of Squares : First Upload February 25, 2012 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11523

11523² = S2(349) + S2(708), where S2(n) = 1² + ... + n².

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

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11550

11550² = (1² + 6)(2² + 6)(3² + 6)(12² + 6)(29² + 6) = (1² + 6)(2² + 6)(3² + 6)(7² + 6)(48² + 6)
= (1² + 6)(2² + 6)(6² + 6)(213² + 6) = (1² + 6)(2² + 6)(7² + 6)(12² + 6)(15² + 6)
= (1² + 6)(3² + 6)(12² + 6)(92² + 6) = (1² + 6)(3² + 6)(18² + 6)(62² + 6)
= (1² + 6)(3² + 6)(4² + 6)(13² + 6)(18² + 6) = (1² + 6)(3² + 6)(4² + 6)(6² + 6)(37² + 6)
= (1² + 6)(3² + 6)(7² + 6)(8² + 6)(18² + 6) = (1² + 6)(6² + 6)(18² + 6)(37² + 6)
= (1² + 6)(7² + 6)(12² + 6)(48² + 6) = (12² + 6)(15² + 6)(62² + 6) = (13² + 6)(18² + 6)(48² + 6)
= (2² + 6)(13² + 6)(15² + 6)(18² + 6) = (2² + 6)(3² + 6)(15² + 6)(62² + 6)
= (2² + 6)(3² + 6)(4² + 6)(13² + 6)(15² + 6) = (2² + 6)(3² + 6)(4² + 6)(7² + 6)(27² + 6)
= (2² + 6)(3² + 6)(7² + 6)(8² + 6)(15² + 6) = (2² + 6)(6² + 6)(15² + 6)(37² + 6)
= (2² + 6)(7² + 6)(18² + 6)(27² + 6) = (3² + 6)(4² + 6)(13² + 6)(48² + 6)
= (3² + 6)(4² + 6)(6² + 6)(7² + 6)(13² + 6) = (3² + 6)(48² + 6)(62² + 6)
= (3² + 6)(6² + 6)(7² + 6)(62² + 6) = (3² + 6)(7² + 6)(18² + 6)(22² + 6)
= (3² + 6)(7² + 6)(8² + 6)(48² + 6) = (3² + 6)(8² + 6)(12² + 6)(29² + 6)
= (4² + 6)(12² + 6)(13² + 6)(15² + 6) = (4² + 6)(15² + 6)(162² + 6)
= (4² + 6)(7² + 6)(12² + 6)(27² + 6) = (6² + 6)(37² + 6)(48² + 6)
= (6² + 6)(7² + 6)(13² + 6)(18² + 6) = (6² + 6)(8² + 6)(213² + 6)
= (7² + 6)(8² + 6)(12² + 6)(15² + 6).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11570

11570² = (1² + 4)(3² + 4)(21² + 4)(68² + 4) = (1² + 9)(2² + 9)(13² + 9)(76² + 9)
= (11² + 9)(13² + 9)(76² + 9) = (3² + 4)(16² + 4)(199² + 4).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11592

11592²± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11600

11600² = (1² + 4)(2² + 4)(5² + 4)(14² + 4)(24² + 4) = (1² + 4)(4² + 4)(14² + 4)(82² + 4)
= (1² + 4)(4² + 4)(5² + 4)(6² + 4)(34² + 4) = (1² + 4)(6² + 4)(24² + 4)(34² + 4)
= (14² + 4)(24² + 4)(34² + 4) = (2² + 4)(4² + 4)(11² + 4)(82² + 4)
= (4² + 4)(5² + 4)(14² + 4)(34² + 4) = (5² + 4)(6² + 4)(14² + 4)(24² + 4).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11616

110² + 11616 = 154², 110² - 11616 = 22².

Page of Squares : First Upload February 25, 2012 ; Last Revised February 25, 2012
by Yoshio Mimura, Kobe, Japan

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11624

11624² = 135117376, 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

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11628

11628² = (1² + 2)(2² + 2)(6² + 2)(10² + 2)(44² + 2) = (14² + 8)(26² + 8)(31² + 8)
= (18² - 1)(647² - 1) = (2² + 2)(6² + 2)(24² + 2)(32² + 2) = (2² + 8)(14² + 8)(235² + 8)
= (2² + 8)(3² + 8)(26² + 8)(31² + 8) = (2² + 8)(7² + 8)(14² + 8)(31² + 8)
= (3² + 8)(7² + 8)(14² + 8)(26² + 8) = (4² + 2)(6² + 2)(10² + 2)(44² + 2).

11628² = (1³ + 2³ + 3³ + ... + 8³)(9³ + 10³ + 11³ + ... + 25³).

Page of Squares : First Upload February 9, 2013 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11638

11638²± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11656

11656²± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11664

11664² = (1² + 8)(8² + 8)(10² + 8)(44² + 8).

11664 is a square (108²) consisting of 3 kinds of digits (1,4,6).

Page of Squares : First Upload December 20, 2011 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11682

11682² = (1² + 2)(2² + 2)(3² + 2)(23² + 2)(36² + 2) = (1² + 2)(8² + 2)(23² + 2)(36² + 2)
= (14² + 2)(23² + 2)(36² + 2) = (3² + 2)(4² + 2)(23² + 2)(36² + 2).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11700

11700² = (1² + 9)(11² + 9)(15² + 9)(21² + 9) = (1² + 9)(2² + 9)(3² + 9)(11² + 9)(21² + 9)
= (1² + 9)(3² + 9)(21² + 9)(41² + 9) = (1² + 9)(3² + 9)(4² + 9)(11² + 9)(15² + 9).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11726

11726² = S2(466) + S2(677), where S2(n) = 1² + ... + n².

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

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11754

The sum of the divisors of 11754² is a square (19019²).

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

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11760

11760² = (8² - 1)(15² - 1)(99² - 1) = (3³ + 8)(4³ + 8)(38³ + 8).

119² + 11760 = 161², 119² - 11760 = 49².

Page of Squares : First Upload February 25, 2012 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11770

11770² = (2² + 6)(3722² + 6).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11776

11776² = (1² + 7)(3² + 7)(4² + 7)(11² + 7)(19² + 7) = (1² + 7)(5² + 7)(11² + 7)(65² + 7)
= (3² + 7)(5² + 7)(19² + 7)(27² + 7) = (65² + 7)(181² + 7).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11780

11780²± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11781

11781² = 214² + 215² + 216² + ... + 752².

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

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11785

The quadratic polynomial 11785X² - 57080X + 76624 takes the values 177², 98², 107², 192², 293², 398² at X = 1, 2,..., 6

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

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11792

11792² = (2² + 7)(9² + 7)(379² + 7) = (31² + 7)(379² + 7) = (5² + 7)(23² + 7)(90² + 7).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11794

11794p>2± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11826

11826² = 139854276, a square consisting of different digits.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

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11866

11866² = (5² + 9)(2035² + 9).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11880

11880² = (10² - 1)(11² - 1)(109² - 1) = (3² - 1)(4² - 1)(10² - 1)(109² - 1).

11880² = 449 * 450 + 450 * 451 + 451 * 452 +...+ 800 * 801.

183² + 11880 = 213², 183² - 11880 = 147².

Page of Squares : First Upload December 20, 2011 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11881

11881 is a square (109²) consisting of 2 kinds of digits 1 and 8.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

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11886

11886²± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11890

11890² = (9² + 1)(32² + 1)(41² + 1) = (7² + 9)(14² + 9)(109² + 9).

Page of Squares : First Upload November 9, 2013 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11894

11894²± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11900

11900 = 18² + 19² + ... + 34² = 35² + 36² + ... + 42².

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

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11934

11934² = (12² + 9)(15² + 9)(63² + 9) = (2² + 9)(3² + 9)(12² + 9)(63² + 9).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11936

11936² = (1² + 7)(3² + 7)(1055² + 7) = (11² + 7)(1055² + 7).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11937

11937²± 2 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11955

11955² = (2³ + 7)(212³ + 7).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11958

11958²± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11960

11960²± 3 are primes.

11960² = S2(144) + S2(752), where S2(n) = 1² + ... + n².

Page of Squares : First Upload December 20, 2011 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11985

11985²± 2 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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11990

11990² = S2(589) + S2(609), where S2(n) = 1² + ... + n².

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

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11997

11997²± 2 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

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