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10000 - 10999

10000

100002 = (12 + 4)(42 + 4)(62 + 4)(112 + 4)(142 + 4).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10032

100322 = (122 + 8)(162 + 8)(502 + 8) = (42 + 8)(162 + 8)(1262 + 8)
= (62 + 8)(72 + 8)(122 + 8)(162 + 8).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10050

10050, 10051, 10052 and 10053 are four consecutive integers having square factors (the 7th case).

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

10080

100802 = (112 - 1)(132 - 1)(712 - 1) = (132 - 1)(192 - 1)(412 - 1) = (22 - 1)(112 - 1)(132 - 1)(412 - 1)
= (22 - 1)(132 - 1)(4492 - 1) = (22 - 1)(32 - 1)(292 - 1)(712 - 1)
= (22 - 1)(32 - 1)(42 - 1)(132 - 1)(412 - 1) = (22 - 1)(32 - 1)(42 - 1)(62 - 1)(72 - 1)(132 - 1)
= (22 - 1)(32 - 1)(52 - 1)(62 - 1)(712 - 1) = (22 - 1)(32 - 1)(52 - 1)(62 - 1)(82 - 1)(92 - 1)
= (22 - 1)(32 - 1)(82 - 1)(92 - 1)(292 - 1) = (22 - 1)(42 - 1)(62 - 1)(152 - 1)(172 - 1)
= (22 - 1)(52 - 1)(292 - 1)(412 - 1) = (22 - 1)(52 - 1)(62 - 1)(72 - 1)(292 - 1)
= (22 - 1)(62 - 1)(72 - 1)(112 - 1)(132 - 1) = (22 - 1)(82 - 1)(152 - 1)(492 - 1)
= (32 - 1)(42 - 1)(132 - 1)(712 - 1) = (32 - 1)(42 - 1)(82 - 1)(92 - 1)(132 - 1)
= (32 - 1)(62 - 1)(112 - 1)(552 - 1) = (32 - 1)(62 - 1)(72 - 1)(82 - 1)(112 - 1)
= (32 - 1)(82 - 1)(112 - 1)(412 - 1) = (32 - 1)(82 - 1)(4492 - 1) = (42 - 1)(52 - 1)(132 - 1)(412 - 1)
= (42 - 1)(52 - 1)(62 - 1)(72 - 1)(132 - 1) = (42 - 1)(72 - 1)(132 - 1)(292 - 1)
= (52 - 1)(292 - 1)(712 - 1) = (52 - 1)(82 - 1)(92 - 1)(292 - 1) = (62 - 1)(312 - 1)(552 - 1)
= (62 - 1)(72 - 1)(132 - 1)(192 - 1) = (62 - 1)(72 - 1)(82 - 1)(312 - 1) = (82 - 1)(312 - 1)(412 - 1)
= (82 - 1)(92 - 1)(112 - 1)(132 - 1).

1062 + 10080 = 1462, 1062 - 10080 = 342.

Page of Squares : First Upload March 10, 2012 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10081

100812 = (32 + 8)(24452 + 8).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10086

100862± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10098

100982 = (12 + 2)(102 + 2)(142 + 2)(412 + 2) = (12 + 2)(22 + 2)(412 + 2)(582 + 2)
= (12 + 2)(22 + 2)(52 + 2)(192 + 2)(242 + 2) = (12 + 2)(22 + 2)(72 + 2)(82 + 2)(412 + 2)
= (12 + 2)(32 + 2)(42 + 2)(102 + 2)(412 + 2) = (12 + 2)(32 + 2)(42 + 2)(72 + 2)(582 + 2)
= (12 + 2)(32 + 2)(52 + 2)(142 + 2)(242 + 2) = (12 + 2)(42 + 2)(72 + 2)(102 + 2)(192 + 2)
= (12 + 2)(72 + 2)(142 + 2)(582 + 2) = (192 + 2)(222 + 2)(242 + 2)
= (22 + 2)(32 + 2)(42 + 2)(72 + 2)(412 + 2) = (22 + 2)(72 + 2)(142 + 2)(412 + 2)
= (32 + 2)(52 + 2)(102 + 2)(582 + 2) = (32 + 2)(52 + 2)(72 + 2)(82 + 2)(102 + 2)
= (42 + 2)(412 + 2)(582 + 2) = (42 + 2)(52 + 2)(192 + 2)(242 + 2)
= (42 + 2)(72 + 2)(82 + 2)(412 + 2) = (72 + 2)(102 + 2)(1402 + 2).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10122

101222± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10143

101432 = (82 + 5)(322 + 5)(382 + 5).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10150

101502 = (132 + 6)(202 + 6)(382 + 6).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10162

101622 = 24 + 434 + 654 + 794 + 814.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

10192

101922 = (12 + 3)(72 + 3)(192 + 3)(372 + 3).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10206

102062 = (22 + 5)(42 + 5)(72 + 5)(1012 + 5).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10216

102162± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10230

102302 = (22 + 6)(32 + 6)(52 + 6)(1502 + 6) = (32 + 6)(52 + 6)(182 + 6)(262 + 6)
= (52 + 6)(122 + 6)(1502 + 6).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10262

102622± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10278

102782 = (22 + 2)(42 + 2)(9892 + 2).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10290

102902 = (12 + 6)(32 + 6)(82 + 6)(1202 + 6) = (12 + 6)(62 + 6)(222 + 6)(272 + 6)
= (22 + 6)(272 + 6)(1202 + 6) = (32 + 6)(222 + 6)(1202 + 6) = (62 + 6)(132 + 6)(1202 + 6).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10296

102962 = 1333 + 1343 + ... + 1643.

56 + 10296 = 1612, 56 - 10296 = 732.

Page of Squares : First Upload December 20, 2011 ; Last Revised March 10, 2012
by Yoshio Mimura, Kobe, Japan

10304

103042 = (72 + 7)(212 + 7)(652 + 7).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10317

10317^2±± 2 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10368

103682± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10370

103702 = (12 + 1)(22 + 1)(42 + 1)(112 + 1)(722 + 1)
= (112 + 1)(132 + 1)(722 + 1) = (32 + 1)(42 + 1)(112 + 1)(722 + 1).

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

10374

103742± 5 are primes.

103742 = (12 + 3)(22 + 3)(42 + 3)(62 + 3)(722 + 3) = (32 + 3)(42 + 3)(62 + 3)(1102 + 3)
= (42 + 3)(332 + 3)(722 + 3) = (42 + 3)(52 + 3)(62 + 3)(722 + 3) = (62 + 3)(122 + 3)(1372 + 3)
= (62 + 3)(152 + 3)(1102 + 3) = (62 + 3)(232 + 3)(722 + 3).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10383

10383^2±± 2 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10384

103842± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10386

103862 = (22 + 2)(52 + 2)(8162 + 2).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10395

103952 = (22 - 1)(82 - 1)(102 - 1)(762 - 1) = (42 - 1)(82 - 1)(102 - 1)(342 - 1).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10400

104002 = (12 + 4)(22 + 4)(32 + 4)(42 + 4)(62 + 4)(162 + 4)
= (12 + 4)(22 + 4)(42 + 4)(102 + 4)(362 + 4) = (12 + 4)(42 + 4)(62 + 4)(102 + 4)(162 + 4)
= (22 + 4)(32 + 4)(42 + 4)(142 + 4)(162 + 4) = (22 + 4)(32 + 4)(42 + 4)(62 + 4)(362 + 4)
= (22 + 4)(62 + 4)(162 + 4)(362 + 4) = (42 + 4)(102 + 4)(142 + 4)(162 + 4)
= (42 + 4)(62 + 4)(102 + 4)(362 + 4).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10416

104162 = (12 + 3)(22 + 3)(32 + 3)(112 + 3)(512 + 3) = (12 + 3)(32 + 3)(112 + 3)(1352 + 3)
= (12 + 3)(92 + 3)(112 + 3)(512 + 3) = (32 + 3)(52 + 3)(112 + 3)(512 + 3).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10438

104382± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10452

104522 = (32 + 3)(62 + 3)(82 + 3)(592 + 3).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10458

104582 = (12 + 5)(22 + 5)(242 + 5)(592 + 5) = (72 + 5)(242 + 5)(592 + 5).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10464

104642± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10488

104882± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10492

104922 = (12 + 3)(132 + 3)(4002 + 3).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10504

105042 = (102 + 4)(10302 + 4) = (22 + 4)(32 + 4)(10302 + 4).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10506

105062± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10509

10509^2±± 2 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10530

105302 = (32 + 9)(62 + 9)(152 + 9)(242 + 9).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10544

105442 = 111175936, 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

10546

105462± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10560

105602 = (22 - 1)(32 - 1)(92 - 1)(2412 - 1) = (52 - 1)(92 - 1)(2412 - 1).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10584

1052 + 10584 = 1472, 1052 - 10584 = 212.

Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012
by Yoshio Mimura, Kobe, Japan

10600

106002 = (12 + 4)(72 + 4)(142 + 4)(462 + 4) = (22 + 4)(72 + 4)(112 + 4)(462 + 4).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10614

106142 = (12 + 5)(422 + 5)(1032 + 5) = (132 + 5)(192 + 5)(422 + 5).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10616

106162± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10626

106262± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10646

106462 = 113337316, 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

10659

10659^2±± 2 are primes.

106592 = (32 + 8)(312 + 8)(832 + 8).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10660

106602 = (12 + 1)(22 + 1)(52 + 1)(92 + 1)(732 + 1) = (32 + 1)(52 + 1)(92 + 1)(732 + 1).

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

10662

106622± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10664

106642 = (112 + 3)(132 + 3)(732 + 3).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10668

106682 = 333 * 334 * 335 + 335 * 336 * 337 + 337 * 338 * 339.

Page of Squares : First Upload October 26, 2103 ; Last Revised October 26, 2103
by Yoshio Mimura, Kobe, Japan

10688

106882 = 114233344, 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

10692

106922 = (12 + 2)(22 + 2)(32 + 2)(42 + 2)(82 + 2)(222 + 2)
= (12 + 2)(22 + 2)(42 + 2)(52 + 2)(82 + 2)(142 + 2) = (12 + 2)(22 + 2)(82 + 2)(142 + 2)(222 + 2)
= (12 + 8)(22 + 8)(52 + 8)(102 + 8)(172 + 8) = (22 + 2)(32 + 2)(42 + 2)(142 + 2)(222 + 2)
= (42 + 2)(82 + 2)(142 + 2)(222 + 2).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10695

106952 = 813 + 823 + ... + 1493.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

10730

107302 = (22 + 1)(412 + 1)(1172 + 1) = (62 + 1)(412 + 1)(432 + 1).

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

10758

107582 = (12 + 2)(182 + 2)(3442 + 2).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10766

107662± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10772

107722± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10800

108002 = (22 - 1)(42 - 1)(72 - 1)(92 - 1)(262 - 1) = (22 - 1)(52 - 1)(262 - 1)(492 - 1).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10816

108162± 3 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10827

10827, 10828, 10829 and 10830 are four consecutive integers having square factors (the 8th case).

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

10834

108342 = 117375556, 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

10850

108502 = (12 + 6)(22 + 6)(132 + 6)(982 + 6) = (12 + 6)(52 + 6)(82 + 6)(882 + 6)
= (52 + 6)(222 + 6)(882 + 6) = (82 + 6)(132 + 6)(982 + 6).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10854

108542 = (22 + 2)(202 + 2)(2212 + 2).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10878

108782 = (22 + 3)(122 + 3)(162 + 3)(212 + 3).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10914

109142 = 119115396, 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

10920

109202 = (142 - 1)(272 - 1)(292 - 1) = (22 - 1)(32 - 1)(62 - 1)(142 - 1)(272 - 1)
= (52 - 1)(62 - 1)(142 - 1)(272 - 1) = (82 - 1)(272 - 1)(512 - 1).

1092 + 10920 = 1512, 1092 - 10920 = 312,
1972 + 10920 = 2232, 1972 - 10920 = 1672.

Page of Squares : First Upload March 10, 2012 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10924

109242 = 119333776, a square with odd digits except the last digit 6.

10924, 10925, 10926, 10927 and 10928 are five consecutive integers having square factors (the 6th case).

Page of Squares : First Upload August 31, 2013 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

10944

109442 = 119771136, 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

10950

109502 = (12 + 9)(42 + 9)(82 + 9)(812 + 9).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10962

109622± 5 are primes.

109622 = (12 + 5)(162 + 5)(2772 + 5) = (12 + 5)(32 + 5)(162 + 5)(742 + 5)
= (12 + 5)(42 + 5)(132 + 5)(742 + 5) = (112 + 5)(132 + 5)(742 + 5)
= (22 + 5)(132 + 5)(162 + 5)(172 + 5) = (22 + 5)(132 + 5)(2772 + 5)
= (22 + 5)(32 + 5)(132 + 5)(742 + 5) = (22 + 5)(32 + 5)(42 + 5)(132 + 5)(162 + 5)
= (22 + 5)(42 + 5)(112 + 5)(712 + 5) = (42 + 5)(112 + 5)(132 + 5)(162 + 5).

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

10978

109782 = 2! + 2! + 8! + 9! + 9! + 11! + 11! + 11!.

Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011
by Yoshio Mimura, Kobe, Japan

10998

109982± 5 are primes.

Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan