14022
140222 = (12 + 2)(22 + 2)(112 + 2)(2982 + 2) = (22 + 2)(62 + 2)(132 + 2)(712 + 2)
= (42 + 2)(112 + 2)(2982 + 2) = (62 + 2)(322 + 2)(712 + 2).
by Yoshio Mimura, Kobe, Japan
14036
140362 = (132 + 7)(10582 + 7) = (22 + 7)(32 + 7)(10582 + 7).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14040
140402 = (142 - 1)(192 - 1)(532 - 1) = (22 - 1)(112 - 1)(142 - 1)(532 - 1)
= (22 - 1)(32 - 1)(42 - 1)(142 - 1)(532 - 1) = (42 - 1)(52 - 1)(142 - 1)(532 - 1).
by Yoshio Mimura, Kobe, Japan
14041
140412 = 3492 + 3512 + 3532 + 3552 + ... + 10692.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14050
140502 = (12 + 1)(22 + 1)(44432 + 1) = (32 + 1)(44432 + 1).
Page of Squares : First Upload November 9, 2013 ; Last Revised November 9, 2013by Yoshio Mimura, Kobe, Japan
14056
140562 = 197571136, a square with odd digits except the last digit 6.
Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013by Yoshio Mimura, Kobe, Japan
14064
140642± 5 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14080
140802± 3 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14091
140912± 2 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14098
140982 = 198753604 is a square consisting of different digits.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14104
141042± 3 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14120
141202± 3 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14124
141242± 5 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14127
141272 = 3022 + 3032 + 3042 + ... + 8552.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14136
141362 = (12 + 3)(112 + 3)(152 + 3)(422 + 3) = (12 + 3)(32 + 3)(42 + 3)(112 + 3)(422 + 3).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14139
141392± 2 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14160
141602 = 1183 + 1193 + 1203 + 1213 + ... + 1773.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14161
14161 is a aigzag square pegged by 1.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14168
141682 = (12 + 7)(22 + 7)(42 + 7)(72 + 7)(422 + 7) = (12 + 7)(422 + 7)(1192 + 7)
= (22 + 7)(42 + 7)(212 + 7)(422 + 7) = (22 + 7)(42 + 7)(72 + 7)(1192 + 7)
= (42 + 7)(72 + 7)(92 + 7)(422 + 7).
by Yoshio Mimura, Kobe, Japan
14170
141702 = (12 + 4)(162 + 4)(3932 + 4) = (12 + 4)(32 + 4)(42 + 4)(3932 + 4)
= (12 + 9)(22 + 9)(102 + 9)(1192 + 9) = (102 + 9)(112 + 9)(1192 + 9) = (362 + 4)(3932 + 4).
by Yoshio Mimura, Kobe, Japan
14190
141902 = (53 + 4)(1163 + 4).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14196
141962 = (12 + 3)(22 + 3)(32 + 3)(62 + 3)(1242 + 3) = (12 + 3)(62 + 3)(92 + 3)(1242 + 3)
= (22 + 3)(62 + 3)(192 + 3)(452 + 3) = (32 + 3)(332 + 3)(1242 + 3)
= (32 + 3)(52 + 3)(62 + 3)(1242 + 3).
by Yoshio Mimura, Kobe, Japan
14210
142102 = (22 + 6)(202 + 6)(2232 + 6).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14224
142242 = (52 + 7)(72 + 7)(3362 + 7).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14248
142482± 3 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14256
142562 = (12 + 8)(102 + 8)(162 + 8)(282 + 8) = (12 + 8)(22 + 8)(42 + 8)(162 + 8)(172 + 8)
= (12 + 8)(22 + 8)(42 + 8)(2802 + 8) = (12 + 8)(22 + 8)(52 + 8)(82 + 8)(282 + 8)
= (12 + 8)(42 + 8)(52 + 8)(102 + 8)(162 + 8) = (12 + 8)(42 + 8)(62 + 8)(82 + 8)(172 + 8)
= (12 + 8)(62 + 8)(162 + 8)(442 + 8) = (22 + 8)(42 + 8)(52 + 8)(82 + 8)(172 + 8)
= (22 + 8)(52 + 8)(162 + 8)(442 + 8) = (22 + 8)(82 + 8)(172 + 8)(282 + 8)
= (22 - 1)(172 - 1)(4852 - 1) = (42 + 8)(102 + 8)(162 + 8)(172 + 8)
= (42 + 8)(102 + 8)(2802 + 8) = (52 + 8)(62 + 8)(82 + 8)(442 + 8)
= (52 + 8)(82 + 8)(102 + 8)(282 + 8) = (82 + 8)(382 + 8)(442 + 8).
by Yoshio Mimura, Kobe, Japan
14274
142742 = (152 + 9)(282 + 9)(332 + 9) = (22 + 9)(32 + 9)(282 + 9)(332 + 9).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14280
142802 = (132 - 1)(162 - 1)(692 - 1) = (32 - 1)(502 - 1)(1012 - 1) = (62 - 1)(352 - 1)(692 - 1).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14283
142832 = S2(213) + S2(844), where S2(n) = 12 + 22 + 32 + ... + n2.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14288
142882± 3 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14289
The quadratic polynomial 14289X2 - 70422X + 83689 takes the values 1662, 12, 322, 1752, 2982, 4192 at X = 1, 2, ..., 6.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14322
143222 + 337382 = 1343372328 (mosaic).
143222 = (12 + 6)(362 + 6)(1502 + 6) = (12 + 6)(52 + 6)(62 + 6)(1502 + 6)
= (152 + 6)(262 + 6)(362 + 6) = (42 + 6)(52 + 6)(152 + 6)(362 + 6)
= (52 + 6)(62 + 6)(152 + 6)(262 + 6).
by Yoshio Mimura, Kobe, Japan
14329
143292 = 152 + 172 + 192 + 212 + ... + 10712.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14331
143312± 2 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14343
143432± 2 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14345
143452 = 1312 + 1322 + 1332 + ... + 8522.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14370
143702 = 117 * 118 + 119 * 120 + 121 * 122 + 123 * 124 + ... + 1073 * 1074.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14394
143942± 5 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14397
143972± 2 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14400
144002 = (22 - 1)(42 - 1)(52 - 1)(92 - 1)(492 - 1) = (22 - 1)(92 - 1)(192 - 1)(492 - 1)
= (42 - 1)(72 - 1)(112 - 1)(492 - 1).
by Yoshio Mimura, Kobe, Japan
14418
144182 = (12 + 2)(42 + 2)(402 + 2)(492 + 2).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14420
144202 = 207936400, and 207936 = 4562, 400 = 202.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14430
144302 = (182 + 9)(192 + 9)(412 + 9) = (22 + 9)(112 + 9)(182 + 9)(192 + 9)
= (22 + 9)(112 + 9)(3512 + 9) = (412 + 9)(3512 + 9).
by Yoshio Mimura, Kobe, Japan
14432
144322 = 208282624 is a square with even digits.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14439
The quadratic polynomial -14439X2 + 171798X - 156959 takes the values 202, 3592, 4782, 5472, 5842, 5952 at X = 1, 2, ..., 6.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14442
144422 = 208571364 is a square consisting of different digits.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14448
144482 = (12 + 3)(32 + 3)(132 + 3)(1592 + 3) = (12 + 3)(32 + 3)(52 + 3)(132 + 3)(302 + 3).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14450
144502 = (22 + 1)(32 + 1)(42 + 1)(132 + 1)(382 + 1) = (42 + 1)(72 + 1)(132 + 1)(382 + 1).
Page of Squares : First Upload November 9, 2013 ; Last Revised November 9, 2013by Yoshio Mimura, Kobe, Japan
14454
144542 = (12 + 2)(22 + 2)(32 + 2)(122 + 2)(852 + 2) = (12 + 2)(82 + 2)(122 + 2)(852 + 2)
= (122 + 2)(142 + 2)(852 + 2) = (32 + 2)(42 + 2)(122 + 2)(852 + 2).
by Yoshio Mimura, Kobe, Japan
14468
144682± 3 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14469
144692 = S2(466) + S2(807), where S2(n) = 12 + 22 + 32 + ... + n2.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14490
144902 = (12 + 5)(102 + 5)(152 + 5)(382 + 5) = (12 + 5)(22 + 5)(152 + 5)(1302 + 5)
= (12 + 5)(22 + 5)(52 + 5)(3602 + 5) = (12 + 5)(42 + 5)(82 + 5)(102 + 5)(152 + 5)
= (12 + 5)(52 + 5)(82 + 5)(1302 + 5) = (152 + 5)(252 + 5)(382 + 5)
= (22 + 5)(102 + 5)(152 + 5)(312 + 5) = (22 + 5)(32 + 5)(82 + 5)(102 + 5)(152 + 5)
= (42 + 5)(52 + 5)(152 + 5)(382 + 5) = (42 + 5)(82 + 5)(152 + 5)(252 + 5)
= (52 + 5)(72 + 5)(3602 + 5) = (52 + 5)(82 + 5)(102 + 5)(312 + 5)
= (72 + 5)(152 + 5)(1302 + 5) = (82 + 5)(102 + 5)(112 + 5)(152 + 5)
= (82 + 5)(152 + 5)(1152 + 5).
by Yoshio Mimura, Kobe, Japan
14491
1841622 is the sum of (30m+1)2 for 1 <= 30m + 1 <= 14491.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14499
144992± 2 are primes.
144992 = 210221001 is a square with 3 kinds of digits.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14500
145002± 3 are primes.
145002 = (12 + 1)(22 + 1)(32 + 1)(72 + 1)(122 + 1)(172 + 1)
= (12 + 4)(42 + 4)(52 + 4)(112 + 4)(242 + 4).
by Yoshio Mimura, Kobe, Japan
14550
145502 = (122 + 6)(11882 + 6) = (22 + 6)(32 + 6)(11882 + 6).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14573
145732 = 2 + 3 + 5 + 7 + 11 + ... + 67187 (the sum of consecutive primes).
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14600
146002 = (12 + 4)(62 + 4)(192 + 4)(542 + 4) = (142 + 4)(192 + 4)(542 + 4).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14601
146012 = 83 + 693 + 4273 + 5133.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14625
146252± 2 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14641
14641 is a palindromic square (1212) (pegged by 4) with 3 kinds of digits.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14651
146512 = 214651801.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14652
146523 + 256413 = 44725232.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14676
146762 = 215384976 is a square consisting of different digits.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14688
146882 = (12 + 8)(22 + 8)(42 + 8)(142 + 8)(202 + 8) = (22 + 8)(32 + 8)(42 + 8)(102 + 8)(202 + 8)
= (22 + 8)(82 + 8)(102 + 8)(482 + 8) = (42 + 8)(102 + 8)(142 + 8)(202 + 8).
by Yoshio Mimura, Kobe, Japan
14690
146902 = (22 + 1)(152 + 1)(4372 + 1).
Page of Squares : First Upload November 9, 2013 ; Last Revised November 9, 2013by Yoshio Mimura, Kobe, Japan
14700
147002 = (12 + 6)(22 + 6)(62 + 6)(122 + 6)(222 + 6) = (22 + 6)(32 + 6)(62 + 6)(82 + 6)(222 + 6)
= (62 + 6)(82 + 6)(122 + 6)(222 + 6).
by Yoshio Mimura, Kobe, Japan
14701
147012 = 12702 + 12712 + 12722 + ... + 13912.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14706
147062 = (132 + 2)(162 + 2)(702 + 2).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14736
147362 = 13 + 33 + 93 + 2463 + 5873.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14743
147432 = 217356049 is a square consisting of different digits.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14748
14748, 14749, 14750, 14751 and 14752 are consecutive integers having square factors (the 7th case).
Page of Squares : First Upload December 14, 2013 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
14750
147502 = 1019 * 1020 + 1020 * 1021 + 1021 * 1022 + 1022 * 1023 + ... + 1195 * 1196.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14752
147522± 3 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14766
147662 = 218034756 is a square consisting of different digits.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14784
147842 = (152 - 1)(232 - 1)(432 - 1).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14790
147902 = (12 + 9)(52 + 9)(222 + 9)(362 + 9) = (92 + 9)(15592 + 9).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14796
147962± 5 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14798
147982 = (22 + 3)(652 + 3)(862 + 3).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14800
148002 = (12 + 4)(42 + 4)(62 + 4)(2342 + 4) = (12 + 4)(62 + 4)(122 + 4)(862 + 4)
= (122 + 4)(142 + 4)(862 + 4) = (42 + 4)(142 + 4)(2342 + 4).
by Yoshio Mimura, Kobe, Japan
14804
148042± 3 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14805
148052 = (22 - 1)(42 - 1)(462 - 1)(482 - 1).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14811
148112± 2 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14824
148242 = 7242 + 7252 + 7262 + ... + 10122.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14833
148332 = S2(443) + S2(830), where S2(n) = 12 + 22 + 32 + ... + n2.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14846
148462± 3 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14848
148482 = (32 + 7)(52 + 7)(152 + 7)(432 + 7).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14859
148592 = 7613 - 7603 + 7593 - 7583 + ... + 13.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14862
148622± 5 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14880
148802 = (42 - 1)(612 - 1)(632 - 1).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14884
14884 is a square (1222) with 3 kinds of digits.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14896
148962 = (12 + 3)(52 + 3)(232 + 3)(612 + 3).
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14908
149082 = 222248464 is a square with even digits.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14922
149222 = 222666084 is a square with even digits.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14951
The 6th prime for which the Legendre symbol (n/14951) = 1 for n = 1,2,...,18.
Page of Squares : First Upload January 14, 2012 ; Last Revised January 14, 2012by Yoshio Mimura, Kobe, Japan
14960
149602± 3 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan
14974
149742± 3 are primes.
Page of Squares : First Upload January 25, 2014 ; Last Revised January 25, 2014by Yoshio Mimura, Kobe, Japan