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5800 - 5899

5800

58002± 3 are primes.

58002 = (12 + 4)(22 + 4)(112 + 4)(822 + 4) = (12 + 4)(52 + 4)(142 + 4)(342 + 4)
= (22 + 4)(52 + 4)(112 + 4)(342 + 4) = (62 + 4)(112 + 4)(822 + 4).

Page of Squares : First Upload December 28, 2013 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

5802

58022 = 194 + 414 + 574 + 674 = 234 + 414 + 534 + 694.

Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008
by Yoshio Mimura, Kobe, Japan

5804

58042 = 1343 + 2053 + 2833.

58045 = 6586231911457025024 : 62 + 52 + 82 + 62 + 22 + 32 + 12 + 92 + 12 + 12 + 42 + 52 + 702 + 22 + 52 + 02 + 242 = 5804.

Page of Squares : First Upload September 22, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

5805

58052 = 1713 + 2433 + 2433.

Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008
by Yoshio Mimura, Kobe, Japan

5806

58062± 3 are primes.

58062 = 33709636 appears in the decimal expressions of e:
  e = 2.71828•••33709636••• (from the 101899th digit)

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

5807

58072 = 94 + 124 + 244 + 764.

Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008
by Yoshio Mimura, Kobe, Japan

5808

58082 = 33732864, 32 + 32 + 72 + 32 + 22 + 82 + 62 + 42 = 142.

Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008
by Yoshio Mimura, Kobe, Japan

5809

5809 = (12 + 22 + 32 + ... + 3142) / (12 + 22 + 32 + ... + 172).

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

5810

5810 = (12 + 22 + 32 + ... + 3322) / (12 + 22 + 32 + ... + 182).

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

5811

1 / 5811 = 0.000172087420409...., 12 + 722 + 082 + 72 + 42 + 202 + 42 + 092 = 5811.

Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008
by Yoshio Mimura, Kobe, Japan

5814

58142 = (102 + 2)(132 + 2)(442 + 2) = (62 + 2)(72 + 2)(102 + 2)(132 + 2).

58142 = (105 + 106 + 107 + ... + 116)2 + (117 + 118 + 119 + ... + 128)2 + (129 + 130 + 131 + ... + 140)2 + ... + (201 + 202 + 203 + ... + 212)2.

58144 = 1142615496339216, and 112 + 422 + 62 + 12 + 52 + 492 + 62 + 332 + 92 + 22 + 162 = 5814.

Page of Squares : First Upload January 7, 2008 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

5815

58152 = 1323 + 2013 + 2863.

1 / 5815 = 0.0001719690455717...., 172 + 192 + 692 + 042 + 52 + 52 + 72 + 172 = 5815.

Page of Squares : First Upload January 7, 2008 ; Last Revised September 22, 2008
by Yoshio Mimura, Kobe, Japan

5816

58162 = 33825856, 3 * 3 * 8 * 2 * 5 * 8 + 56 = 5816.

58164 = 1144188534132736, and 12 + 12 + 442 + 12 + 82 + 82 + 52 + 32 + 412 + 32 + 272 + 362 = 5816.

Page of Squares : First Upload January 7, 2008 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

5819

58192 = S2(39) + S2(466), where S2(n) = 12 + 22 + 32 + ... + n2.

Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008
by Yoshio Mimura, Kobe, Japan

5823

58232 = 583 + 863 + 3213 = 813 + 1153 + 3173.

Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008
by Yoshio Mimura, Kobe, Japan

5825

58252 = (112 + 4)(5212 + 4).

Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

5827

1 / 5827 = 0.00017161...., and 17161 = 1312.

Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008
by Yoshio Mimura, Kobe, Japan

5828

58285 = 6723535704575034368 : 62 + 72 + 232 + 52 + 32 + 52 + 72 + 02 + 42 + 52 + 72 + 502 + 342 + 362 + 82 = 5828.

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

5830

S2(5830) = S2(3647) + S2(5309), where S2(n) = 12 + 22 + 32 + ... + n2.

Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008
by Yoshio Mimura, Kobe, Japan

5831

58312 = (32 + 33 + 34 + ... + 80)2 + (81 + 82 + 83 + ... + 129)2.

Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008
by Yoshio Mimura, Kobe, Japan

5832

58322± 5 are primes.

58322 = 363 + 2163 + 2883 = 393 + 1533 + 3123 = 413 + 1143 + 3193 = 453 + 2463 + 2673
= 723 + 1143 + 3183 = 1003 + 1923 + 2963 = 1023 + 2273 + 2773 = 1183 + 1863 + 2963
= 1623 + 2163 + 2703 = 1733 + 2143 + 2673 = 264 + 264 + 424 + 744 = 544 + 544 + 544 + 544.

58322 = (71 + 72 + 73 + ... + 94)2 + (95 + 96 + 97 + ... + 118)2 + (119 + 120 + 121 + ... + 142)2 + ... + (143 + 144 + 145 + ... + 166)2.

Komachi equations:
58322 = 92 * 82 / 72 / 62 * 542 * 32 * 212,
58322 = 986 / 76 / 66 * 546 * 36 / 216.

Page of Squares : First Upload January 7, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

5833

58334 = 1157625022684321, and 112 + 572 + 62 + 22 + 52 + 02 + 22 + 22 + 62 + 82 + 432 + 212 = 5833.

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

5840

58402 = 26 + 66 + 66 + 186.

Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008
by Yoshio Mimura, Kobe, Japan

5841

58412 = 34117281, 3 + 4 + 1 + 1 + 72 * 81 = 34 * 1 * 172 - 8 + 1 = 5841.

Komachi equation: 58412 = 96 - 86 - 76 - 66 + 546 / 36 + 26 + 16.

Page of Squares : First Upload January 7, 2008 ; Last Revised October 25, 2010
by Yoshio Mimura, Kobe, Japan

5843

58432 = 34140649, a zigzag square.

Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008
by Yoshio Mimura, Kobe, Japan

5844

58442± 5 are primes.

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

5845

58453 = 199688726125, and 192 + 92 + 682 + 82 + 72 + 22 + 62 + 12 + 252 = 5845.

58455 = 6822170631552653125 : 62 + 82 + 22 + 22 + 12 + 702 + 62 + 32 + 12 + 52 + 52 + 262 + 52 + 32 + 12 + 22 + 52 = 5845.

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

5846

58462 = 34175716, a zigzag square.

58462 = 34175716, 3 * 41 + 7 + 5716 = 5846.

Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008
by Yoshio Mimura, Kobe, Japan

5847

58472 = 343 + 2573 + 2583 = 144 + 224 + 544 + 714.

Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008
by Yoshio Mimura, Kobe, Japan

5850

58502 = (12 + 9)(22 + 9)(212 + 9)(242 + 9) = (12 + 9)(22 + 9)(32 + 9)(42 + 9)(242 + 9)
= (12 + 9)(22 + 9)(42 + 9)(62 + 9)(152 + 9) = (12 + 9)(22 + 9)(92 + 9)(542 + 9)
= (12 + 9)(42 + 9)(152 + 9)(242 + 9) = (12 + 9)(62 + 9)(112 + 9)(242 + 9)
= (22 + 9)(32 + 9)(42 + 9)(62 + 9)(112 + 9) = (22 + 9)(42 + 9)(152 + 9)(212 + 9)
= (22 + 9)(62 + 9)(112 + 9)(212 + 9) = (22 + 9)(92 + 9)(1712 + 9)
= (32 + 9)(42 + 9)(112 + 9)(242 + 9) = (32 + 9)(42 + 9)(62 + 9)(412 + 9)
= (42 + 9)(62 + 9)(112 + 9)(152 + 9) = (62 + 9)(212 + 9)(412 + 9) = (92 + 9)(112 + 9)(542 + 9)
= (112 + 9)(212 + 9)(242 + 9).

58502 = (362 + 363 + 364)2 + (365 + 366 + 367)2 + (368 + 369 + 370)2 + (371 + 372 + 373)2 + ... + (431 + 432 + 433)2.

Page of Squares : First Upload January 7, 2008 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

5853

58532 = 34257609, a square consisting of just 3 kinds of digits.

58532± 2 are primes.

Page of Squares : First Upload January 7, 2008 ; Last Revised December 29, 2013
by Yoshio Mimura, Kobe, Japan

5856

58562 = 34292736, a zigzag square.

Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008
by Yoshio Mimura, Kobe, Japan

5859

58592 = (23 + 1)(63 + 1)(263 + 1).

58592 = 543 + 2403 + 2733.

A cubic polynomial :
(X + 14402)(X + 16122)(X + 58592) = X3 + 62452X2 + 128752922X + 136003795202.

58595 = 6904265602333993299 : 62 + 92 + 02 + 422 + 62 + 52 + 62 + 02 + 22 + 332 + 392 + 92 + 322 + 92 + 92 = 5859.

Page of Squares : First Upload January 7, 2008 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

5860

58602± 3 are primes.

58602 = 1563 + 2433 + 2533 = 1663 + 1903 + 2843.

Loop of length 14 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
5860 - 6964 - 8857 - 10993 - ... - 6505 - 4250 - 4264 - 5860
(Note f(5860) = 582 + 602 = 6964,   f(6964) = 692 + 642 = 8857, etc. See 1946)

Page of Squares : First Upload September 22, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

5863

58632 = 34374769, a zigzag square.

Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008
by Yoshio Mimura, Kobe, Japan

5864

58642 = 663 + 1103 + 3203.

Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008
by Yoshio Mimura, Kobe, Japan

5866

665k + 1421k + 2401k + 5117k are squares for k = 1,2,3 (982, 58662, 3885702).

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

5868

58682± 5 are primes.

58682 = 34433424, a square consisting of just 3 kinds of digits.

58682 = (38 + 39 + 40)2 + (41 + 42 + 43)2 + (44 + 45 + 46)2 + ... + (323 + 324 + 325)2.

Page of Squares : First Upload January 7, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

5871

58712 = 973 + 2553 + 2573.

Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008
by Yoshio Mimura, Kobe, Japan

5872

58722 = 84 + 164 + 324 + 764.

1 / 5872 = 0.0001702997...., 12 + 702 + 292 + 92 + 72 = 5872.

Page of Squares : First Upload January 7, 2008 ; Last Revised September 22, 2008
by Yoshio Mimura, Kobe, Japan

5874

5874 = (32 + 2)(82 + 2)(2182 + 2).

5874 = (12 + 22 + 32 + ... + 442) / (12 + 22).

58745 = 6993099554303310624 : 62 + 92 + 92 + 32 + 02 + 92 + 92 + 552 + 432 + 02 + 32 + 32 + 12 + 02 + 62 + 242 = 5874.

Page of Squares : First Upload November 25, 2008 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

5876

Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
5876 - 9140 - 9881 - 16165 - ... - 6409 - 4177 - 7610 - 5876
(Note f(5876) = 582 + 762 = 9140,   f(9140) = 912 + 402 = 9881, etc. See 41)

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

5878

58782 = 1713 + 2223 + 2653.

Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008
by Yoshio Mimura, Kobe, Japan

5879

58792 = 15 + 15 + 125 + 155 + 325.

Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008
by Yoshio Mimura, Kobe, Japan

5880

58802 = 313 + 1613 + 3123.

58802 = 643 + 653 + 663 + 673 + 683 + 693 + ... + 1113.

912 + 5880 = 1192, 912 - 5880 = 492.

Page of Squares : First Upload September 22, 2008 ; Last Revised August 2, 2011
by Yoshio Mimura, Kobe, Japan

5883

1 / N = 0.000169...., and 169 = 132 for N = 5883, 5884,..., 5917.

58832 = 34609689, 34 + 60 * 96 + 89 = 5883.

Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008
by Yoshio Mimura, Kobe, Japan

5885

58855 = 7058823711905178125 : 72 + 02 + 52 + 82 + 82 + 22 + 32 + 712 + 12 + 92 + 02 + 52 + 172 + 82 + 122 + 52 = 702 + 52 + 82 + 82 + 22 + 32 + 72 + 12 + 192 + 02 + 52 + 172 + 82 + 12 + 22 + 52 = 5885.

1276k + 1529k + 1738k + 5258k are squares for k = 1,2,3 (992, 58852, 3953072).

Page of Squares : First Upload December 8, 2008 ; Last Revised June 21, 2011
by Yoshio Mimura, Kobe, Japan

5886

58862± 5 are primes.

58862 = 1073 + 1453 + 3123.

58862 + 58872 + 58882 + ... + 59402 = 59412 + 59422 + 59432 + ... + 59942.

58865 = 7064823051786334176 : 72 + 02 + 642 + 82 + 22 + 302 + 52 + 172 + 82 + 62 + 32 + 32 + 42 + 172 + 62 = 5886.

Page of Squares : First Upload September 22, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

5887

58872 = 294 + 584 + 584 + 584.

Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008
by Yoshio Mimura, Kobe, Japan

5888

58882 = (12 + 7)(32 + 7)(192 + 7)(272 + 7) = (12 + 7)(32 + 7)(42 + 7)(52 + 7)(192 + 7)
= (32 + 7)(42 + 7)(112 + 7)(272 + 7) = (42 + 7)(52 + 7)(112 + 7)(192 + 7)
= (112 + 7)(192 + 7)(272 + 7).

58882 = 164 + 324 + 644 + 644 = 85 + 85 + 165 + 325.

The square root of 5888 is 76.7333...., and 76 = 72 + 32 + 32 + 32.

Page of Squares : First Upload January 7, 2008 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

5894

58942 = 1273 + 2453 + 2623.

Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008
by Yoshio Mimura, Kobe, Japan

5895

58952 = (200 + 201 + 202)2 + (203 + 204 + 205)2 + (206 + 207 + 208)2 + (209 + 210 + 211)2 + ... + (347 + 348 + 349)2.

Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008
by Yoshio Mimura, Kobe, Japan

5896

58962 = (12 + 7)(232 + 7)(902 + 7).

Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

5897

58972 = 44 + 524 + 524 + 674.

58972 = 34774609, 32 + 42 + 72 + 72 + 42 + 62 + 02 + 92 = 162.

Page of Squares : First Upload January 7, 2008 ; Last Revised September 22, 2008
by Yoshio Mimura, Kobe, Japan

5898

58982 = 34786404, 3 / 4 * 7864 + 0 * 4 = 5898.

Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008
by Yoshio Mimura, Kobe, Japan

5899

58992 = 34798201, a square with different digits.

Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008
by Yoshio Mimura, Kobe, Japan