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).
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, 2008by 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, 2008by Yoshio Mimura, Kobe, Japan
5805
58052 = 1713 + 2433 + 2433.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by 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)
by Yoshio Mimura, Kobe, Japan
5807
58072 = 94 + 124 + 244 + 764.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by 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, 2008by 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, 2008by 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, 2008by 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, 2008by 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, 2013by 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, 2008by 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, 2008by 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, 2008by Yoshio Mimura, Kobe, Japan
5823
58232 = 583 + 863 + 3213 = 813 + 1153 + 3173.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by Yoshio Mimura, Kobe, Japan
5825
58252 = (112 + 4)(5212 + 4).
Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013by Yoshio Mimura, Kobe, Japan
5827
1 / 5827 = 0.00017161...., and 17161 = 1312.
Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008by 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, 2008by 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, 2008by 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, 2008by 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.
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, 2008by Yoshio Mimura, Kobe, Japan
5840
58402 = 26 + 66 + 66 + 186.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by 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, 2010by Yoshio Mimura, Kobe, Japan
5843
58432 = 34140649, a zigzag square.
Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008by Yoshio Mimura, Kobe, Japan
5844
58442± 5 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by 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, 2008by 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, 2008by 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, 2008by 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, 2013by 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, 2013by Yoshio Mimura, Kobe, Japan
5856
58562 = 34292736, a zigzag square.
Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008by 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, 2013by 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)
by Yoshio Mimura, Kobe, Japan
5863
58632 = 34374769, a zigzag square.
Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008by Yoshio Mimura, Kobe, Japan
5864
58642 = 663 + 1103 + 3203.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by 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, 2011by 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, 2014by Yoshio Mimura, Kobe, Japan
5871
58712 = 973 + 2553 + 2573.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by 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, 2008by 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, 2013by 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)
by Yoshio Mimura, Kobe, Japan
5878
58782 = 1713 + 2223 + 2653.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by Yoshio Mimura, Kobe, Japan
5879
58792 = 15 + 15 + 125 + 155 + 325.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by 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, 2011by 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, 2008by 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, 2011by 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, 2014by Yoshio Mimura, Kobe, Japan
5887
58872 = 294 + 584 + 584 + 584.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by 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, 2013by Yoshio Mimura, Kobe, Japan
5894
58942 = 1273 + 2453 + 2623.
Page of Squares : First Upload September 22, 2008 ; Last Revised September 22, 2008by 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, 2008by Yoshio Mimura, Kobe, Japan
5896
58962 = (12 + 7)(232 + 7)(902 + 7).
Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013by 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, 2008by 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, 2008by Yoshio Mimura, Kobe, Japan
5899
58992 = 34798201, a square with different digits.
Page of Squares : First Upload January 7, 2008 ; Last Revised January 7, 2008by Yoshio Mimura, Kobe, Japan