---

55024

55024²= 1097 x 1098 + 1098 x 1099 + 1099 x 1100 + ... + 2182 x 2183.

Page of Squares : First Upload September 8, 2012 ; Last Revised September 8, 2012
by Yoshio Mimura, Kobe, Japan

---

55052

55052²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55111

55111² = (2² + 3)(20830² + 3).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55112

55112²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55119

55119²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55120

55120² = (2² + 4)(3² + 4)(4² + 4)(7² + 4)(166² + 4) = (2² + 4)(3² + 4)(7² + 4)(16² + 4)(46² + 4)
= (2² + 4)(7² + 4)(16² + 4)(166² + 4) = (3² + 4)(4² + 4)(7² + 4)(10² + 4)(46² + 4)
= (4² + 4)(7² + 4)(10² + 4)(166² + 4) = (7² + 4)(10² + 4)(16² + 4)(46² + 4).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55130

55130² = (17² + 9)(19² + 9)(166² + 9).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55144

55144² = (22² + 4)(30² + 4)(83² + 4).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55176

55176² = (12² + 8)(28² + 8)(159² + 8) = (4² + 8)(5² + 8)(12² + 8)(159² + 8).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55182

55182²± 5 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55200

55200² = (24² - 1)(47² - 1)(49² - 1) = (3² - 1)(9² - 1)(24² - 1)(91² - 1).

577² + 55200 = 623², 577² - 55200 = 527².

Page of Squares : First Upload September 8, 2012 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55221

55221²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55225

55225 = 235² is a square with 2kinds of digits.

55225 = (5 + 5 + 225)².

Page of Squares : First Upload September 8, 2012 ; Last Revised September 8, 2012
by Yoshio Mimura, Kobe, Japan

---

55233

55233² = (7² + 8)(31² + 8)(235² + 8).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55250

55250² = (1² + 1)(2² + 1)(3² + 1)(8² + 1)(18² + 1)(38² + 1) = (1² + 1)(2² + 1)(8² + 1)(38² + 1)(57² + 1)
= (1² + 1)(7² + 1)(8² + 1)(18² + 1)(38² + 1) = (1² + 1)(18² + 1)(38² + 1)(57² + 1)
= (2² + 1)(3² + 1)(4² + 1)(7² + 1)(268² + 1) = (2² + 1)(3² + 1)(4² + 1)(8² + 1)(13² + 1)(18² + 1)
= (2² + 1)(4² + 1)(7² + 1)(18² + 1)(47² + 1) = (2² + 1)(4² + 1)(8² + 1)(13² + 1)(57² + 1)
= (2² + 1)(5² + 1)(7² + 1)(18² + 1)(38² + 1) = (2² + 1)(7² + 1)(13² + 1)(268² + 1)
= (3² + 1)(8² + 1)(38² + 1)(57² + 1) = (4² + 1)(13² + 1)(18² + 1)(57² + 1)
= (4² + 1)(7² + 1)(8² + 1)(13² + 1)(18² + 1) = (1² + 4)(8² + 4)(9² + 4)(11² + 4)(29² + 4)
= (1² + 4)(11² + 4)(29² + 4)(76² + 4) = (9² + 4)(11² + 4)(536² + 4)
= (1² + 9)(46² + 9)(379² + 9) = (2² + 9)(4² + 9)(5² + 9)(11² + 9)(46² + 9)
= (2² + 9)(11² + 9)(29² + 9)(46² + 9) = (4² + 9)(5² + 9)(41² + 9)(46² + 9)
= (4² + 9)(29² + 9)(379² + 9) = (29² + 9)(41² + 9)(46² + 9).

Page of Squares : First Upload November 16, 2013 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55263

55263²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55272

55272²± 5 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55296

240² + 55296 = 336², 240² - 55296 = 48².

Page of Squares : First Upload September 8, 2012 ; Last Revised September 8, 2012
by Yoshio Mimura, Kobe, Japan

---

55299

55299²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55347

55347²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55350

55350² = (1² + 9)(6² + 9)(27² + 9)(96² + 9) = (3² + 9)(4² + 9)(6² + 9)(14² + 9)(27² + 9)
= (3² + 9)(4² + 9)(27² + 9)(96² + 9) = (3² + 9)(9² + 9)(14² + 9)(96² + 9)
= (6² + 9)(14² + 9)(21² + 9)(27² + 9) = (21² + 9)(27² + 9)(96² + 9).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55364

55364²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55380

55380² = 6112 x 6113 + 6114 x 6115 + 6116 x 6117 + 6118 x 6119 + ... + 6270 x 6271.

55380²= 781 x 782 + 782 x 783 + 783 x 784 + ... + 2130 x 2131.

Page of Squares : First Upload September 8, 2012 ; Last Revised September 8, 2012
by Yoshio Mimura, Kobe, Japan

---

55386

55386² = 331² + 333² + 335² + 337² + 339² + ... + 2641².

Page of Squares : First Upload September 8, 2012 ; Last Revised September 8, 2012
by Yoshio Mimura, Kobe, Japan

---

55404

55404² = (2² + 2)(5² + 2)(6² + 2)(22² + 2)(32² + 2).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55409

95540955409 = 309097².

Page of Squares : First Upload September 8, 2012 ; Last Revised September 8, 2012
by Yoshio Mimura, Kobe, Japan

---

55420

55420²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55440

55440² = (2² - 1)(3² - 1)(6² - 1)(8² - 1)(241² - 1) = (2² - 1)(3² - 1)(10² - 1)(15² - 1)(76² - 1)
= (2² - 1)(5² - 1)(6² - 1)(10² - 1)(111² - 1) = (2² - 1)(6² - 1)(7² - 1)(23² - 1)(34² - 1)
= (2² - 1)(10² - 1)(29² - 1)(111² - 1) = (2² - 1)(23² - 1)(34² - 1)(41² - 1)
= (3² - 1)(4² - 1)(10² - 1)(15² - 1)(34² - 1) = (3² - 1)(19601² - 1)
= (4² - 1)(10² - 1)(13² - 1)(111² - 1) = (5² - 1)(6² - 1)(8² - 1)(241² - 1)
= (5² - 1)(10² - 1)(15² - 1)(76² - 1) = (6² - 1)(10² - 1)(23² - 1)(41² - 1)
= (8² - 1)(9² - 1)(23² - 1)(34² - 1) = (8² - 1)(29² - 1)(241² - 1)
= (10² - 1)(11² - 1)(15² - 1)(34² - 1) = (15² - 1)(34² - 1)(109² - 1)
= (17² - 1)(43² - 1)(76² - 1) = (23² - 1)(34² - 1)(71² - 1).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55446

55446² = 3074258916 is a square with different digits.

Page of Squares : First Upload September 8, 2012 ; Last Revised September 8, 2012
by Yoshio Mimura, Kobe, Japan

---

55447

55447, 55448, 55449, 55450, 55451 and 55452 are six consecutive integers having square factors (the 5th case).

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

---

55482

55482²± 5 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55518

55518²± 5 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55524

55524² = 3082914576 is a square with different digits.

Page of Squares : First Upload September 8, 2012 ; Last Revised September 8, 2012
by Yoshio Mimura, Kobe, Japan

---

55566

55566² = (2² + 5)(4² + 5)(7² + 5)(17² + 5)(32² + 5) = (3² + 5)(4² + 5)(32² + 5)(101² + 5)
= (17² + 5)(32² + 5)(101² + 5).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55581

55581² = 3089247561 is a square with different digits.

Page of Squares : First Upload September 8, 2012 ; Last Revised September 8, 2012
by Yoshio Mimura, Kobe, Japan

---

55599

55599²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55604

55604²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55616

55616² = (1² + 7)(2² + 7)(3² + 7)(5² + 7)(262² + 7) = (1² + 7)(5² + 7)(13² + 7)(262² + 7)
= (1² + 7)(75² + 7)(262² + 7) = (2² + 7)(5² + 7)(11² + 7)(262² + 7)
= (3² + 7)(5² + 7)(9² + 7)(262² + 7) = (3² + 7)(53² + 7)(262² + 7).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55626

55626² = 3094251876 is a square with different digits.

Page of Squares : First Upload September 8, 2012 ; Last Revised September 8, 2012
by Yoshio Mimura, Kobe, Japan

---

55629

55629²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55650

55650² = (1² + 6)(3² + 6)(6² + 6)(838² + 6) = (1² + 6)(3² + 6)(8² + 6)(10² + 6)(63² + 6)
= (1² + 6)(3² + 6)(10² + 6)(12² + 6)(43² + 6) = (2² + 6)(6² + 6)(43² + 6)(63² + 6)
= (2² + 6)(10² + 6)(27² + 6)(63² + 6) = (3² + 6)(10² + 6)(22² + 6)(63² + 6)
= (6² + 6)(10² + 6)(13² + 6)(63² + 6).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55692

55692² = 550*551*552 + 552*553*554 + 554*555*556 + 556*557*558 + ... + 582*583*584.

Page of Squares : First Upload October 26, 2013 ; Last Revised October 26, 2013
by Yoshio Mimura, Kobe, Japan

---

55696

55696 = 236² is a square with 3 kinds of digits.

Page of Squares : First Upload September 8, 2012 ; Last Revised September 8, 2012
by Yoshio Mimura, Kobe, Japan

---

55713

55713²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55728

55728² = (1² + 8)(4² + 8)(10² + 8)(11² + 8)(32² + 8) = (1² + 8)(4² + 8)(32² + 8)(118² + 8)
= (2² + 8)(11² + 8)(32² + 8)(44² + 8) = (4² + 8)(8² + 8)(11² + 8)(118² + 8).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55760

55760² = (1² + 4)(2² + 4)(8² + 4)(18² + 4)(59² + 4) = (2² + 4)(26² + 4)(756² + 4)
= (6² + 4)(8² + 4)(18² + 4)(59² + 4).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55776

55776²± 5 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55796

55796² = (1² + 1)(5² + 1)(6² + 1)(31² + 1)(41² + 1).

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

---

55859

55859² = 3289² + 3291² + 3293² + 3295² + ... + 3785².

Page of Squares : First Upload September 8, 2012 ; Last Revised September 8, 2012
by Yoshio Mimura, Kobe, Japan

---

55868

55868² = 3121233424, a square every digit of which is non-zero and smaller than 5.

Page of Squares : First Upload September 18, 2013 ; Last Revised September 18, 2013
by Yoshio Mimura, Kobe, Japan

---

55888

55888²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55890

55890² = (2² + 5)(5² + 5)(20² + 5)(169² + 5) = (2² + 5)(7² + 5)(8² + 5)(15² + 5)(20² + 5)
= (5² + 5)(8² + 5)(20² + 5)(61² + 5) = (2² + 5)(15² + 5)(20² + 5)(61² + 5).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55930

55930² = 1009² + 1010² + 1011² + ... + 2183².

Page of Squares : First Upload September 8, 2012 ; Last Revised September 8, 2012
by Yoshio Mimura, Kobe, Japan

---

55932

55932²± 5 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

55973

55973² = 3132976729, and 31329 = 177², 76729 = 277².

Page of Squares : First Upload September 8, 2012 ; Last Revised September 8, 2012
by Yoshio Mimura, Kobe, Japan

---

55990

55990² = 5925² + 5926² + 5927² + ... + 6012².

Page of Squares : First Upload September 8, 2012 ; Last Revised September 8, 2012
by Yoshio Mimura, Kobe, Japan

---