---

23008

23008²± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23019

23019² = 529874361 is a square with different digits.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23023

23023² = (1² + 2³ + 3³ + 4³ + 5³ + 6²)(7² + 8³ + 9³ + ... + 259²).

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

---

23029

A cubic polynomial :
(X + 1128²)(X + 2464²)(X + 22869²) = X³ + 23029²X² + 62035512² + 63561915648².

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23040

23040² = (2² - 1)(3² - 1)(9² - 1)(17² - 1)(31² - 1) = (3² - 1)(5² - 1)(9² - 1)(11² - 1)(17² - 1)
= (5² - 1)(9² - 1)(17² - 1)(31² - 1).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23046

23046²± 5 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23056

23056² = 531579136, 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

---

23058

23058² = (1² + 5)(2² + 5)(19² + 5)(164² + 5) = (4² + 5)(19² + 5)(263² + 5)
= (7² + 5)(19² + 5)(164² + 5).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23064

155² + 23064 = 217², 155² - 23064 = 31².

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23086

23086²± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23100

23100² = (1² + 6)(2² + 6)(3² + 6)(4² + 6)(8² + 6)(18² + 6)
= (1² + 6)(2² + 6)(4² + 6)(12² + 6)(48² + 6) = (1² + 6)(2² + 6)(4² + 6)(6² + 6)(7² + 6)(12² + 6)
= (1² + 6)(4² + 6)(8² + 6)(12² + 6)(18² + 6) = (2² + 6)(3² + 6)(4² + 6)(18² + 6)(22² + 6)
= (2² + 6)(3² + 6)(4² + 6)(6² + 6)(62² + 6) = (2² + 6)(3² + 6)(4² + 6)(6² + 6)(7² + 6)(8² + 6)
= (2² + 6)(3² + 6)(4² + 6)(8² + 6)(48² + 6) = (2² + 6)(4² + 6)(6² + 6)(13² + 6)(18² + 6)
= (2² + 6)(4² + 6)(8² + 6)(12² + 6)(15² + 6) = (2² + 6)(6² + 6)(12² + 6)(92² + 6)
= (2² + 6)(6² + 6)(18² + 6)(62² + 6) = (2² + 6)(6² + 6)(7² + 6)(8² + 6)(18² + 6)
= (2² + 6)(8² + 6)(18² + 6)(48² + 6) = (4² + 6)(12² + 6)(18² + 6)(22² + 6)
= (4² + 6)(6² + 6)(12² + 6)(62² + 6) = (4² + 6)(6² + 6)(7² + 6)(8² + 6)(12² + 6)
= (4² + 6)(8² + 6)(12² + 6)(48² + 6) = (9² - 1)(34² - 1)(76² - 1).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23104

23104 = 152² is a square with different digita.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23112

23112²± 5 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23113

23113² = 534210769 is a square with different digits.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23121

23121²± 2 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23126

23126² = 212 x 213 + 213 x 214 + 214 x 215 + ... + 1172 x 1173.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23140

23140² = (16² + 4)(21² + 4)(68² + 4) = (3² + 4)(4² + 4)(21² + 4)(68² + 4).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23146

23146² = 535737316, 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

---

23166

23166² = 536663556 is a square consists of 3 kinds of digits.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23175

23175²± 2 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23178

23178² = 537219684 is a square with different digits.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23180

23180²± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23184

23184² = (2² - 1)(13² - 1)(22² - 1)(47² - 1) = (3² - 1)(8² - 1)(22² - 1)(47² - 1).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23183

23183² = 1567² + 1568² + 1569² + ... + 1760².

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23200

23200² = 150 x 151 + 151 x 152 + 152 x 153 + ... + 1173 x 1174.

23200² = (1² + 4)(2² + 4)(4² + 4)(24² + 4)(34² + 4) = (4² + 4)(6² + 4)(24² + 4)(34² + 4)
= (1² + 4)(2² + 4)(4² + 4)(5² + 4)(6² + 4)(24² + 4) = (2² + 4)(4² + 4)(5² + 4)(14² + 4)(24² + 4).

Page of Squares : First Upload March 24, 2012 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23234

23234²± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23236

23236²± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23247

23247² = 144³ + 145³ + 146³ + 147² + 148² + ... + 225³.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23250

23350² = (3² + 6)(5² + 6)(12² + 6)(88² + 6).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23256

23256² = (18² - 1)(35² - 1)(37² - 1) = (1² + 8)(12² + 8)(20² + 8)(31² + 8)
= (1² + 8)(3² + 8)(4² + 8)(12² + 8)(31² + 8) = (1² + 8)(3² + 8)(7² + 8)(12² + 8)(20² + 8)
= (3² + 8)(64² + 8)(88² + 8) = (3² + 8)(7² + 8)(8² + 8)(88² + 8) = (4² + 8)(20² + 8)(235² + 8)
= (4² + 8)(7² + 8)(20² + 8)(31² + 8) = (7² + 8)(48² + 8)(64² + 8) = (8² + 8)(31² + 8)(88² + 8).

325² + 23256 = 359², 325² - 23256 = 287².

Page of Squares : First Upload March 24, 2012 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23262

23262²± 5 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23272

23272²± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23276

23276² = 439² + 441² + 443² + 445² + 447² + 449² + ... + 1493².

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23296

23296²± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23322

23322² = 1627² + 1628² + 1629² + ... + 1810².

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23326

23326²= 892 x 893 + 893 x 894 + 894 x 895 + ... + 1327 x 1328.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23328

23328² = (1² + 8)(2² + 8)(4² + 8)(10² + 8)(44² + 8).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23330

23330²± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23331

A cubic polynomial :
(X + 448²)(X + 1584²)(X + 23331²) = X³ + 23389²X² + 38412528² + 16556424192².

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23335

23335² = 544522225 is a square consists of 3 kinds of digits.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23357

23357² = 545549449 is a square consists of 3 kinds of digits.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23360

23360² = 2698² + 2699² + 2700² + ... + 2770².

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23364

23364² = (13² + 8)(38² + 8)(46² + 8) = (5² + 8)(6² + 8)(13² + 8)(46² + 8).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23384

23384² = (17² + 7)(25² + 7)(54² + 7).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23400

23400² = (2² - 1)(14² - 1)(19² - 1)(51² - 1) = (2² - 1)(4² - 1)(5² - 1)(14² - 1)(51² - 1).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23404

23404² = 2341² + 2342² + 2343² + ... + 2436².

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23409

23409 = 153² is a square with different digits.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23425

23425² = S2(924) + S2(949), where S2(n) = 1² + 2² + 3² + ... + n².

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23426

23426² = (2² + 9)(37² + 9)(175² + 9).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23439

23439² = 549386721 is a square with different digits.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23490

23490² = (2² + 5)(5² + 5)(20² + 5)(71² + 5) = (5² + 5)(13² + 5)(16² + 5)(20² + 5).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23515

23515² = 552955225 is a square consists of 3 kinds of digits.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23520

23520² = (2² - 1)(3² - 1)(4801² - 1) = (5² - 1)(4801² - 1) = (6² - 1)(41² - 1)(97² - 1).

182² + 23520 = 238², 182² - 23520 = 98².

Page of Squares : First Upload March 24, 2012 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23552

23552² = (1² + 7)(4² + 7)(5² + 7)(11² + 7)(27² + 7) = (3² + 7)(11² + 7)(19² + 7)(27² + 7)
= (3² + 7)(4² + 7)(5² + 7)(11² + 7)(19² + 7) = (4² + 7)(27² + 7)(181² + 7).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23556

23556²± 5 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23566

23566² = 555356356 is a square consists of 3 kinds of digits.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23569

23569² = 84⁴ + 105⁴ + 140⁴.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23584

23584² = (1² + 7)(3² + 7)(23² + 7)(90² + 7) = (11² + 7)(23² + 7)(90² + 7).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23585

23585² = 556252225 is a square consists of 3 kinds of digits.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23626

23626²± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23634

23634² = (15² + 9)(1545² + 9) = (2² + 9)(3² + 9)(1545² + 9).

23634² = 558565956 is a square pegged by 5.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23646

23646² = 559133316, 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

---

23654

23654² = 559511716, 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

---

23667

23667²± 2 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23682

23682² = 560837124 is a square with different digits.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23716

23716 = 154² is a square with different digits.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23718

23718²± 5 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23724

23724²± 5 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23725

23725² = (2² + 9)(4² + 9)(8² + 9)(154² + 9).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23728

23728² = 563017984 is a square with different digits.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23746

23746² = 234² + 235² + 236² + ... + 1194².

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23749

23749² = 1099² + 1101² + 1103² + 1105² + ... + 1675².

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23760

23760² = (2² - 1)(4² - 1)(10² - 1)(17² - 1)(21² - 1) = (2² - 1)(7² - 1)(10² - 1)(199² - 1)
= (4² - 1)(7² - 1)(10² - 1)(89² - 1) = (49² - 1)(485² - 1).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23790

23790² = (9² + 9)(28² + 9)(89² + 9).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23800

23800² = 34 x 35 + 36 x 37 + 38 x 39 + 40 x 41 + ... + 1502 x 1503.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23814

23814² = (1² + 5)(2² + 5)(32² + 5)(101² + 5) = (2² + 5)(4² + 5)(17² + 5)(101² + 5)
= (7² + 5)(32² + 5)(101² + 5).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23818

23818²± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23826

23826² = (2² + 2)(6² + 2)(25² + 2)(63² + 2).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23850

23850² = (1² + 9)(6² + 9)(16² + 9)(69² + 9) = (16² + 9)(21² + 9)(69² + 9)
= (3² + 9)(4² + 9)(16² + 9)(69² + 9).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23859

23859² = (1² + 2)(13775² + 2).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23868

23868² = (3² + 9)(5² + 9)(15² + 9)(63² + 9).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23870

23870² = (1² + 6)(2² + 6)(29² + 6)(98² + 6) = (1² + 6)(4² + 6)(5² + 6)(13² + 6)(26² + 6)
= (1² + 6)(5² + 6)(26² + 6)(62² + 6) = (1² + 6)(5² + 6)(7² + 6)(8² + 6)(26² + 6)
= (1² + 6)(92² + 6)(98² + 6) = (5² + 6)(7² + 6)(22² + 6)(26² + 6) = (8² + 6)(29² + 6)(98² + 6).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23872

23872² = (3² + 7)(5² + 7)(1055² + 7).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23889

23889² = 570684321 is a square with different digits.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---

23898

23898²± 5 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23902

23902²± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23922

23922² = (2² + 2)(21² + 2)(464² + 2).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23934

23934²± 5 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23940

23940² = (4² - 1)(8² - 1)(20² - 1)(39² - 1) = (8² - 1)(20² - 1)(151² - 1) = (9² - 1)(20² - 1)(134² - 1).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23944

23944² = 573315136, 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

---

23949

23949²± 2 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

---

23958

23958²= 838 x 839 + 839 x 840 + 840 x 841 +...+ 1321 x 1322.

Page of Squares : First Upload March 24, 2012 ; Last Revised March 24, 2012
by Yoshio Mimura, Kobe, Japan

---