logo
6000 - 6099

6000

60002 = 1003 + 2003 + 3003.

852 + 6000 = 1152, 852 - 6000 = 352.

60002 = 36000000 appears in the decimal expressions of e:
  e = 2.71828•••36000000••• (from the 89294th digit)

Page of Squares : First Upload September 26, 2008 ; Last Revised August 2, 2011
by Yoshio Mimura, Kobe, Japan

6001

60012 = 1992 + 2002 + 2012 + 2022 + ... + 4872.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 21, 2008
by Yoshio Mimura, Kobe, Japan

6002

60022 = 36024004, 32 + 62 + 02 + 22 + 42 + 02 + 02 + 42 = 92.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 21, 2008
by Yoshio Mimura, Kobe, Japan

6003

60032 = 36036009, 3 - 6 + 0 - 3 + 6009 = 6003.

52k + 190k + 233k + 254k are squares for k = 1,2,3 (272, 3972, 60032).

Page of Squares : First Upload January 21, 2008 ; Last Revised June 24, 2011
by Yoshio Mimura, Kobe, Japan

6005

60052 = 36060025, 36 = 62 and 60025 = 2452.

60055 = 7808454045018753125 :
72 + 82 + 02 + 82 + 452 + 402 + 452 + 02 + 12 + 82 + 72 + 52 + 32 + 12 + 22 + 52 = 6005.

Page of Squares : First Upload January 21, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

6006

60062 = 393 + 2063 + 3013.

The integral triangle of sides 3528, 20735, 21601 (or 5626, 66297, 71825) has square area 60062.

Page of Squares : First Upload September 26, 2008 ; Last Revised October 14, 2011
by Yoshio Mimura, Kobe, Japan

6009

1 / 6009 = 0.00016641...., and 16641 = 1292.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 21, 2008
by Yoshio Mimura, Kobe, Japan

6011

1 / 6011 = 0.00016636167027...., 12 + 662 + 362 + 162 + 72 + 02 + 22 + 72 = 6011,
1 / 6011 = 0.00016636167027...., 12 + 662 + 362 + 162 + 72 + 022 + 72 = 6011.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 21, 2008
by Yoshio Mimura, Kobe, Japan

6012

60122 = 1183 + 1833 + 3053.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6013

60132 = 36156169, where 361 = 192 and 56169 = 2372.

60132 = 36156169, 32 + 62 + 12 + 52 + 62 + 12 + 62 + 92 = 152.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 21, 2008
by Yoshio Mimura, Kobe, Japan

6014

60142± 3 are primes.

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

6016

60162 = 36192256, 32 + 62 + 12 + 92 + 22 + 22 + 52 + 62 = 142.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 21, 2008
by Yoshio Mimura, Kobe, Japan

6017

60172 = 484 + 484 + 564 + 634.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6020

60202± 3 are primes.

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

6022

60222 = 1853 + 1873 + 2863.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6024

60242 = 1563 + 1823 + 2983.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6025

60252 = 36300625, 3 * 6 * 300 + 625 = 3 * 6 + 3006 * 2 - 5 = 36300 / 6 - 25 = 6025.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 21, 2008
by Yoshio Mimura, Kobe, Japan

6027

60274 = 1319485936923441,
and 12 + 312 + 92 + 42 + 82 + 592 + 362 + 92 + 22 + 32 + 42 + 42 + 12 = 6027,
60274 = 1319485936923441,
and 132 + 192 + 482 + 52 + 92 + 362 + 92 + 22 + 32 + 42 + 412 = 6027.

Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

6030

60302 = 36360900, 3 - 63 + 6090 + 0 = 6030.

Komachi equation: 60302 = 122 / 32 * 42 * 52 * 672 / 82 * 92.

Page of Squares : First Upload January 21, 2008 ; Last Revised October 29, 2010
by Yoshio Mimura, Kobe, Japan

6031

60312 = 93 + 1443 + 3223.

60312 = 36372961, 32 + 62 + 32 + 72 + 22 + 92 + 62 + 12 = 152.

Page of Squares : First Upload January 21, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6032

60324 = 1323869971480576,
and 12 + 32 + 232 + 82 + 62 + 92 + 92 + 712 + 42 + 82 + 02 + 52 + 72 + 62 = 6032.

Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

6034

60342 = 54 + 294 + 654 + 654.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6037

60372 = 36445369 appears in the decimal expressions of π:
  π = 3.14159•••36445369••• (from the 11258th digit)
  (36445369 is the first 8-digit square in the expression of π.)

Page of Squares : First Upload November 4, 2008 ; Last Revised November 4, 2008
by Yoshio Mimura, Kobe, Japan

6038

60384 = 1329145223013136, and 12 + 322 + 92 + 12 + 42 + 522 + 22 + 302 + 12 + 32 + 12 + 362 = 6038.

Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

6040

60402 = 1843 + 2283 + 2643.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6042

60422 = 36505764, 32 + 62 + 52 + 02 + 52 + 72 + 62 + 42 = 142.

6042k + 223554k + 310156k + 474297k are squares for k = 1,2,3 (10072, 6092352, 3843245712).

60425 = 8051997005161571232 : 82 + 02 + 52 + 12 + 92 + 92 + 702 + 02 + 52 + 162 + 12 + 52 + 72 + 12 + 232 + 22 = 6042.

Page of Squares : First Upload January 21, 2008 ; Last Revised June 24, 2011
by Yoshio Mimura, Kobe, Japan

6043

60432 = 2013 + 2363 + 2483.

60432 = 36517849, a square with different digits.

Page of Squares : First Upload January 21, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6045

60452 = 113 + 2533 + 2733.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6047

60472 = 144 + 144 + 344 + 774.

60474 = 1337087640631681,
and 132 + 32 + 72 + 02 + 82 + 72 + 62 + 402 + 632 + 12 + 62 + 82 + 12 = 6047.

Page of Squares : First Upload September 26, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

6048

60482 = (22 - 1)(52 - 1)(132 - 1)(552 - 1) = (22 - 1)(52 - 1)(72 - 1)(82 - 1)(132 - 1),br /> = (32 - 1)(52 - 1)(82 - 1)(552 - 1).

60482 = 1983 + 2343 + 2523.

60484 = 1337972323516416,
and 132 + 372 + 92 + 72 + 22 + 32 + 22 + 32 + 512 + 62 + 412 + 62 = 6048.

Page of Squares : First Upload September 26, 2008 ; Last Revised January 4, 2014
by Yoshio Mimura, Kobe, Japan

6049

60492 = 36590401, a zigzag square.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 21, 2008
by Yoshio Mimura, Kobe, Japan

6050

60502 = 554 + 554 + 554 + 554.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6052

578k + 2074k + 2890k + 4862k are squares for k = 1,2,3 (1022, 60522, 3849482).

Page of Squares : First Upload June 24, 2011 ; Last Revised June 24, 2011
by Yoshio Mimura, Kobe, Japan

6056

Loop of length 35 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
6056 - 6736 - 5785 - 10474 - ... - 673 - 5365 - 7034 - 6056
(Note f(6056) = 602 + 562 = 6736,   f(6736) = 672 + 362 = 5785, etc. See 37)

The square root of 6056 is 77.8203...., and 77 = 82 + 22 + 02 + 32.

Page of Squares : First Upload January 21, 2008 ; Last Revised October 9, 2008
by Yoshio Mimura, Kobe, Japan

6057

60572 = 144 + 574 + 584 + 624.

60572 = 36687249, 3 + 6 + 6 * 8 * 7 / 2 * 4 * 9 = 36 * 6 * 8 * 7 * 2 / 4 + 9 = 6057.

Page of Squares : First Upload January 21, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6058

60582 = 36699364, 36 + 6 * 993 + 64 = 6058.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 21, 2008
by Yoshio Mimura, Kobe, Japan

6059

60594 = 1347732837213361, and 132 + 472 + 72 + 32 + 282 + 372 + 22 + 132 + 362 + 12 = 6059.

Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

6060

Komachi equation: 60602 = 984 - 74 - 64 * 54 - 434 * 24 + 14.

Page of Squares : First Upload October 29, 2010 ; Last Revised October 29, 2010
by Yoshio Mimura, Kobe, Japan

6061

60612 = 323 + 1853 + 3123.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6062

1 / 6062 = 0.00016496205872...., 162 + 42 + 92 + 62 + 202 + 52 + 82 + 722 = 6062.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 21, 2008
by Yoshio Mimura, Kobe, Japan

6063

60632 = 84 + 84 + 514 + 744.

Komachi equation: 60632 = 9872 * 62 * 52 * 432 / 2102.

Page of Squares : First Upload September 26, 2008 ; Last Revised October 29, 2010
by Yoshio Mimura, Kobe, Japan

6064

60642 = (47 + 48 + 49 + 50)2 + (51 + 52 + 53 + 54)2 + (55 + 56 + 57 + 58)2 + ... + (299 + 300 + 301 + 302)2.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 21, 2008
by Yoshio Mimura, Kobe, Japan

6067

60672 = 1033 + 2513 + 2713 = 1533 + 1663 + 3063.

60675 = 8219965120563755107 :
82 + 22 + 12 + 92 + 92 + 62 + 52 + 12 + 22 + 02 + 52 + 62 + 32 + 752 + 52 + 12 + 02 + 72 = 6067.

Page of Squares : First Upload September 26, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

6068

60682± 3 are primes.

60682 = 36820624, 32 + 62 + 82 + 22 + 02 + 62 + 22 + 42 = 132.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

6069

60692 = 1613 + 1983 + 2923.

51k + 1683k + 6069k + 10693k are squares for k = 1,2,3 (1362, 124102, 12045522).

Page of Squares : First Upload September 26, 2008 ; Last Revised June 24, 2011
by Yoshio Mimura, Kobe, Japan

6071

60712 = 36857041, a square with different digita.

60712 = 36857041, 368 + 5704 - 1 = 6071.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 21, 2008
by Yoshio Mimura, Kobe, Japan

6072

60722 = 743 + 2313 + 2893 = 1763 + 1963 + 2883 = 1913 + 2173 + 2703.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6075

60752 = 1053 + 1653 + 3153 = 1803 + 2253 + 2703.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6076

60762 = (12 + 3)(372 + 3)(822 + 3).

60762 = 1763 + 2383 + 2623.

Page of Squares : First Upload September 26, 2008 ; Last Revised January 4, 2014
by Yoshio Mimura, Kobe, Japan

6078

60782± 5 are primes.

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

6080

Komchi equation: 60802 = 92 * 82 * 762 / 542 * 32 * 22 * 102.

Page of Squares : First Upload October 29, 2010 ; Last Revised October 29, 2010
by Yoshio Mimura, Kobe, Japan

6081

60812± 2 are primes.

Page of Squares : First Upload January 4, 2014 ; Last Revised January 4, 2014
by Yoshio Mimura, Kobe, Japan

6082

60822± 3 are primes.

60822 = 36990724 appears in the decimal expressions of π:
  π = 3.14159•••36990724••• (from the 74009th digit)
  (36990724 is the tenth 8-digit square in the expression of π.)

Page of Squares : First Upload November 4, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

6083

60832 = (292 + 6)(2092 + 6).

Page of Squares : First Upload January 4, 2014 ; Last Revised January 4, 2014
by Yoshio Mimura, Kobe, Japan

6084

The square of 78.

60842 = 1023 + 1563 + 3183.

Page of Squares : First Upload January 21, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6085

60852 = 1243 + 2013 + 3003.

60852 = 37027225, 32 + 72 + 02 + 22 + 72 + 22 + 22 + 52 = 122.

60852 = 37027225, 3 + 7 + 0 + 27 * 225 = 6085.

Page of Squares : First Upload January 21, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6086

60862 = S2(56) + S2(480), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 21, 2008
by Yoshio Mimura, Kobe, Japan

6087

60872 = 164 + 224 + 514 + 744.

Page of Squares : First Upload September 26, 2008 ; Last Revised September 26, 2008
by Yoshio Mimura, Kobe, Japan

6088

60885 = 8363214174283399168 : 82 + 32 + 632 + 212 + 42 + 172 + 42 + 282 + 32 + 32 + 92 + 92 + 162 + 82 = 82 + 32 + 632 + 22 + 142 + 12 + 72 + 42 + 22 + 82 + 32 + 392 + 92 + 12 + 62 + 82 = 6088.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

6089

1 / 6089 = 0.00016423057973...., 12 + 62 + 422 + 302 + 572 + 92 + 72 + 32 = 6089.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 21, 2008
by Yoshio Mimura, Kobe, Japan

6090

60902 = (12 + 6)(22 + 6)(32 + 6)(92 + 6)(202 + 6) = (12 + 6)(22 + 6)(92 + 6)(782 + 6)
= (12 + 6)(62 + 6)(92 + 6)(382 + 6) = (12 + 6)(92 + 6)(122 + 6)(202 + 6)
= (102 + 5)(132 + 5)(452 + 5) = (32 + 6)(202 + 6)(782 + 6) = (32 + 6)(82 + 6)(92 + 6)(202 + 6)
= (82 + 6)(92 + 6)(782 + 6).

The integral triangle of sides 10585, 355251, 365834 has square area 60902.

Komachi equation: 60902 = 92 * 872 * 62 / 542 / 32 * 2102.

Page of Squares : First Upload October 29, 2010 ; Last Revised January 4, 2014
by Yoshio Mimura, Kobe, Japan

6092

60924 = 1377334984151296,
and 12 + 372 + 72 + 332 + 492 + 82 + 42 + 152 + 12 + 292 + 62 = 6092.

60925 = 8390724723449695232 :
82 + 32 + 92 + 02 + 72 + 242 + 72 + 22 + 32 + 42 + 492 + 62 + 92 + 522 + 32 + 22 = 6092.

Page of Squares : First Upload December 1, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

6095

60952 = 37149025, a square with different digits.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 21, 2008
by Yoshio Mimura, Kobe, Japan

6096

60962 = 37161216, a zigzag square.

6096 = (12 + 22 + 32 + ... + 632) / (12 + 22 + 32).

Page of Squares : First Upload January 21, 2008 ; Last Revised November 25, 2008
by Yoshio Mimura, Kobe, Japan

6097

60972 = 37173409, a zigzag square.

1716k + 2184k + 6097k + 10452k are squares for k = 1,2,3 (1432, 124152, 11764092).

Page of Squares : First Upload January 21, 2008 ; Last Revised June 24, 2011
by Yoshio Mimura, Kobe, Japan

6098

60982 = 37185604, a zigzag square with different digits.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 21, 2008
by Yoshio Mimura, Kobe, Japan

6099

60992 = 37197801, a zigzag square.

60996100 = 78102.

Page of Squares : First Upload January 21, 2008 ; Last Revised January 21, 2008
by Yoshio Mimura, Kobe, Japan