2600
26002 = (12 + 4)(102 + 4)(1142 + 4) = (12 + 4)(22 + 4)(142 + 4)(292 + 4)
= (12 + 4)(22 + 4)(32 + 4)(102 + 4)(112 + 4) = (12 + 4)(22 + 4)(32 + 4)(1142 + 4)
= (32 + 4)(62 + 4)(102 + 4)(112 + 4) = (32 + 4)(62 + 4)(1142 + 4)
= (42 + 4)(162 + 4)(362 + 4) = (62 + 4)(142 + 4)(292 + 4) = (24 + 4)(44 + 4)(64 + 4).
by Yoshio Mimura, Kobe, Japan
2601
The square of 51.
1 / 2601 = 0.0003844..., and 3844 = 622.
408k + 1156k + 2601k + 3060k are squares for k = 1,2,3 (852, 41992, 2187732).
Page of Squares : First Upload May 1, 2007 ; Last Revised May 20, 2011by Yoshio Mimura, Kobe, Japan
2604
26042 = (32 + 3)(92 + 3)(822 + 3).
Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
2607
26072 = 6796449 appears in the decimal expressions of π:
π = 3.14159•••6796449••• (from the 102403rd digit)
by Yoshio Mimura, Kobe, Japan
2609
Komachi equation: 26092 = 14 / 24 * 344 + 54 - 674 + 84 * 94.
Page of Squares : First Upload September 24, 2010 ; Last Revised September 24, 2010by Yoshio Mimura, Kobe, Japan
2610
26102 = 564 x 565 + 566 x 567 + 568 x 569 + 570 x 571 + 572 x 573 + ... + 602 x 603.
26102 = (12 + 9)(62 + 9)(1232 + 9) = (212 + 9)(1232 + 9) = (32 + 9)(42 + 9)(1232 + 9)
= (62 + 9)(72 + 9)(512 + 9) = (72 + 9)(92 + 9)(362 + 9).
by Yoshio Mimura, Kobe, Japan
2613
The square root of 2613 is 51.117..., and 51 = 12 + 12 + 72.
Page of Squares : First Upload May 1, 2007 ; Last Revised May 1, 2007by Yoshio Mimura, Kobe, Japan
2616
26162± 5 are primes.
26162 = 343 + 1293 + 1673.
Page of Squares : First Upload July 24, 2008 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
2617
26172 = 6848689, a square pegged by 8.
26172 = 6848689, 62 + 82 + 42 + 82 + 62 + 82 + 92 = 192.
Page of Squares : First Upload May 1, 2007 ; Last Revised May 1, 2007by Yoshio Mimura, Kobe, Japan
2618
26182 = 6853924, a square with different digits.
26182 = 234 + 374 + 374 + 414.
26182 = 6853924 appears in the decimal expressions of e:
e = 2.71828•••6853924••• (from the 60086th digit)
by Yoshio Mimura, Kobe, Japan
2619
26192 = 6859161, a zigzag square.
26192 = 832 + 842 + 852 + 862 + 872 + 882 + ... + 2762.
Page of Squares : First Upload May 1, 2007 ; Last Revised May 1, 2007by Yoshio Mimura, Kobe, Japan
2621
26212 = 1562 + 6592 + 25322 = 23522 + 9562 + 6512.
Page of Squares : First Upload September 7, 2013 ; Last Revised September 7, 2013by Yoshio Mimura, Kobe, Japan
2624
26242 = 6885376, and 6 * 88 * 5 - 3 - 7 - 6 = 2624.
Page of Squares : First Upload May 1, 2007 ; Last Revised May 1, 2007by Yoshio Mimura, Kobe, Japan
2625
26252 = 603 + 703 + 1853.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2626
26262 = (52 + 1)(5152 + 1).
Page of Squares : First Upload November 2, 2013 ; Last Revised November 2, 2013by Yoshio Mimura, Kobe, Japan
2628
26282 = 6906384, a zigzag square.
26282 + 26292 + 26302 + ... + 26642 = 26652 + 26662 + 26672 + ... + 27002.
Komachi equations:
26282 = 92 * 8762 * 52 * 42 / 32 / 22 / 102 = 92 * 8762 / 52 / 42 / 32 * 22 * 102.
26282 = 573 + 843 + 1833 = 244 + 324 + 324 + 464.
Page of Squares : First Upload May 1, 2007 ; Last Revised September 13, 2011by Yoshio Mimura, Kobe, Japan
2631
26312 = 6922161, and 69 + 2 * 21 * 61 = 2631.
26312 = 6922161 appears in the decimal expressions of π:
π = 3.14159•••6922161••• (from the 66460th digit)
by Yoshio Mimura, Kobe, Japan
2632
Komachi equation: 26322 = 9872 / 62 / 52 / 42 * 322 * 102.
Page of Squares : First Upload September 24, 2010 ; Last Revised September 24, 2010by Yoshio Mimura, Kobe, Japan
2634
26342± 5 are primes.
26342 = 6937956 appears in the decimal expressions of π:
π = 3.14159•••6937956••• (from the 26353rd digit)
(6937956 is the eighth 7-digit square in the expression of π.)
by Yoshio Mimura, Kobe, Japan
2635
The square root of 2635 is 51.33225..., and 51 = 32 + 32 + 22 + 22 + 52.
Page of Squares : First Upload May 1, 2007 ; Last Revised May 1, 2007by Yoshio Mimura, Kobe, Japan
2636
26362 = 6948496, a palindromic and zigzag square.
Page of Squares : First Upload May 1, 2007 ; Last Revised May 1, 2007by Yoshio Mimura, Kobe, Japan
2639
A cubic polynomial :
(X + 10442)(X + 26392)(X + 43682) = X3 + 52092X2 + 126988682X + 120343466882.
26392 = 6964321 appears in the decimal expressions of π:
π = 3.14159•••6964321••• (from the 73594th digit)
by Yoshio Mimura, Kobe, Japan
2640
26402 = 13 + 123 + 1913 = 23 + 483 + 1903 = 93 + 103 + 1913 = 343 + 1443 + 1583 = 603 + 1483 + 1523.
26402 = (112 - 1)(2412 - 1) = (32 - 1)(42 - 1)(2412 - 1).
26402 = (12)(22 + 32 + 42 + 52 + 62)(72 + 82 + 92 + ... + 612).
Page of Squares : First Upload July 24, 2008 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
2644
264452644 = 162622.
26442 = 30 + 31 + 33 + 34 + 35 + 36 + 37 + 39 + 310 + 312 + 313 + 314.
Page of Squares : First Upload May 1, 2007 ; Last Revised August 29, 2011by Yoshio Mimura, Kobe, Japan
2645
26452 = 13 + 1203 + 1743 = 253 + 1343 + 1663.
26452 = (58 + 59 + 60 + ... + 80)2 + (81 + 82 + 83 + ... + 103)2 + (104 + 105 + 106 + ... + 126)2 + ... + (81 + 82 + 83 + ... + 103)2.
Page of Squares : First Upload May 1, 2007 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2646
26462 = 633 + 1893 = 93 + 1263 + 1713.
The integral triangle of sides 449, 117657, 118090 has square area 26462.
26462 = (12 + 5)(22 + 5)(112 + 5)(322 + 5) = (12 + 5)(42 + 5)(72 + 5)(322 + 5)
= (22 + 5)(32 + 5)(72 + 5)(322 + 5) = (22 + 5)(42 + 5)(112 + 5)(172 + 5) = (72 + 5)(112 + 5)(322 + 5).
Komachi equations:
26462 = 12 / 22 * 32 * 42 * 562 * 72 / 82 * 92 = 92 * 82 * 72 / 62 / 52 / 42 * 32 * 2102
= 92 / 82 * 72 * 62 / 52 * 42 / 32 * 2102 = 982 / 72 * 62 / 52 / 42 * 32 * 2102.
by Yoshio Mimura, Kobe, Japan
2647
26472 = 673 + 1273 + 1673.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2648
26482 = 85 + 185 + 185 + 205.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2650
26502 = (22 + 6)(8382 + 6) = (72 + 4)(3642 + 4).
26502 = (43 + 44 + 45 + 46 + 47)2 + (48 + 49 + 50 + 51 + 52)2 + (53 + 54 + 55 + 56 + 57)2 + ... + (158 + 159 + 160 + 161 + 162)2.
Page of Squares : First Upload May 1, 2007 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
2652
26522 = 943 + 1343 + 1563.
2550k + 2652k + 6681k + 11526k are squares for k = 1,2,3 (1532, 138212, 13655252).
Page of Squares : First Upload July 24, 2008 ; Last Revised May 20, 2011by Yoshio Mimura, Kobe, Japan
2654
26542 = 7043716, a zigzag square.
Page of Squares : First Upload May 1, 2007 ; Last Revised May 1, 2007by Yoshio Mimura, Kobe, Japan
2656
26562 = 7054336, 72 + 02 + 52 + 42 + 32 + 32 + 62 = 122.
Page of Squares : First Upload May 1, 2007 ; Last Revised May 1, 2007by Yoshio Mimura, Kobe, Japan
2657
26572 = 164 + 284 + 284 + 494.
1 / 2657 = 0.00037636... and 37636 = 1942.
Page of Squares : First Upload May 1, 2007 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2660
26602± 3 are primes.
26602 = 213 + 1103 + 1793.
Page of Squares : First Upload July 24, 2008 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
2661
26612 = 863 + 1423 + 1533.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2662
26622 = 116 + 116 + 116 + 116.
26622 = 30 + 31 + 32 + 33 + 34 + 35 + 311 + 312 + 313 + 314.
Page of Squares : First Upload July 24, 2008 ; Last Revised August 29, 2011by Yoshio Mimura, Kobe, Japan
2669
26692 = S2(11) + S2(277), where S2(n) = 12 + 22 + 32 + ... + n2.
Page of Squares : First Upload May 1, 2007 ; Last Revised May 1, 2007by Yoshio Mimura, Kobe, Japan
2672
26722 = 7139584, a square with different digits.
Page of Squares : First Upload May 1, 2007 ; Last Revised May 1, 2007by Yoshio Mimura, Kobe, Japan
2678
26782 = 7171684 appears in the decimal expressions of e:
e = 2.71828•••7171684••• (from the 32712nd digit)
(7171684 is the eighth 7-digit square in the expression of e.)
by Yoshio Mimura, Kobe, Japan
2679
A cubic polynomial :
(X + 4482)(X + 6842)(X + 26792) = X2 + 328012X2 + 22118282X + 8209313282.
by Yoshio Mimura, Kobe, Japan
2680
Komachi equations:
26802 = 122 * 32 / 42 + 52 * 672 * 82 - 92 = 122 * 32 / 42 * 52 * 672 * 82 / 92
= - 122 * 32 / 42 + 52 * 672 * 82 + 92.
by Yoshio Mimura, Kobe, Japan
2682
26822 = 14 + 14 + 394 + 474 = 57 + 77 + 87 + 87 + 87.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2684
26842 = 7203856, a square with different digits.
1 / 2684 = 0.000372578241..., and 372 + 252 + 72 + 82 + 242 + 12 = 2684.
Page of Squares : First Upload May 1, 2007 ; Last Revised May 1, 2007by Yoshio Mimura, Kobe, Japan
2686
26862 = 7214596, a square with different digits.
Page of Squares : First Upload May 1, 2007 ; Last Revised May 1, 2007by Yoshio Mimura, Kobe, Japan
2687
26872 = 233 + 773 + 1893.
1 / 2687 = 0.0003721... and 3721 = 612.
Page of Squares : First Upload May 1, 2007 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2688
26882 = (32 - 1)(52 - 1)(132 - 1)(152 - 1).
Cubic polynomials ;
(X + 8282)(X + 26882)(X + 45312) = X3 + 53332X2 + 129369482X + 100844835842,
(X + 15042)(X + 26882)(X + 38072) = X3 + 48972X2 + 124034882X + 153907568642,
(X + 19352)(X + 26882)(X + 28002) = X3 + 43372X2 + 106327202X + 145635840002.
by Yoshio Mimura, Kobe, Japan
2689
2689 is the 6th prime for which the Legendre symbol (a / 2689) = 1 for a = 1,2,...,12.
Page of Squares : First Upload May 1, 2007 ; Last Revised May 1, 2007by Yoshio Mimura, Kobe, Japan
2691
26912 = 813 + 883 + 1823.
Page of Squares : First Upload July 24, 2008 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2694
26942 = 1! + 1! + 2! + 2! + 3! + 4! + 10! + 10! = 2! + 2! + 2! + 3! + 4! + 10! + 10!
= 3! + 3! + 3! + 3! + 3! + 3! + 10! + 10! = 3! + 3! + 4! + 10! + 10!.
26942 = 7257636, and 7 * 2 * 576 / 3 + 6 = 2694.
Page of Squares : First Upload May 1, 2007 ; Last Revised May 1, 2007by Yoshio Mimura, Kobe, Japan
2695
26952 = 1! + 4! + 5! + 5! + 5! + 7! + 10! + 10!.
2695k + 10615k + 12485k + 22605k are squares for k = 1,2,3 (2202, 280502, 38357002).
Page of Squares : First Upload May 1, 2007 ; Last Revised May 20, 2011by Yoshio Mimura, Kobe, Japan
2696
26962 = 383 + 923 + 1863.
26962 = 7268416, and 7 + 2684 - 1 + 6 = 2696.
Page of Squares : First Upload May 1, 2007 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2697
26972 = 7273809, a zigzag square.
26972 = 24 + 344 + 414 + 424.
26972 = 7273809, 72 + 22 + 72 + 32 + 82 + 02 + 92 = 162.
Page of Squares : First Upload May 1, 2007 ; Last Revised July 24, 2008by Yoshio Mimura, Kobe, Japan
2699
26992 = 7284601, a zigzag square with different digits.
Page of Squares : First Upload May 1, 2007 ; Last Revised May 1, 2007by Yoshio Mimura, Kobe, Japan