---

33000

305² + 33000 = 355², 305² - 33000 = 245².

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33002

33002²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33008

33008²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33032

33032²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33048

33048² = (20² + 8)(37² + 8)(44² + 8) = (3² + 8)(4² + 8)(37² + 8)(44² + 8).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33049

33049 is the tenth prime for which Lendre Symbol (a/33049) = 1 for a = 1, 2, 3,..., 18.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33087

33087²± 2 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33099

33099² = (3² + 8)(5² + 8)(13² + 8)(105² + 8).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33110

33110² = 1600 x 1601 + 1602 x 1603 + 1604 x 1605 + 1606 x 1607 + ... + 2200 x 2201.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33120

33120² = (2² - 1)(17² - 1)(24² - 1)(47² - 1).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33124

33124² = (2² + 3)(5² + 3)(19² + 3)(124² + 3) = (7² + 3)(37² + 3)(124² + 3).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33142

33142²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33144

33144² = 1098524736 is a square with different digits.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33150

33150² = (1² + 9)(2² + 9)(46² + 9)(63² + 9) = (11² + 9)(46² + 9)(63² + 9)
= (2² + 9)(4² + 9)(29² + 9)(63² + 9) = (2² + 9)(5² + 9)(29² + 9)(54² + 9).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33152

33152² = (1² + 7)(7² + 7)(17² + 7)(91² + 7) = (17² + 7)(21² + 7)(91² + 7).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33153

33153²± 2 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33176

33176²= 1817 x 1818 + 1818 x 1819 + 1819 x 1820 +...+ 2102 x 2103.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33186

33186²± 5 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33210

33210² = (1² + 5)(2² + 5)(6² + 5)(20² + 5)(35² + 5) = (20² + 5)(35² + 5)(47² + 5)
= (5² + 5)(6² + 5)(20² + 5)(47² + 5) = (6² + 5)(7² + 5)(20² + 5)(35² + 5).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33240

33240²= 671 x 672 + 672 x 673 + 673 x 674 +...+ 1534 x 1535.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33243

33243²± 2 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33264

33264² = (10² - 1)(17² - 1)(197² - 1).

195² + 33264 = 267², 195² - 33264 = 69².

Page of Squares : First Upload June 2, 2012 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33288

33288² = (1² + 8)(12² + 8)(900² + 8) = (15² + 3)(17² + 3)(129² + 3)
= (3² + 3)(4² + 3)(17² + 3)(129² + 3) = (4² + 8)(7² + 8)(900² + 8).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33300

33300² = (1² + 9)(3² + 9)(19² + 9)(129² + 9).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33315

33315²± 2 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33330

33330² = 3233 x 3234 + 3235 x 3236 + 3237 x 3238 + 3239 x 3240 + ... + 3431 x 3432.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33334

33334² = 1111155556 is a square with 3 kinds of digits and its digits are non-decreasing.

33334² = 1111155556, a square with odd digits except the last digit 6.

Page of Squares : First Upload June 2, 2012 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

---

33335

33335² = 1111222225 is a square with 3 kinds of digits and its digits are non-decreasing.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33337

33337² = 1111355569 is a square with 3 kinds of digits and its digits are non-decreasing.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33338

33338² = 1111422244 is a square with 3 kinds of digits.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33346

33346² = 1111955716, 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

---

33354

33354² = (3² + 9)(10² + 9)(753² + 9).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33359

33359² = 1112822881 is a square with 3 kinds of digits.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33367

33367² = 1113356689 is a square with the non-decreasing digits.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33368

33368² = 1113423424, 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

---

33369

33369²± 2 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33370

33370²= 325 x 326 + 326 x 327 + 327 x 328 + ... + 1499 x 1500.

33370² = 1530² + 1531² + 1532² + ... + 1905².

33370² = 181² + 183² + 185² + 187² + ... + 1883².

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33373

33373² = 451² + 452² + 453² + ... + 1508².

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33376

33376² = 1113957376, 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

---

33386

33386²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33405

33405²± 2 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33410

33410² = (1² + 1)(2² + 1)(5² + 1)(2072² + 1) = (3² + 1)(5² + 1)(2072² + 1)
= (1² + 4)(3² + 4)(4144² + 4) = (3² + 4)(32² + 4)(289² + 4).

Page of Squares : First Upload November 9, 2013 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33422

33422²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33456

33456² = (4² + 8)(48² + 8)(142² + 8).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33461

33461² = 23660² + 23661² + 23662² + ... + 23661².

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33466

33466² = 1119973156, 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

---

33478

33478² = 5⁴ + 9⁴ + 43⁴ + 67⁴ + 182⁴.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33489

33489² = 1121513121 is a square pegged by 1.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33490

33490² = (1² + 1)(2² + 1)(4² + 1)(14² + 1)(183² + 1)
= (13² + 1)(14² + 1)(183² + 1) = (3² + 1)(4² + 1)(14² + 1)(183² + 1).

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

---

33495

33495² = (1² + 6)(7² + 6)(9² + 6)(183² + 6) = (3² + 6)(7² + 6)(9² + 6)(125² + 6).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33528

33528²± 5 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33594

33594²± 5 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33600

33600² = (11² - 1)(31² - 1)(99² - 1) = (3² - 1)(4² - 1)(31² - 1)(99² - 1)
= (3² - 1)(6² - 1)(41² - 1)(49² - 1) = (4² - 1)(6² - 1)(9² - 1)(11² - 1)(15² - 1)
= (6² - 1)(9² - 1)(13² - 1)(49² - 1) = (7² - 1)(49² - 1)(99² - 1) = (9² - 1)(15² - 1)(251² - 1).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33616

33616² = (5² + 7)(39² + 7)(152² + 7).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33632

33632² = 1131111424, 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

---

33640

33640² = (1² + 4)(5² + 4)(34² + 4)(82² + 4).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33642

33642² = (101² + 5)(333² + 5) = (2² + 5)(4² + 5)(7² + 5)(333² + 5)
= (2² + 5)(7² + 5)(23² + 5)(66² + 5).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33652

33652²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33654

33654²± 5 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33662

33662²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33666

33666² = 1133399556, 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

---

33667

33667² = 1133466889 is a square with the non-decreasing digits.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33489

33489 = 183² is a square with the non-decreasing digits.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33591

The quadratic polynomial -33591X² + 494298X - 196511 takes the values 514², 811², 992², 1115², 1198², 1249² at X = 1, 2,..., 6.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33600

250² + 33600 = 310², 250² - 33600 = 170².

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33659

33659² = 479² + 480² + 481² + ... + 1519².

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33696

33696²=1135420416, and 1 x 13 x 54 x 2 x 04 x 1 x 6 = 33696.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33698

33698² = (20² + 6)(34² + 6)(49² + 6).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33704

33704²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33738

14322² + 33738² = 1343372328 (mosaic).

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33744

33744² = (1² + 3)(15² + 3)(21² + 3)(53² + 3) = (1² + 3)(3² + 3)(4² + 3)(21² + 3)(53² + 3).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33800

33800² = (1² + 4)(2² + 4)(11² + 4)(478² + 4) = (1² + 4)(3² + 4)(10² + 4)(14² + 4)(29² + 4)
= (10² + 4)(29² + 4)(114² + 4) = (2² + 4)(3² + 4)(10² + 4)(11² + 4)(29² + 4)
= (2² + 4)(3² + 4)(29² + 4)(114² + 4) = (6² + 4)(11² + 4)(478² + 4).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33810

33810² = (1² + 5)(3² + 5)(10² + 5)(360² + 5) = (15² + 5)(17² + 5)(130² + 5)
= (3² + 5)(25² + 5)(360² + 5) = (3² + 5)(4² + 5)(15² + 5)(130² + 5)
= (3² + 5)(4² + 5)(5² + 5)(360² + 5) = (5² + 5)(17² + 5)(360² + 5).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33828

33828² = 692² + 693² + 694² + ... + 1555².

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33852

33852² = (1² + 3)(2² + 3)(6² + 3)(20² + 3)(51² + 3) = (1² + 3)(6² + 3)(11² + 3)(12² + 3)(20² + 3)
= (1² + 3)(6² + 3)(20² + 3)(135² + 3) = (1² + 3)(6² + 3)(33² + 3)(82² + 3)
= (2² + 3)(3² + 3)(45² + 3)(82² + 3) = (2² + 3)(3² + 3)(6² + 3)(7² + 3)(82² + 3)
= (2² + 3)(6² + 3)(9² + 3)(11² + 3)(20² + 3) = (20² + 3)(33² + 3)(51² + 3)
= (3² + 3)(6² + 3)(19² + 3)(82² + 3) = (5² + 3)(6² + 3)(20² + 3)(51² + 3)
= (6² + 3)(7² + 3)(9² + 3)(82² + 3) = (9² + 3)(45² + 3)(82² + 3).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33856

33856² = (19² + 7)(27² + 7)(65² + 7) = (3² + 7)(4² + 7)(27² + 7)(65² + 7)
= (4² + 7)(5² + 7)(19² + 7)(65² + 7).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33858

33858² = (1² + 2)(2² + 2)(3² + 2)(13² + 2)(184² + 2)
= (1² + 2)(2² + 2)(5² + 2)(6² + 2)(13² + 2)(19² + 2) = (1² + 2)(2² + 2)(13² + 2)(19² + 2)(32² + 2)
= (1² + 2)(3² + 2)(4² + 2)(22² + 2)(63² + 2) = (1² + 2)(3² + 2)(5² + 2)(6² + 2)(13² + 2)(14² + 2)
= (1² + 2)(3² + 2)(5² + 2)(6² + 2)(184² + 2) = (1² + 2)(3² + 2)(13² + 2)(14² + 2)(32² + 2)
= (1² + 2)(3² + 2)(32² + 2)(184² + 2) = (1² + 2)(4² + 2)(5² + 2)(14² + 2)(63² + 2)
= (1² + 2)(4² + 2)(13² + 2)(14² + 2)(25² + 2) = (1² + 2)(4² + 2)(25² + 2)(184² + 2)
= (1² + 2)(5² + 2)(6² + 2)(19² + 2)(32² + 2) = (1² + 2)(8² + 2)(13² + 2)(184² + 2)
= (1² + 2)(14² + 2)(22² + 2)(63² + 2) = (2² + 2)(3² + 2)(5² + 2)(25² + 2)(32² + 2)
= (2² + 2)(5² + 2)(8² + 2)(13² + 2)(25² + 2) = (3² + 2)(4² + 2)(13² + 2)(184² + 2)
= (4² + 2)(5² + 2)(6² + 2)(13² + 2)(19² + 2) = (4² + 2)(13² + 2)(19² + 2)(32² + 2)
= (5² + 2)(8² + 2)(25² + 2)(32² + 2) = (6² + 2)(13² + 2)(19² + 2)(22² + 2)
= (13² + 2)(14² + 2)(184² + 2).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33891

(33891² - 6) = (5² - 6)(7² - 6)(9² - 6)(11² - 6)(13² - 6).

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33902

33902²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33915

33915² = (6² - 1)(16² - 1)(18² - 1)(20² - 1).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33916

33916²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33930

33930² = (1² + 9)(2² + 9)(24² + 9)(123² + 9) = (1² + 9)(36² + 9)(297² + 9)
= (1² + 9)(51² + 9)(210² + 9) = (1² + 9)(6² + 9)(7² + 9)(210² + 9)
= (11² + 9)(24² + 9)(123² + 9) = (2² + 9)(4² + 9)(15² + 9)(123² + 9)
= (2² + 9)(6² + 9)(11² + 9)(123² + 9) = (2² + 9)(7² + 9)(24² + 9)(51² + 9)
= (3² + 9)(4² + 9)(7² + 9)(210² + 9) = (6² + 9)(41² + 9)(123² + 9)
= (7² + 9)(21² + 9)(210² + 9).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33958

33958²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33968

33968² = (1² + 7)(2² + 7)(3621² + 7) = (9² + 7)(3621² + 7).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33978

33978² = (1² + 5)(4² + 5)(3027² + 5) = (11² + 5)(3027² + 5) = (2² + 5)(3² + 5)(3027² + 5).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---

33989

33989² = 1155252121 is a square with 3 kinds of digits.

Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012
by Yoshio Mimura, Kobe, Japan

---

33998

33998²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

---