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40000 - 40999

40000

40000400001 = 2000012.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

40016

4000162 = (182 + 4)(222 + 4)(1002 + 4).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40032

400322± 5 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40040

400402± 3 are primes.

400402 = (62 - 1)(122 - 1)(212 - 1)(272 - 1).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40054

400542± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40101

401012± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40112

401122 = (12 + 7)(42 + 7)(502 + 7)(592 + 7).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40150

401502 = (22 + 6)(72 + 6)(17122 + 6).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40166

401662 = 3117 x 3118 + 3119 x 3120 + 3121 x 3122 + 3123 x 3124 + ... + 3417 x 3418.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

40188

401882± 5 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40204

402042 = 1616361616, a square with 3 kinds of digits 1,3,6.

402042 = 1616361616, a square pegged by 6.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

40282

402822± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40320

2122 + 40320 = 2922, 2122 - 40320 = 682.

403202 = (22 - 1)(32 - 1)(42 - 1)(52 - 1)(152 - 1)(292 - 1)
= (22 - 1)(32 - 1)(42 - 1)(112 - 1)(132 - 1)(152 - 1) = (22 - 1)(32 - 1)(52 - 1)(62 - 1)(72 - 1)(412 - 1)
= (22 - 1)(32 - 1)(52 - 1)(62 - 1)(152 - 1)(192 - 1) = (22 - 1)(32 - 1)(52 - 1)(172 - 1)(992 - 1)
= (22 - 1)(32 - 1)(62 - 1)(112 - 1)(1272 - 1) = (22 - 1)(32 - 1)(72 - 1)(292 - 1)(412 - 1)
= (22 - 1)(32 - 1)(92 - 1)(132 - 1)(712 - 1) = (22 - 1)(32 - 1)(152 - 1)(192 - 1)(292 - 1)
= (22 - 1)(42 - 1)(72 - 1)(92 - 1)(972 - 1) = (22 - 1)(42 - 1)(132 - 1)(152 - 1)(312 - 1)
= (22 - 1)(52 - 1)(62 - 1)(72 - 1)(92 - 1)(132 - 1) = (22 - 1)(52 - 1)(92 - 1)(132 - 1)(412 - 1)
= (22 - 1)(52 - 1)(112 - 1)(152 - 1)(292 - 1) = (22 - 1)(52 - 1)(492 - 1)(972 - 1)
= (22 - 1)(62 - 1)(312 - 1)(1272 - 1) = (22 - 1)(72 - 1)(92 - 1)(132 - 1)(292 - 1)
= (32 - 1)(42 - 1)(52 - 1)(62 - 1)(1272 - 1) = (32 - 1)(42 - 1)(72 - 1)(132 - 1)(412 - 1)
= (32 - 1)(42 - 1)(82 - 1)(152 - 1)(312 - 1) = (32 - 1)(42 - 1)(132 - 1)(152 - 1)(192 - 1)
= (32 - 1)(42 - 1)(292 - 1)(1272 - 1) = (32 - 1)(52 - 1)(62 - 1)(72 - 1)(82 - 1)(92 - 1)
= (32 - 1)(52 - 1)(62 - 1)(72 - 1)(712 - 1) = (32 - 1)(52 - 1)(62 - 1)(92 - 1)(552 - 1)
= (32 - 1)(52 - 1)(62 - 1)(172 - 1)(292 - 1) = (32 - 1)(52 - 1)(82 - 1)(92 - 1)(412 - 1)
= (32 - 1)(52 - 1)(412 - 1)(712 - 1) = (32 - 1)(62 - 1)(112 - 1)(132 - 1)(172 - 1)
= (32 - 1)(62 - 1)(152 - 1)(1612 - 1) = (32 - 1)(62 - 1)(192 - 1)(1272 - 1)
= (32 - 1)(72 - 1)(82 - 1)(92 - 1)(292 - 1) = (32 - 1)(72 - 1)(292 - 1)(712 - 1)
= (32 - 1)(92 - 1)(292 - 1)(552 - 1) = (42 - 1)(52 - 1)(112 - 1)(132 - 1)(152 - 1)
= (42 - 1)(62 - 1)(72 - 1)(152 - 1)(172 - 1) = (42 - 1)(152 - 1)(172 - 1)(412 - 1)
= (52 - 1)(62 - 1)(112 - 1)(1272 - 1) = (52 - 1)(72 - 1)(292 - 1)(412 - 1)
= (52 - 1)(92 - 1)(132 - 1)(712 - 1) = (52 - 1)(152 - 1)(192 - 1)(292 - 1)
= (62 - 1)(132 - 1)(172 - 1)(312 - 1) = (72 - 1)(82 - 1)(152 - 1)(492 - 1)
= (72 - 1)(112 - 1)(132 - 1)(412 - 1) = (72 - 1)(132 - 1)(4492 - 1) = (82 - 1)(112 - 1)(152 - 1)(312 - 1)
= (112 - 1)(132 - 1)(152 - 1)(192 - 1) = (112 - 1)(292 - 1)(1272 - 1) = (152 - 1)(492 - 1)(552 - 1).

Page of Squares : First Upload July 21, 2012 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40330

403302 = (12 + 1)(62 + 1)(332 + 1)(1422 + 1).

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

40334

403342 = (22 + 3)(82 + 3)(132 + 3)(1422 + 3).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40341

403412± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40344

2052 + 40344 = 2872, 2052 - 40344 = 412.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

40391

403912 = 1 + 2 + 3 + 4 + ... + 57121 = 12 - 22 + 32 - 42 + ... + 571212.

403912 is the sum of (2x + 1)3, where 0 < 2x + 1 <= 337.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

40392

403922± 5 are primes.

403922 = (12 + 8)(32 + 8)(42 + 8)(52 + 8)(1162 + 8) = (12 + 8)(32 + 8)(52 + 8)(202 + 8)(282 + 8)
= (12 + 8)(32 + 8)(282 + 8)(1162 + 8) = (12 + 8)(52 + 8)(202 + 8)(1162 + 8)
= (12 + 8)(162 + 8)(172 + 8)(482 + 8) = (12 + 8)(482 + 8)(2802 + 8)
= (22 - 1)(102 - 1)(352 - 1)(672 - 1) = (32 + 8)(42 + 8)(52 + 8)(172 + 8)(202 + 8)
= (32 + 8)(42 + 8)(172 + 8)(1162 + 8) = (32 + 8)(42 + 8)(282 + 8)(712 + 8)
= (32 + 8)(82 + 8)(162 + 8)(712 + 8) = (32 + 8)(172 + 8)(202 + 8)(282 + 8)
= (42 + 8)(52 + 8)(202 + 8)(712 + 8) = (42 + 8)(712 + 8)(1162 + 8)
= (52 + 8)(82 + 8)(172 + 8)(482 + 8) = (172 + 8)(202 + 8)(1162 + 8)
= (202 + 8)(282 + 8)(712 + 8).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40401

40401 = 2012, a zigzag square with 3 kinds of digits.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

40404

404042 = (12 + 3)(22 + 3)(62 + 3)(212 + 3)(582 + 3) = (12 + 3)(32 + 3)(62 + 3)(162 + 3)(582 + 3)
= (12 + 3)(62 + 3)(162 + 3)(2012 + 3) = (22 + 3)(62 + 3)(72 + 3)(162 + 3)(212 + 3)
= (22 + 3)(162 + 3)(212 + 3)(452 + 3) = (32 + 3)(582 + 3)(2012 + 3)
= (52 + 3)(62 + 3)(212 + 3)(582 + 3) = (62 + 3)(162 + 3)(192 + 3)(212 + 3)
= (212 + 3)(332 + 3)(582 + 3).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40412

404122± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40414

404142± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40425

404252 = (12 + 6)(152 + 6)(272 + 6)(372 + 6) = (32 + 6)(132 + 6)(272 + 6)(292 + 6)
= (72 + 6)(132 + 6)(152 + 6)(272 + 6).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40440

404402= 921 x 922 + 922 x 923 + 923 x 924 + 925 x 926 + ... + 1784 x 1785.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

40467

404672 = (42 + 5)(62 + 5)(182 + 5)(762 + 5).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40492

404922± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40495

4049540496 = 636362.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

40501

405012 = (102 + 1)(40302 + 1).

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

40545

405452 = 1643897025, a square with different digits.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

40557

405572± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40560

2212 + 40560 = 2992, 2212 - 40560 = 912.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

40566

405662 = (12 + 5)(165612 + 5).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40572

405722 = (12 + 5)(32 + 5)(82 + 5)(172 + 5)(312 + 5).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40584

405842 = (72 + 8)(122 + 8)(4362 + 8).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40624

406242± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40636

406362± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40646

406462± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40656

2752 + 40656 = 3412, 2752 - 40656 = 1872.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

40679

406792 = 11392 + 11402 + 11412 + ... + 18602.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

40689

406892 = (12 + 8)(172 + 8)(7872 + 8).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40700

407002 = 18112 + 18122 + 18132 + ... + 22172.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

40718

407182± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40754

407542= 27 x 28 + 28 x 29 + 29 x 30 + 31 x 32 + ... + 1707 x 1708.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

40776

407762± 5 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40800

408002 = (32 - 1)(92 - 1)(162 - 1)(1012 - 1).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40804

40804 = 2022, a palindromic and zigzag square with even digits.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

40810

408102 = (12 + 6)(42 + 6)(72 + 6)(102 + 6)(432 + 6) = (12 + 6)(72 + 6)(102 + 6)(2022 + 6)
= (22 + 6)(72 + 6)(102 + 6)(1692 + 6) = (22 + 6)(102 + 6)(292 + 6)(432 + 6)
= (42 + 6)(432 + 6)(2022 + 6) = (102 + 6)(432 + 6)(922 + 6).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40824

408242± 5 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40832

408322 = (12 + 7)(22 + 7)(432 + 7)(1012 + 7) = (12 + 7)(92 + 7)(152 + 7)(1012 + 7)
= (92 + 7)(432 + 7)(1012 + 7).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40836

408362 = (182 + 8)(222 + 8)(1012 + 8).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40885

408852 = (32 + 4)(92 + 4)(252 + 4)(492 + 4).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40920

409202 = (212 - 1)(322 - 1)(612 - 1).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40934

409342 = 16792 + 16812 + 16832 + 16852 + 16872 + ... + 24532.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

40942

409422± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40956

409562± 5 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

40962

409622± 5 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan