---

59019

59019²± 2 are primes.

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

---

59052

59052² = (2² + 3)(4² + 3)(15² + 3)(16² + 3)(21² + 3) = (2² + 3)(4² + 3)(21² + 3)(243² + 3)
= (3² + 3)(4² + 3)(16² + 3)(243² + 3) = (4² + 3)(12² + 3)(21² + 3)(53² + 3)
= (15² + 3)(16² + 3)(243² + 3).

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

---

59055

59055² = (3² + 6)(5² + 6)(11² + 6)(243² + 6).

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

---

59082

59082²± 5 are primes.

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

---

59094

59094² = (1² + 5)(14² + 5)(32² + 5)(53² + 5) = (2² + 5)(3² + 5)(4² + 5)(14² + 5)(81² + 5)
= (2² + 5)(4² + 5)(53² + 5)(81² + 5) = (2² + 5)(14² + 5)(17² + 5)(81² + 5)
= (4² + 5)(11² + 5)(14² + 5)(81² + 5) = (4² + 5)(14² + 5)(17² + 5)(53² + 5).

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

---

59106

59106²± 5 are primes.

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

---

59118

59118² = 612² + 613² + 614² + ... + 2204².

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

59127

59127²± 2 are primes.

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

---

59136

260² + 59136 = 356², 260² - 59136 = 92².

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

59145

The quadratic polynomial 59145X² - 238320X + 265024 takes the values 293², 158², 287², 508², 743², 982² at X = 1, 2,..., 6.

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

59157

59157²± 2 are primes.

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

---

59160

59160² = (2² - 1)(59² - 1)(579² - 1).

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

---

59169

59169²± 2 are primes.

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

---

59170

59170² = (1² + 1)(11² + 1)(22² + 1)(172² + 1) = (11² + 1)(5357² + 1).

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

---

59192

59192² = (1² + 3)(5² + 3)(65² + 3)(86² + 3).

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

---

59200

59200² = (2² + 4)(6² + 4)(14² + 4)(234² + 4).

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

---

59211

59211² = (5² + 2)(7² + 2)(27² + 2)(59² + 2).

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

---

59212

59212²± 3 are primes.

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

---

59220

59220² = 1107² + 1108² + 1109² + ... + 2281².

59220² = (1² + 5)(3² + 5)(5² + 5)(18² + 5)(65² + 5) = (4² - 1)(7² - 1)(46² - 1)(48² - 1).

Page of Squares : First Upload September 22, 2012 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

59245

59245² = (4² + 1)(38² + 1)(378² + 1).

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

---

59280

59280² = (9² - 1)(39² - 1)(170² - 1).

761² + 59280 = 799², 761² - 59280 = 721².

Page of Squares : First Upload September 22, 2012 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

59283

59283²± 2 are primes.

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

---

59290

59290² = (1² + 6)(4² + 6)(7² + 6)(22² + 6)(29² + 6) = (1² + 6)(8² + 6)(29² + 6)(92² + 6)
= (22² + 6)(29² + 6)(92² + 6).

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

---

59298

59298²± 5 are primes.

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

---

59308

59308²± 3 are primes.

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

---

59318

59318² = (4² + 3)(23² + 3)(590² + 3).

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

---

59330

59330² = (4² + 9)(5² + 9)(2035² + 9) = (29² + 9)(2035² + 9).

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

---

59340

59340² = (5² + 5)(9² + 5)(15² + 5)(77² + 5).

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

---

59364

59364² = (3² + 8)(34² + 8)(422² + 8).

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

---

59368

59368²± 3 are primes.

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

---

59400

59400² = (3² - 1)(4² - 1)(10² - 1)(21² - 1)(26² - 1) = (10² - 1)(11² - 1)(21² - 1)(26² - 1)
= (21² - 1)(26² - 1)(109² - 1).

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

---

59403

59403² = 3528716409 is a square with different digits.

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

59409

59409² = (2² + 5)(8² + 5)(2384² + 5).

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

---

59410

59410²± 3 are primes.

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

---

59450

59450² = 9244 x 9245 + 9246 x 9247 + 9248 x 9249 + 9250 x 9251 + ... + 9324 x 9325.

59450² = (9² + 1)(12² + 1)(17² + 1)(32² + 1) = (4² + 9)(7² + 9)(14² + 9)(109² + 9).

Page of Squares : First Upload September 22, 2012 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

59472

59472²± 5 are primes.

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

---

59514

59514² = (6² + 3)(18² + 3)(527² + 3).

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

---

59520

59520² = (2² - 1)(9² - 1)(61² - 1)(63² - 1) = (3² - 1)(11² - 1)(1921² - 1) = (31² - 1)(1921² - 1).

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

---

59540

59540² = (3² + 4)(4² + 4)(15² + 4)(244² + 4) = (15² + 4)(16² + 4)(244² + 4).

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

---

59552

59552²± 3 are primes.

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

---

59564

59564²± 3 are primes.

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

---

59566

59566²± 3 are primes.

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

---

59568

59568² = (3² + 8)(4² + 8)(24² + 8)(122² + 8) = (20² + 8)(24² + 8)(122² + 8).

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

---

59619

59619²± 2 are primes.

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

---

59625

59625² = (6² + 9)(16² + 9)(546² + 9).

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

---

59632

59632² = 688² + 689² + 690² + ... + 2223².

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

59634

59634²± 5 are primes.

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

---

59640

59640² = (6² - 1)(10081² - 1).

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

---

59644

59644² = (1² + 3)(7² + 3)(20² + 3)(206² + 3).

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

---

59658

59658² = (19² + 5)(22² + 5)(141² + 5).

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

---

59670

59670² = (1² + 9)(2² + 9)(6² + 9)(12² + 9)(63² + 9) = (1² + 9)(12² + 9)(24² + 9)(63² + 9)
= (2² + 9)(3² + 9)(4² + 9)(12² + 9)(63² + 9) = (2² + 9)(3² + 9)(5² + 9)(12² + 9)(54² + 9)
= (2² + 9)(5² + 9)(9² + 9)(12² + 9)(24² + 9) = (2² + 9)(6² + 9)(39² + 9)(63² + 9)
= (2² + 9)(9² + 9)(12² + 9)(141² + 9) = (2² + 9)(9² + 9)(15² + 9)(114² + 9)
= (2² + 9)(12² + 9)(21² + 9)(63² + 9) = (4² + 9)(12² + 9)(15² + 9)(63² + 9)
= (5² + 9)(12² + 9)(15² + 9)(54² + 9) = (5² + 9)(6² + 9)(24² + 9)(63² + 9)
= (6² + 9)(11² + 9)(12² + 9)(63² + 9) = (6² + 9)(63² + 9)(141² + 9)
= (24² + 9)(39² + 9)(63² + 9).

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

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59682

59682² = (1² + 6)(9² + 6)(20² + 6)(120² + 6).

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

---

59697

59697² = (1² + 2)(3² + 2)(47² + 2)(221² + 2).

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

---

59720

59720²± 3 are primes.

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

---

59738

59738² = 197² + 198² + 199² + ... + 2204².

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

59739

59739²± 2 are primes.

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

---

59751

The quadratic polynomial -59751X² + 427182X - 341831 takes the values 160², 523², 634², 641², 548², 265² at X = 1, 2,..., 6.

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

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59766

59766² = 4072 x 4073 + 4074 x 4075 + 4076 x 4077 + 4078 x 4079 + ... + 4462 x 4463.

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

59778

59778² = (1² + 2)(4² + 2)(5² + 2)(22² + 2)(71² + 2).

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

---

59803

59803² = 717² + 718² + 719² + ... + 2230².

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

59856

59856²± 5 are primes.

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

---

59860

59860² = (1² + 1)(9² + 1)(27² + 1)(173² + 1).

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

---

59904

40³ + 59904 = 352², 40³ - 59904 = 64².

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

59928

59928² = 841² + 842² + 843² + ... + 2248².

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

59954

59954² = 1434² + 1435² + 1436² + ... + 2394².

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

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