---

56014

56014²± 3 are primes.

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

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56048

56048²± 3 are primes.

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

---

56070

56070² = (2² + 5)(5² + 5)(10² + 5)(333² + 5) = (5² + 5)(66² + 5)(155² + 5).

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

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56080

56080²± 3 are primes.

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

---

56085

56085²± 2 are primes.

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

---

56088

56088² = (4² + 8)(19² + 8)(596² + 8).

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

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56144

56144² = (1² + 7)(2² + 7)(5² + 7)(1058² + 7) = (3² + 7)(13² + 7)(1058² + 7)
= (5² + 7)(9² + 7)(1058² + 7) = (53² + 7)(1058² + 7).

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

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56160

267² + 56160 = 357², 267² - 56160 = 123².

56160² = (2² - 1)(5² - 1)(9² - 1)(14² - 1)(53² - 1) = (2² - 1)(5² - 1)(14² - 1)(19² - 1)(25² - 1)
= (3² - 1)(4² - 1)(7² - 1)(14² - 1)(53² - 1) = (4² - 1)(11² - 1)(25² - 1)(53² - 1)
= (7² - 1)(11² - 1)(14² - 1)(53² - 1) = (14² - 1)(25² - 1)(161² - 1).

Page of Squares : First Upload September 15, 2012 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

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56169

56169 = 237² is a square pegged by 6.

Page of Squares : First Upload September 15, 2012 ; Last Revised September 15, 2012
by Yoshio Mimura, Kobe, Japan

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56175

56175² = (1² + 6)(3² + 6)(23² + 6)(237² + 6).

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

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56200

56200² = (1² + 4)(2² + 4)(8886² + 4) = (6² + 4)(8886² + 4).

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

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56210

56210² = (1² + 6)(4² + 6)(40² + 6)(113² + 6) = (4² + 6)(106² + 6)(113² + 6)
= (13² + 6)(40² + 6)(106² + 6).

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

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56230

56230²± 3 are primes.

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

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56250

56250² = (4² + 9)(6² + 9)(21² + 9)(79² + 9).

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

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56252

56252²± 3 are primes.

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

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56260

56260² = (4² + 4)(5² + 4)(44² + 4)(53² + 4) = (24² + 4)(44² + 4)(53² + 4).

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

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56290

56290²± 3 are primes.

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

---

56316

56316² = (4² + 3)(6² + 3)(15² + 3)(137² + 3).

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

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56322

56322² = (1² + 5)(2² + 5)(4² + 5)(12² + 5)(137² + 5) = (2² + 5)(11² + 5)(12² + 5)(137² + 5)
= (4² + 5)(7² + 5)(12² + 5)(137² + 5).

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

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56334

56334² = 3173519556, 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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56354

56354² = 3175773316, 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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56355

56355² = (54² + 9)(1042² + 9).

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

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56448

56448² = (2² - 1)(3² - 1)(8² - 1)(15² - 1)(97² - 1) = (5² - 1)(8² - 1)(15² - 1)(97² - 1).

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

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56472

56472² = (1² + 3)(3² + 3)(84² + 3)(97² + 3) = (1² + 3)(6² + 3)(7² + 3)(627² + 3)
= (1² + 3)(45² + 3)(627² + 3).

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

---

56486

56486² = 683² + 684² + 685² + ... + 2146².

Page of Squares : First Upload September 15, 2012 ; Last Revised September 15, 2012
by Yoshio Mimura, Kobe, Japan

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56510

56510² = 2001² + 2002² + 2003² + ... + 2600².

Page of Squares : First Upload September 15, 2012 ; Last Revised September 15, 2012
by Yoshio Mimura, Kobe, Japan

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56532

56532² = 3195867024 is a square with different digits.

Page of Squares : First Upload September 15, 2012 ; Last Revised September 15, 2012
by Yoshio Mimura, Kobe, Japan

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56541

56541²± 2 are primes.

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

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56550

56550² = (2² + 9)(4² + 9)(7² + 9)(11² + 9)(36² + 9) = (4² + 9)(7² + 9)(36² + 9)(41² + 9).

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

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56592

56592² = (4² + 8)(56² + 8)(206² + 8).

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

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56610

56610² = (1² + 9)(18² + 9)(981² + 9) = (3² + 9)(12² + 9)(19² + 9)(56² + 9)
= (5² + 9)(9² + 9)(18² + 9)(56² + 9).

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

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56602

56602²± 3 are primes.

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

---

56628

56628²± 5 are primes.

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

---

56644

56644 = 238² is a square with 3 kinds of digits.

Page of Squares : First Upload September 15, 2012 ; Last Revised September 15, 2012
by Yoshio Mimura, Kobe, Japan

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56650

56650² = (7² + 6)(32² + 6)(238² + 6).

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

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56672

56672² = (1² + 7)(2² + 7)(3² + 7)(4² + 7)(7² + 7)(42² + 7)
= (1² + 7)(2² + 7)(7² + 7)(19² + 7)(42² + 7) = (1² + 7)(3² + 7)(42² + 7)(119² + 7)
= (1² + 7)(4² + 7)(7² + 7)(13² + 7)(42² + 7) = (1² + 7)(4² + 7)(35² + 7)(119² + 7)
= (2² + 7)(3² + 7)(4² + 7)(21² + 7)(42² + 7) = (2² + 7)(3² + 7)(4² + 7)(7² + 7)(119² + 7)
= (2² + 7)(4² + 7)(7² + 7)(11² + 7)(42² + 7) = (2² + 7)(7² + 7)(19² + 7)(119² + 7)
= (2² + 7)(7² + 7)(35² + 7)(65² + 7) = (2² + 7)(19² + 7)(21² + 7)(42² + 7)
= (3² + 7)(4² + 7)(7² + 7)(9² + 7)(42² + 7) = (4² + 7)(7² + 7)(13² + 7)(119² + 7)
= (4² + 7)(13² + 7)(21² + 7)(42² + 7) = (7² + 7)(9² + 7)(19² + 7)(42² + 7)
= (11² + 7)(42² + 7)(119² + 7).

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

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56680

56680²± 3 are primes.

56680² = (1² + 4)(2² + 4)(3² + 4)(6² + 4)(393² + 4) = (1² + 4)(6² + 4)(10² + 4)(393² + 4)
= (10² + 4)(14² + 4)(393² + 4) = (2² + 4)(3² + 4)(14² + 4)(393² + 4).

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

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56700

56700² = (2² - 1)(4² - 1)(6² - 1)(7² - 1)(8² - 1)(26² - 1) = (2² - 1)(4² - 1)(6² - 1)(26² - 1)(55² - 1)
= (2² - 1)(4² - 1)(8² - 1)(26² - 1)(41² - 1) = (4² - 1)(8² - 1)(26² - 1)(71² - 1)
= (9² - 1)(26² - 1)(244² - 1).

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

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56722

56722567225 = 238165².

Page of Squares : First Upload September 15, 2012 ; Last Revised September 15, 2012
by Yoshio Mimura, Kobe, Japan

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56742

56742² = (1² + 3)(12² + 3)(2340² + 3) = (2² + 3)(9² + 3)(2340² + 3).

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

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56745

56745² = (6² + 9)(66² + 9)(128² + 9).

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

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56784

325² + 56784 = 403², 325² - 56784 = 221².

56784² = (1² + 3)(2² + 3)(5² + 3)(6² + 3)(7² + 3)(45² + 3)
= (1² + 3)(2² + 3)(7² + 3)(33² + 3)(45² + 3) = (1² + 3)(3² + 3)(7² + 3)(9² + 3)(124² + 3)
= (1² + 3)(5² + 3)(6² + 3)(19² + 3)(45² + 3) = (1² + 3)(6² + 3)(7² + 3)(19² + 3)(33² + 3)
= (1² + 3)(19² + 3)(33² + 3)(45² + 3) = (2² + 3)(3² + 3)(7² + 3)(19² + 3)(45² + 3)
= (5² + 3)(7² + 3)(33² + 3)(45² + 3) = (7² + 3)(9² + 3)(19² + 3)(45² + 3).

Page of Squares : First Upload September 15, 2012 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

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56792

56792²± 3 are primes.

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

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56793

56793² = 2995² + 2997² + 2999² + 3001² + ... + 3587².

Page of Squares : First Upload September 15, 2012 ; Last Revised September 15, 2012
by Yoshio Mimura, Kobe, Japan

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56836

56836²± 3 are primes.

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

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56837

56837² = 17132² + 17133² + 17134² + ... + 17142².

Page of Squares : First Upload September 15, 2012 ; Last Revised September 15, 2012
by Yoshio Mimura, Kobe, Japan

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56855

56855² = 58² + 59² + 60² + ... + 2132².

Page of Squares : First Upload September 15, 2012 ; Last Revised September 15, 2012
by Yoshio Mimura, Kobe, Japan

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56880

56880² = 702*703*704 + 704*705*706 + 706*707*708 + 708*709*710 + ... + 718*719*720.

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

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56889

56889² = (32² + 5)(34² + 5)(52² + 5).

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

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56896

56896² = (3² + 7)(5² + 7)(7² + 7)(336² + 7).

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

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56925

56925² = 3240455625, and 324 = 18², 455625 = 675².

Page of Squares : First Upload September 15, 2012 ; Last Revised September 15, 2012
by Yoshio Mimura, Kobe, Japan

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56956

56956²± 3 are primes.

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

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56967

56967²± 2 are primes.

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

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56994

56994²± 5 are primes.

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

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