## 14022

14022^{2} = (1^{2} + 2)(2^{2} + 2)(11^{2} + 2)(298^{2} + 2) = (2^{2} + 2)(6^{2} + 2)(13^{2} + 2)(71^{2} + 2)

= (4^{2} + 2)(11^{2} + 2)(298^{2} + 2) = (6^{2} + 2)(32^{2} + 2)(71^{2} + 2).

by Yoshio Mimura, Kobe, Japan

## 14036

14036^{2} = (13^{2} + 7)(1058^{2} + 7) = (2^{2} + 7)(3^{2} + 7)(1058^{2} + 7).

by Yoshio Mimura, Kobe, Japan

## 14040

14040^{2} = (14^{2} - 1)(19^{2} - 1)(53^{2} - 1) = (2^{2} - 1)(11^{2} - 1)(14^{2} - 1)(53^{2} - 1)

= (2^{2} - 1)(3^{2} - 1)(4^{2} - 1)(14^{2} - 1)(53^{2} - 1) = (4^{2} - 1)(5^{2} - 1)(14^{2} - 1)(53^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 14041

14041^{2} = 349^{2} + 351^{2} + 353^{2} + 355^{2} + ... + 1069^{2}.

by Yoshio Mimura, Kobe, Japan

## 14050

14050^{2} = (1^{2} + 1)(2^{2} + 1)(4443^{2} + 1) = (3^{2} + 1)(4443^{2} + 1).

by Yoshio Mimura, Kobe, Japan

## 14056

14056^{2} = 197571136, a square with odd digits except the last digit 6.

by Yoshio Mimura, Kobe, Japan

## 14064

14064^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 14080

14080^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 14091

14091^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 14098

14098^{2} = 198753604 is a square consisting of different digits.

by Yoshio Mimura, Kobe, Japan

## 14104

14104^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 14120

14120^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 14124

14124^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 14127

14127^{2} = 302^{2} + 303^{2} + 304^{2} + ... + 855^{2}.

by Yoshio Mimura, Kobe, Japan

## 14136

14136^{2} = (1^{2} + 3)(11^{2} + 3)(15^{2} + 3)(42^{2} + 3) = (1^{2} + 3)(3^{2} + 3)(4^{2} + 3)(11^{2} + 3)(42^{2} + 3).

by Yoshio Mimura, Kobe, Japan

## 14139

14139^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 14160

14160^{2} = 118^{3} + 119^{3} + 120^{3} + 121^{3} + ... + 177^{3}.

by Yoshio Mimura, Kobe, Japan

## 14161

14161 is a aigzag square pegged by 1.

Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan

## 14168

14168^{2} = (1^{2} + 7)(2^{2} + 7)(4^{2} + 7)(7^{2} + 7)(42^{2} + 7) = (1^{2} + 7)(42^{2} + 7)(119^{2} + 7)

= (2^{2} + 7)(4^{2} + 7)(21^{2} + 7)(42^{2} + 7) = (2^{2} + 7)(4^{2} + 7)(7^{2} + 7)(119^{2} + 7)

= (4^{2} + 7)(7^{2} + 7)(9^{2} + 7)(42^{2} + 7).

by Yoshio Mimura, Kobe, Japan

## 14170

14170^{2} = (1^{2} + 4)(16^{2} + 4)(393^{2} + 4) = (1^{2} + 4)(3^{2} + 4)(4^{2} + 4)(393^{2} + 4)

= (1^{2} + 9)(2^{2} + 9)(10^{2} + 9)(119^{2} + 9) = (10^{2} + 9)(11^{2} + 9)(119^{2} + 9) = (36^{2} + 4)(393^{2} + 4).

by Yoshio Mimura, Kobe, Japan

## 14190

14190^{2} = (5^{3} + 4)(116^{3} + 4).

by Yoshio Mimura, Kobe, Japan

## 14196

14196^{2} = (1^{2} + 3)(2^{2} + 3)(3^{2} + 3)(6^{2} + 3)(124^{2} + 3) = (1^{2} + 3)(6^{2} + 3)(9^{2} + 3)(124^{2} + 3)

= (2^{2} + 3)(6^{2} + 3)(19^{2} + 3)(45^{2} + 3) = (3^{2} + 3)(33^{2} + 3)(124^{2} + 3)

= (3^{2} + 3)(5^{2} + 3)(6^{2} + 3)(124^{2} + 3).

by Yoshio Mimura, Kobe, Japan

## 14210

14210^{2} = (2^{2} + 6)(20^{2} + 6)(223^{2} + 6).

by Yoshio Mimura, Kobe, Japan

## 14224

14224^{2} = (5^{2} + 7)(7^{2} + 7)(336^{2} + 7).

by Yoshio Mimura, Kobe, Japan

## 14248

14248^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 14256

14256^{2} = (1^{2} + 8)(10^{2} + 8)(16^{2} + 8)(28^{2} + 8) = (1^{2} + 8)(2^{2} + 8)(4^{2} + 8)(16^{2} + 8)(17^{2} + 8)

= (1^{2} + 8)(2^{2} + 8)(4^{2} + 8)(280^{2} + 8) = (1^{2} + 8)(2^{2} + 8)(5^{2} + 8)(8^{2} + 8)(28^{2} + 8)

= (1^{2} + 8)(4^{2} + 8)(5^{2} + 8)(10^{2} + 8)(16^{2} + 8) = (1^{2} + 8)(4^{2} + 8)(6^{2} + 8)(8^{2} + 8)(17^{2} + 8)

= (1^{2} + 8)(6^{2} + 8)(16^{2} + 8)(44^{2} + 8) = (2^{2} + 8)(4^{2} + 8)(5^{2} + 8)(8^{2} + 8)(17^{2} + 8)

= (2^{2} + 8)(5^{2} + 8)(16^{2} + 8)(44^{2} + 8) = (2^{2} + 8)(8^{2} + 8)(17^{2} + 8)(28^{2} + 8)

= (2^{2} - 1)(17^{2} - 1)(485^{2} - 1) = (4^{2} + 8)(10^{2} + 8)(16^{2} + 8)(17^{2} + 8)

= (4^{2} + 8)(10^{2} + 8)(280^{2} + 8) = (5^{2} + 8)(6^{2} + 8)(8^{2} + 8)(44^{2} + 8)

= (5^{2} + 8)(8^{2} + 8)(10^{2} + 8)(28^{2} + 8) = (8^{2} + 8)(38^{2} + 8)(44^{2} + 8).

by Yoshio Mimura, Kobe, Japan

## 14274

14274^{2} = (15^{2} + 9)(28^{2} + 9)(33^{2} + 9) = (2^{2} + 9)(3^{2} + 9)(28^{2} + 9)(33^{2} + 9).

by Yoshio Mimura, Kobe, Japan

## 14280

14280^{2} = (13^{2} - 1)(16^{2} - 1)(69^{2} - 1) = (3^{2} - 1)(50^{2} - 1)(101^{2} - 1) = (6^{2} - 1)(35^{2} - 1)(69^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 14283

14283^{2} = S2(213) + S2(844), where S2(n) = 1^{2} + 2^{2} + 3^{2} + ... + n^{2}.

by Yoshio Mimura, Kobe, Japan

## 14288

14288^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 14289

The quadratic polynomial 14289X^{2} - 70422X + 83689 takes the values 166^{2}, 1^{2}, 32^{2}, 175^{2}, 298^{2}, 419^{2} at X = 1, 2, ..., 6.

by Yoshio Mimura, Kobe, Japan

## 14322

14322^{2} + 33738^{2} = 1343372328 (mosaic).

14322^{2} = (1^{2} + 6)(36^{2} + 6)(150^{2} + 6) = (1^{2} + 6)(5^{2} + 6)(6^{2} + 6)(150^{2} + 6)

= (15^{2} + 6)(26^{2} + 6)(36^{2} + 6) = (4^{2} + 6)(5^{2} + 6)(15^{2} + 6)(36^{2} + 6)

= (5^{2} + 6)(6^{2} + 6)(15^{2} + 6)(26^{2} + 6).

by Yoshio Mimura, Kobe, Japan

## 14329

14329^{2} = 15^{2} + 17^{2} + 19^{2} + 21^{2} + ... + 1071^{2}.

by Yoshio Mimura, Kobe, Japan

## 14331

14331^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 14343

14343^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 14345

14345^{2} = 131^{2} + 132^{2} + 133^{2} + ... + 852^{2}.

by Yoshio Mimura, Kobe, Japan

## 14370

14370^{2} = 117 * 118 + 119 * 120 + 121 * 122 + 123 * 124 + ... + 1073 * 1074.

by Yoshio Mimura, Kobe, Japan

## 14394

14394^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 14397

14397^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 14400

14400^{2} = (2^{2} - 1)(4^{2} - 1)(5^{2} - 1)(9^{2} - 1)(49^{2} - 1) = (2^{2} - 1)(9^{2} - 1)(19^{2} - 1)(49^{2} - 1)

= (4^{2} - 1)(7^{2} - 1)(11^{2} - 1)(49^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 14418

14418^{2} = (1^{2} + 2)(4^{2} + 2)(40^{2} + 2)(49^{2} + 2).

by Yoshio Mimura, Kobe, Japan

## 14420

14420^{2} = 207936400, and 207936 = 456^{2}, 400 = 20^{2}.

by Yoshio Mimura, Kobe, Japan

## 14430

14430^{2} = (18^{2} + 9)(19^{2} + 9)(41^{2} + 9) = (2^{2} + 9)(11^{2} + 9)(18^{2} + 9)(19^{2} + 9)

= (2^{2} + 9)(11^{2} + 9)(351^{2} + 9) = (41^{2} + 9)(351^{2} + 9).

by Yoshio Mimura, Kobe, Japan

## 14432

14432^{2} = 208282624 is a square with even digits.

by Yoshio Mimura, Kobe, Japan

## 14439

The quadratic polynomial -14439X^{2} + 171798X - 156959 takes the values 20^{2}, 359^{2}, 478^{2}, 547^{2}, 584^{2}, 595^{2} at X = 1, 2, ..., 6.

by Yoshio Mimura, Kobe, Japan

## 14442

14442^{2} = 208571364 is a square consisting of different digits.

by Yoshio Mimura, Kobe, Japan

## 14448

14448^{2} = (1^{2} + 3)(3^{2} + 3)(13^{2} + 3)(159^{2} + 3) = (1^{2} + 3)(3^{2} + 3)(5^{2} + 3)(13^{2} + 3)(30^{2} + 3).

by Yoshio Mimura, Kobe, Japan

## 14450

14450^{2} = (2^{2} + 1)(3^{2} + 1)(4^{2} + 1)(13^{2} + 1)(38^{2} + 1) = (4^{2} + 1)(7^{2} + 1)(13^{2} + 1)(38^{2} + 1).

by Yoshio Mimura, Kobe, Japan

## 14454

14454^{2} = (1^{2} + 2)(2^{2} + 2)(3^{2} + 2)(12^{2} + 2)(85^{2} + 2) = (1^{2} + 2)(8^{2} + 2)(12^{2} + 2)(85^{2} + 2)

= (12^{2} + 2)(14^{2} + 2)(85^{2} + 2) = (3^{2} + 2)(4^{2} + 2)(12^{2} + 2)(85^{2} + 2).

by Yoshio Mimura, Kobe, Japan

## 14468

14468^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 14469

14469^{2} = S2(466) + S2(807), where S2(n) = 1^{2} + 2^{2} + 3^{2} + ... + n^{2}.

by Yoshio Mimura, Kobe, Japan

## 14490

14490^{2} = (1^{2} + 5)(10^{2} + 5)(15^{2} + 5)(38^{2} + 5) = (1^{2} + 5)(2^{2} + 5)(15^{2} + 5)(130^{2} + 5)

= (1^{2} + 5)(2^{2} + 5)(5^{2} + 5)(360^{2} + 5) = (1^{2} + 5)(4^{2} + 5)(8^{2} + 5)(10^{2} + 5)(15^{2} + 5)

= (1^{2} + 5)(5^{2} + 5)(8^{2} + 5)(130^{2} + 5) = (15^{2} + 5)(25^{2} + 5)(38^{2} + 5)

= (2^{2} + 5)(10^{2} + 5)(15^{2} + 5)(31^{2} + 5) = (2^{2} + 5)(3^{2} + 5)(8^{2} + 5)(10^{2} + 5)(15^{2} + 5)

= (4^{2} + 5)(5^{2} + 5)(15^{2} + 5)(38^{2} + 5) = (4^{2} + 5)(8^{2} + 5)(15^{2} + 5)(25^{2} + 5)

= (5^{2} + 5)(7^{2} + 5)(360^{2} + 5) = (5^{2} + 5)(8^{2} + 5)(10^{2} + 5)(31^{2} + 5)

= (7^{2} + 5)(15^{2} + 5)(130^{2} + 5) = (8^{2} + 5)(10^{2} + 5)(11^{2} + 5)(15^{2} + 5)

= (8^{2} + 5)(15^{2} + 5)(115^{2} + 5).

by Yoshio Mimura, Kobe, Japan

## 14491

184162^{2} is the sum of (30m+1)^{2} for 1 <= 30m + 1 <= 14491.

by Yoshio Mimura, Kobe, Japan

## 14499

14499^{2}± 2 are primes.

14499^{2} = 210221001 is a square with 3 kinds of digits.

by Yoshio Mimura, Kobe, Japan

## 14500

14500^{2}± 3 are primes.

14500^{2} = (1^{2} + 1)(2^{2} + 1)(3^{2} + 1)(7^{2} + 1)(12^{2} + 1)(17^{2} + 1)

= (1^{2} + 4)(4^{2} + 4)(5^{2} + 4)(11^{2} + 4)(24^{2} + 4).

by Yoshio Mimura, Kobe, Japan

## 14550

14550^{2} = (12^{2} + 6)(1188^{2} + 6) = (2^{2} + 6)(3^{2} + 6)(1188^{2} + 6).

by Yoshio Mimura, Kobe, Japan

## 14573

14573^{2} = 2 + 3 + 5 + 7 + 11 + ... + 67187 (the sum of consecutive primes).

by Yoshio Mimura, Kobe, Japan

## 14600

14600^{2} = (1^{2} + 4)(6^{2} + 4)(19^{2} + 4)(54^{2} + 4) = (14^{2} + 4)(19^{2} + 4)(54^{2} + 4).

by Yoshio Mimura, Kobe, Japan

## 14601

14601^{2} = 8^{3} + 69^{3} + 427^{3} + 513^{3}.

by Yoshio Mimura, Kobe, Japan

## 14625

14625^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 14641

14641 is a palindromic square (121^{2}) (pegged by 4) with 3 kinds of digits.

by Yoshio Mimura, Kobe, Japan

## 14651

14651^{2} = 214651801.

by Yoshio Mimura, Kobe, Japan

## 14652

14652^{3} + 25641^{3} = 4472523^{2}.

by Yoshio Mimura, Kobe, Japan

## 14676

14676^{2} = 215384976 is a square consisting of different digits.

by Yoshio Mimura, Kobe, Japan

## 14688

14688^{2} = (1^{2} + 8)(2^{2} + 8)(4^{2} + 8)(14^{2} + 8)(20^{2} + 8) = (2^{2} + 8)(3^{2} + 8)(4^{2} + 8)(10^{2} + 8)(20^{2} + 8)

= (2^{2} + 8)(8^{2} + 8)(10^{2} + 8)(48^{2} + 8) = (4^{2} + 8)(10^{2} + 8)(14^{2} + 8)(20^{2} + 8).

by Yoshio Mimura, Kobe, Japan

## 14690

14690^{2} = (2^{2} + 1)(15^{2} + 1)(437^{2} + 1).

by Yoshio Mimura, Kobe, Japan

## 14700

14700^{2} = (1^{2} + 6)(2^{2} + 6)(6^{2} + 6)(12^{2} + 6)(22^{2} + 6) = (2^{2} + 6)(3^{2} + 6)(6^{2} + 6)(8^{2} + 6)(22^{2} + 6)

= (6^{2} + 6)(8^{2} + 6)(12^{2} + 6)(22^{2} + 6).

by Yoshio Mimura, Kobe, Japan

## 14701

14701^{2} = 1270^{2} + 1271^{2} + 1272^{2} + ... + 1391^{2}.

by Yoshio Mimura, Kobe, Japan

## 14706

14706^{2} = (13^{2} + 2)(16^{2} + 2)(70^{2} + 2).

by Yoshio Mimura, Kobe, Japan

## 14736

14736^{2} = 1^{3} + 3^{3} + 9^{3} + 246^{3} + 587^{3}.

by Yoshio Mimura, Kobe, Japan

## 14743

14743^{2} = 217356049 is a square consisting of different digits.

by Yoshio Mimura, Kobe, Japan

## 14748

14748, 14749, 14750, 14751 and 14752 are consecutive integers having square factors (the 7th case).

Page of Squares : First Upload December 14, 2013 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan

## 14750

14750^{2} = 1019 * 1020 + 1020 * 1021 + 1021 * 1022 + 1022 * 1023 + ... + 1195 * 1196.

by Yoshio Mimura, Kobe, Japan

## 14752

14752^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 14766

14766^{2} = 218034756 is a square consisting of different digits.

by Yoshio Mimura, Kobe, Japan

## 14784

14784^{2} = (15^{2} - 1)(23^{2} - 1)(43^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 14790

14790^{2} = (1^{2} + 9)(5^{2} + 9)(22^{2} + 9)(36^{2} + 9) = (9^{2} + 9)(1559^{2} + 9).

by Yoshio Mimura, Kobe, Japan

## 14796

14796^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 14798

14798^{2} = (2^{2} + 3)(65^{2} + 3)(86^{2} + 3).

by Yoshio Mimura, Kobe, Japan

## 14800

14800^{2} = (1^{2} + 4)(4^{2} + 4)(6^{2} + 4)(234^{2} + 4) = (1^{2} + 4)(6^{2} + 4)(12^{2} + 4)(86^{2} + 4)

= (12^{2} + 4)(14^{2} + 4)(86^{2} + 4) = (4^{2} + 4)(14^{2} + 4)(234^{2} + 4).

by Yoshio Mimura, Kobe, Japan

## 14804

14804^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 14805

14805^{2} = (2^{2} - 1)(4^{2} - 1)(46^{2} - 1)(48^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 14811

14811^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 14824

14824^{2} = 724^{2} + 725^{2} + 726^{2} + ... + 1012^{2}.

by Yoshio Mimura, Kobe, Japan

## 14833

14833^{2} = S2(443) + S2(830), where S2(n) = 1^{2} + 2^{2} + 3^{2} + ... + n^{2}.

by Yoshio Mimura, Kobe, Japan

## 14846

14846^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 14848

14848^{2} = (3^{2} + 7)(5^{2} + 7)(15^{2} + 7)(43^{2} + 7).

by Yoshio Mimura, Kobe, Japan

## 14859

14859^{2} = 761^{3} - 760^{3} + 759^{3} - 758^{3} + ... + 1^{3}.

by Yoshio Mimura, Kobe, Japan

## 14862

14862^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 14880

14880^{2} = (4^{2} - 1)(61^{2} - 1)(63^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 14884

14884 is a square (122^{2}) with 3 kinds of digits.

by Yoshio Mimura, Kobe, Japan

## 14896

14896^{2} = (1^{2} + 3)(5^{2} + 3)(23^{2} + 3)(61^{2} + 3).

by Yoshio Mimura, Kobe, Japan

## 14908

14908^{2} = 222248464 is a square with even digits.

by Yoshio Mimura, Kobe, Japan

## 14922

14922^{2} = 222666084 is a square with even digits.

by Yoshio Mimura, Kobe, Japan

## 14951

The 6th prime for which the Legendre symbol (n/14951) = 1 for n = 1,2,...,18.

Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan

## 14960

14960^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 14974

14974^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan