---

50005

50005² = 2500500025, a square wuth 3 kinds of digits.

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

---

50013

50013²± 2 are primes.

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

---

50020

50020² = (1² + 1)(2² + 1)(3² + 1)(9² + 1)(11² + 1)(50² + 1) = (1² + 1)(7² + 1)(9² + 1)(11² + 1)(50² + 1).

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

---

50028

50028² = (1² + 8)(6² + 8)(2514² + 8) = (2² + 8)(5² + 8)(2514² + 8).

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

---

50049

50049²± 2 are primes.

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

---

50050

50050²= 244 x 245 + 245 x 246 + 246 x 247 + ... + 1959 x 1960.

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

---

50064

50064²± 5 are primes.

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

---

50074

50074²± 3 are primes.

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

---

50086

50086²± 3 are primes.

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

---

50133

50133²± 2 are primes.

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

---

50160

50160² = (3² - 1)(49² - 1)(362² - 1) = (23² - 1)(39² - 1)(56² - 1).

241² + 50160 = 329², 241² - 50160 = 89².

Page of Squares : First Upload August 25, 2012 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

---

50176

224² = 50176 is a square with different digits.

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

---

50235

50235² = 2523555225, a square wuth 3 kinds of digits.

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

---

50246

50246²± 3 are primes.

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

---

50281

50281² = 2528178961, and 25281 = 159², 78961 = 281².

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

---

50316

50316² = 64³ + 857³ + 1239³.

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

---

50320

50320² = (1² + 4)(2² + 4)(12² + 4)(25² + 4)(26² + 4) = (1² + 4)(2² + 4)(12² + 4)(654² + 4)
= (2² + 4)(6² + 4)(9² + 4)(12² + 4)(25² + 4) = (2² + 4)(8² + 4)(9² + 4)(234² + 4)
= (2² + 4)(8² + 4)(25² + 4)(86² + 4) = (2² + 4)(76² + 4)(234² + 4)
= (6² + 4)(12² + 4)(25² + 4)(26² + 4) = (6² + 4)(12² + 4)(654² + 4)
= (8² + 4)(26² + 4)(234² + 4).

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

---

50327

50327² = 262² + 263² + 264² + 265² + ... + 1967².

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

---

50400

325² + 50400 = 395², 325² - 50400 = 235².

50400² = (2² - 1)(3² - 1)(4² - 1)(6² - 1)(11² - 1)(41² - 1) = (2² - 1)(3² - 1)(4² - 1)(6² - 1)(449² - 1)
= (2² - 1)(3² - 1)(6² - 1)(7² - 1)(251² - 1) = (2² - 1)(3² - 1)(41² - 1)(251² - 1)
= (2² - 1)(4² - 1)(5² - 1)(6² - 1)(9² - 1)(29² - 1) = (2² - 1)(4² - 1)(6² - 1)(9² - 1)(11² - 1)(13² - 1)
= (2² - 1)(4² - 1)(6² - 1)(31² - 1)(41² - 1) = (2² - 1)(4² - 1)(7² - 1)(11² - 1)(99² - 1)
= (2² - 1)(6² - 1)(9² - 1)(19² - 1)(29² - 1) = (2² - 1)(6² - 1)(11² - 1)(449² - 1)
= (2² - 1)(9² - 1)(13² - 1)(251² - 1) = (3² - 1)(4² - 1)(6² - 1)(8² - 1)(9² - 1)(11² - 1)
= (3² - 1)(4² - 1)(6² - 1)(11² - 1)(71² - 1) = (3² - 1)(4² - 1)(6² - 1)(19² - 1)(41² - 1)
= (3² - 1)(6² - 1)(9² - 1)(13² - 1)(26² - 1) = (3² - 1)(7² - 1)(26² - 1)(99² - 1)
= (3² - 1)(8² - 1)(9² - 1)(251² - 1) = (3² - 1)(71² - 1)(251² - 1)
= (4² - 1)(5² - 1)(6² - 1)(11² - 1)(41² - 1) = (4² - 1)(5² - 1)(6² - 1)(449² - 1)
= (4² - 1)(6² - 1)(7² - 1)(11² - 1)(29² - 1) = 4² - 1)(6² - 1)(8² - 1)(9² - 1)(31² - 1)
= (4² - 1)(6² - 1)(9² - 1)(13² - 1)(19² - 1) = (4² - 1)(6² - 1)(31² - 1)(71² - 1)
= (4² - 1)(7² - 1)(19² - 1)(99² - 1) = (4² - 1)(11² - 1)(29² - 1)(41² - 1)
= (4² - 1)(29² - 1)(449² - 1) = (5² - 1)(6² - 1)(7² - 1)(251² - 1) = (5² - 1)(41² - 1)(251² - 1)
= (6² - 1)(11² - 1)(19² - 1)(41² - 1) = (6² - 1)(19² - 1)(449² - 1) = (7² - 1)(29² - 1)(251² - 1).

Page of Squares : First Upload August 25, 2012 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

---

50470

50470² = (1² + 6)(8² + 6)(32² + 6)(71² + 6) = (22² + 6)(32² + 6)(71² + 6).

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

---

50499

50499²± 2 are primes.

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

---

50511

50511²± 2 are primes.

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

---

50568

50568² = (1² + 3)(5² + 3)(12² + 3)(13² + 3)(30² + 3) = (1² + 3)(5² + 3)(30² + 3)(159² + 3)
= (1² + 3)(12² + 3)(13² + 3)(159² + 3) = (2² + 3)(5² + 3)(9² + 3)(13² + 3)(30² + 3)
= (2² + 3)(9² + 3)(13² + 3)(159² + 3) = (3² + 3)(13² + 3)(30² + 3)(37² + 3).

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

---

50578

50578²± 3 are primes.

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

---

50600

50600²= 1485 x 1486 + 1486 x 1487 + 1487 x 1488 + ... + 2220 x 2221.

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

---

50616

685² + 50616 = 721², 685² - 50616 = 647².

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

---

50624

50624² = (1² + 7)(7² + 7)(28² + 7)(85² + 7) = (21² + 7)(28² + 7)(85² + 7).

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

---

50625

50625 = 225² is a zigzag square.

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

---

50643

50643²± 2 are primes.

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

---

50652

50652² = (1² + 5)(3² + 5)(7² + 5)(14² + 5)(53² + 5).

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

---

50656

50656²± 3 are primes.

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

---

50688

50688² = (2² - 1)(3² - 1)(7² - 1)(23² - 1)(65² - 1) = (5² - 1)(7² - 1)(23² - 1)(65² - 1).

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

---

50700

50700² = (1² + 9)(2² + 9)(9² + 9)(11² + 9)(41² + 9).

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

---

50702

50702²± 3 are primes.

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

---

50706

50706² = 2571098436 is a square with different digits.

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

---

50715

50715² = (2² - 1)(4² - 1)(22² - 1)(344² - 1) = (10² + 5)(38² + 5)(130² + 5)
= (2² + 5)(4² + 5)(10² + 5)(360² + 5) = (4² + 5)(8² + 5)(10² + 5)(130² + 5).

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

---

50784

230² + 50784 = 322², 230² - 50784 = 46².

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

---

50787

50787² = (5² + 8)(7² + 8)(1171² + 8).

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

---

50796

50796² = (1² + 8)(2² + 8)(3² + 8)(18² + 8)(65² + 8) = (1² + 8)(14² + 8)(18² + 8)(65² + 8)
= (3² + 8)(10² + 8)(18² + 8)(65² + 8).

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

---

50806

50806²± 3 are primes.

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

---

50820

50820² = (2² + 6)(4² + 6)(6² + 6)(18² + 6)(29² + 6) = (4² + 6)(6² + 6)(18² + 6)(92² + 6).

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

---

50895

50895² = (6² + 9)(36² + 9)(210² + 9).

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

---

50912

50912² = (3² + 7)(6² + 7)(1941² + 7).

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

---

50918

50918²± 3 are primes.

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

---

50922

50922² = (6² + 5)(47² + 5)(169² + 5).

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

---

50951

50951 is the 7th prime for which the Legendre Symbol (a/50951) = 1 for a = 1,2,...,22.

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

---

50974

50974²± 3 are primes.

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

---

50978

50978²± 3 are primes.

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

---

50979

50979²± 2 are primes.

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

---