---

18012

18012² = 324432144, 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

---

18015

18015² = 324540225, 324 = 18², 540225 = 735².

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18020

18020² = (4² + 4)(7² + 4)(9² + 4)(60² + 4).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18025

18025² = 324900625, 324900 = 570², 625 = 25².

18025² = 324900625, 3249 = 57², 625 = 25².

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18055

18055² = S2(65) + S2(992), where S2(n) = 1² + 2² + 3² + ... + n².

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18060

18060² = (3² + 5)(5² + 5)(9² + 5)(95² + 5).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18069

18069²± 2 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18070

18070²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18072

18072² = 326597184 is a square consisting of different digits.

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18081

18081² = (6² + 5)(32² + 5)(88² + 5).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18084

18084² = (2² + 8)(6² + 8)(787² + 8).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18096

18096²± 5 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18108

18108²± 5 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18109

18109² = S2(287) + S2(986), where S2(n) = 1² + 2² + 3² + ... + n².

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18144

18144²± 5 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18150

18150² = (4² + 6)(18² + 6)(213² + 6).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18156

18156²± 5 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18191

18191 is the third prime for which the Legendre symbol (n/18191) = 1 for n = 1,2,3,...,22
18191 is the first prime for which the Legendre symbol (n/18191) = 1 for n = 1,2,3,...,28

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18216

18216² = (2² - 1)(10² - 1)(1057² - 1).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18228

18228² = (1² + 3)(2² + 3)(3² + 3)(12² + 3)(82² + 3) = (1² + 3)(9² + 3)(12² + 3)(82² + 3)
= (11² + 3)(12² + 3)(135² + 3) = (2² + 3)(11² + 3)(12² + 3)(51² + 3) = (2² + 3)(51² + 3)(135² + 3)
= (3² + 3)(5² + 3)(12² + 3)(82² + 3).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18232

18232² = (1² + 7)(6² + 7)(983² + 7).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18239

18239² = S2(781) + S2(804), where S2(n) = 1² + 2² + 3² + ... + n².

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18240

18240² = (3² - 1)(9² - 1)(721² - 1).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18250

18250²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18261

The sum of (23m + 22)² is a square (297353²) where 22<= 23m + 22 <= 18261.

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18270

18270² = (1² + 5)(10² + 5)(16² + 5)(45² + 5) = (10² + 5)(25² + 5)(71² + 5)
= (16² + 5)(25² + 5)(45² + 5) = (2² + 5)(10² + 5)(13² + 5)(45² + 5)
= (3² + 6)(6² + 6)(9² + 6)(78² + 6) = (4² + 5)(5² + 5)(10² + 5)(71² + 5)
= (4² + 5)(5² + 5)(16² + 5)(45² + 5) = (5² + 5)(45² + 5)(74² + 5).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18276

18276²± 5 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18304

18304²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18312

18312² = (1² + 3)(2² + 3)(3² + 3)(999² + 3) = (1² + 3)(9² + 3)(999² + 3)
= (3² + 3)(5² + 3)(999² + 3).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18318

18318²± 5 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18330

The sum of the divisors of 18330 is a square (22100²).

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18333

18333² = 97³ + 98³ + 99³ + 100³ + ... + 194³.

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18343

18343² = 456² + 457² + 458² + ... + 1033².

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18360

18360² = (2² - 1)(16² - 1)(19² - 1)(35² - 1) = (2² - 1)(4² - 1)(5² - 1)(16² - 1)(35² - 1).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18363

18363²± 2 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18376

18376² = 337677376 is a square with 3 kinds of digits (3,6,7).

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18382

18382²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18387

18387² = 297³ + 318³ + 654³.

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18400

18400²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18423

18423²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18424

18424²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18441

18441² = 9² + 576² + 18432².

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18450

18450² = (1² + 9)(3² + 9)(14² + 9)(96² + 9) = (4² + 9)(9² + 9)(14² + 9)(27² + 9).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18465

18465²± 2 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18468

18468² = (1² + 2)(2² + 2)(4² + 2)(5² + 2)(6² + 2)(32² + 2)
= (1² + 2)(2² + 2)(6² + 2)(22² + 2)(32² + 2)
= (2² + 2)(4² + 2)(6² + 2)(13² + 2)(22² + 2) = (4² + 2)(6² + 2)(22² + 2)(32² + 2).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18471

18471²± 2 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18476

18476² = 47 * 48 + 48 * 49 + 49 * 50 + 50 * 51 + ... + 1007 * 1008.

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18480

18480² = (2² - 1)(15² - 1)(21² - 1)(34² - 1) = (2² - 1)(3² - 1)(34² - 1)(111² - 1) = (21² - 1)(881² - 1)
= (3² - 1)(6² - 1)(10² - 1)(111² - 1) = (4² - 1)(43² - 1)(111² - 1) = (5² - 1)(34² - 1)(111² - 1)
= (6² - 1)(10² - 1)(15² - 1)(21² - 1) = (6² - 1)(13² - 1)(241² - 1) = (8² - 1)(21² - 1)(111² - 1).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18493

18493² = 341991049, 34199104 = 5848², 9 = 3².

The sum of (16m + 13)² is a square (363222²) where 13<= 16 m + 3 <= 18492.

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18496

18496 is a zigzag square (136²) with different digits.

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18497

18497² = 322² + 323² + 324² + ... + 1019².

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18500

18500² = (1² + 1)(2² + 1)(3² + 1)(6² + 1)(7² + 1)(43² + 1) = (11² + 4)(12² + 4)(136² + 4).

Page of Squares : First Upload November 9, 2013 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18513

18513² = (3² + 2)(7² + 2)(19² + 2)(41² + 2).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18522

18522²± 5 are primes.

18522² = (1² + 5)(2² + 5)(4² + 5)(17² + 5)(32² + 5)
= (2² + 5)(11² + 5)(17² + 5)(32² + 5) = (2² + 5)(3² + 5)(4² + 5)(11² + 5)(32² + 5)
= (4² + 5)(7² + 5)(17² + 5)(32² + 5).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18530

18530² = (2² + 1)(33² + 1)(251² + 1).

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

---

18550

18550² = (1² + 6)(8² + 6)(838² + 6) = (2² + 6)(10² + 6)(13² + 6)(43² + 6) = (22² + 6)(838² + 6).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18573

18573²± 2 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18576

18576² = (1² + 8)(2² + 8)(4² + 8)(11² + 8)(32² + 8) = (4² + 8)(10² + 8)(11² + 8)(32² + 8)
= (4² + 8)(32² + 8)(118² + 8).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18630

18630² = (1² + 5)(2² + 5)(8² + 5)(15² + 5)(20² + 5) = (15² + 5)(20² + 5)(61² + 5)
= (5² + 5)(20² + 5)(169² + 5) = (7² + 5)(8² + 5)(15² + 5)(20² + 5).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18644

18644²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18652

18652²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18656

18656²± 3 are primes.

18656² = (1² + 7)(9² + 7)(24² + 7)(29² + 7).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18668

18668²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18690

18690² = (5² + 5)(10² + 5)(333² + 5).

18690² = 12² / 3² - 4² + 5² * 6² * 7² * 89²
=12² - 3² * 4² + 5² * 6² * 7² * 89².

Page of Squares : First Upload February 11, 2012 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18694

18694² = 899² + 900² + 901² + ... + 1210².

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18704

18704² = S2(591) + S2(944), where S2(n) = 1² + 2² + 3² + ... + n².

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18710

18710²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18720

18720² = (14² - 1)(17² - 1)(79² - 1) = (2² - 1)(14² - 1)(25² - 1)(31² - 1)
= (2² - 1)(3² - 1)(11² - 1)(14² - 1)(25² - 1) = (3² - 1)(14² - 1)(19² - 1)(25² - 1)
= (3² - 1)(4² - 1)(5² - 1)(14² - 1)(25² - 1) = (3² - 1)(5² - 1)(1351² - 1)
= (3² - 1)(9² - 1)(14² - 1)(53² - 1) = (5² - 1)(11² - 1)(14² - 1)(25² - 1)
= (7² - 1)(51² - 1)(53² - 1).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18732

18732² = (3² + 3)(9² + 3)(590² + 3).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18744

18744² = 351337536, 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

---

18759

18759² = 329² + 331² + 333² + 335² + ... + 1289².

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18764

18764²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18769

18769 is a square (137²) with different digits.

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18774

18774² = (1² + 5)(4² + 5)(12² + 5)(137² + 5) = (11² + 5)(12² + 5)(137² + 5)
= (2² + 5)(3² + 5)(12² + 5)(137² + 5).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18778

18778² = 306 * 307 + 308 * 309 + 310 * 311 + 312 * 313 + ... + 1288 * 1289.

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18785

18785² = (2² + 9)(4² + 9)(1042² + 9).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18810

18810² = 804 * 805 + 805 * 806 + 806 * 807 + 807 * 808 + ... + 1164 * 1165.

18810² = 176³ + 177³ + 178³ + 179³ + ... + 220³.

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

---

18816

18816² = (13² - 1)(15² - 1)(97² - 1).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18819

18819² = (71² + 2)(265² + 2).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18832

18832² = (2² + 7)(5² + 7)(10² + 7)(97² + 7).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18843

18843² = (19² + 2)(989² + 2).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18846

18846²± 5 are primes.

18846² = 355171716, 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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18850

18850² = (1² + 1)(2² + 1)(7² + 1)(12² + 1)(70² + 1) = (1² + 1)(2² + 1)(8² + 1)(18² + 1)(41² + 1)
= (2² + 1)(5² + 1)(8² + 1)(12² + 1)(17² + 1) = (2² + 1)(7² + 1)(12² + 1)(99² + 1)
= (2² + 1)(7² + 1)(17² + 1)(70² + 1) = (3² + 1)(7² + 1)(12² + 1)(70² + 1)
= (3² + 1)(8² + 1)(18² + 1)(41² + 1) = (5² + 1)(12² + 1)(17² + 1)(18² + 1)
= (5² + 1)(12² + 1)(307² + 1) = (8² + 1)(41² + 1)(57² + 1) = (1² + 4)(5² + 4)(11² + 4)(140² + 4).

Page of Squares : First Upload November 9, 2013 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18864

18864²± 5 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18870

18870² = (1² + 9)(5² + 9)(18² + 9)(56² + 9) = (19² + 9)(981² + 9).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18891

18891²± 2 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18900

18900² = (2² - 1)(6² - 1)(26² - 1)(71² - 1) = (2² - 1)(6² - 1)(8² - 1)(9² - 1)(26² - 1).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18910

18910²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18914

18914² = 357739396, 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

---

18956

18956²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

---

18975

18975² = 360050625, 3600 = 60², 50625 = 225².

18975² = 360050625, 36 = 60², 50625 = 225².

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

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18992

18992² = S2(572) + S2(963), where S2(n) = 1² + 2² + 3² + ... + n².

18992² = 360696064 is a square pegged by 6.

Page of Squares : First Upload February 11, 2012 ; Last Revised February 11, 2012
by Yoshio Mimura, Kobe, Japan

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