A prime pn such that the sum of digits of n and pn is the same. more
The first 600 Honaker primes :
131,
263,
457,
1039,
1049,
1091,
1301,
1361,
1433,
1571,
1913,
1933,
2141,
2221,
2273,
2441,
2591,
2663,
2707,
2719,
2729,
2803,
3067,
3137,
3229,
3433,
3559,
3631,
4091,
4153,
4357,
4397,
4703,
4723,
4903,
5009,
5507,
5701,
5711,
5741,
5801,
5843,
5927,
6301,
6311,
6343,
6353,
6553,
6563,
6653,
6737,
6827,
6971,
7013,
7213,
7283,
7411,
7481,
7523,
7741,
8011,
8821,
9103,
10247,
10429,
10559,
10711,
11071,
11173,
11251,
11353,
11701,
11731,
11821,
12277,
12347,
12613,
13007,
13037,
13127,
13217,
13297,
13327,
13339,
13367,
13417,
13457,
13933,
14159,
14437,
14447,
14843,
14923,
15173,
15193,
15263,
15671,
15761,
15803,
15913,
16073,
16193,
16273,
16451,
16661,
17159,
17189,
17317,
17359,
18013,
18041,
18307,
20533,
20543,
21523,
21617,
22189,
22277,
22613,
22807,
23059,
23531,
24019,
24091,
24733,
24841,
24971,
25219,
25229,
25339,
26119,
26189,
26209,
26309,
26339,
26731,
27059,
27091,
27277,
29023,
29101,
29131,
29243,
29423,
30071,
30091,
30253,
30293,
31177,
31391,
31517,
31567,
32009,
32029,
32059,
32191,
32261,
33493,
33533,
34171,
34259,
34471,
34543,
34703,
35027,
35129,
35149,
35227,
35327,
35537,
35617,
36217,
36307,
36433,
36523,
37019,
37039,
37049,
37117,
37463,
37493,
37717,
37783,
38011,
38711,
40361,
40427,
40627,
40637,
40763,
40823,
41131,
41141,
41333,
41491,
41801,
41851,
41941,
42323,
42373,
42509,
42727,
42737,
43543,
43781,
44221,
44417,
45119,
45181,
45191,
45821,
45833,
46147,
46237,
46723,
47017,
47147,
47293,
47491,
47623,
48109,
48119,
48247,
48463,
48473,
49031,
49411,
49531,
50047,
50119,
50417,
51131,
51203,
51263,
51421,
51473,
52051,
52543,
52553,
52691,
52733,
53309,
53407,
53437,
53591,
53881,
53923,
54013,
54217,
54617,
54727,
54941,
55049,
55207,
55541,
55733,
55823,
56807,
57059,
57089,
57119,
57139,
57271,
57301,
57713,
57943,
58073,
58321,
58411,
58921,
59083,
59093,
59183,
60251,
60601,
61051,
61253,
61703,
62017,
62057,
62273,
62303,
62323,
62617,
62627,
63031,
63313,
63607,
64123,
64151,
64231,
64513,
64621,
64817,
65371,
65713,
65831,
65843,
66089,
66301,
66923,
67073,
67801,
68059,
68147,
68813,
68903,
69127,
69247,
69257,
69383,
69463,
69911,
70039,
70079,
70139,
70379,
70459,
70489,
71261,
71353,
72019,
72337,
72701,
73009,
73607,
74231,
74713,
75503,
75941,
76129,
76159,
76403,
76423,
77023,
77237,
77249,
77291,
77339,
77611,
77711,
77813,
78007,
78017,
78163,
78283,
78427,
78437,
79133,
79273,
79333,
79609,
80657,
81199,
81239,
82051,
82207,
82217,
82813,
83231,
83311,
84017,
84067,
84313,
85081,
85093,
85133,
86113,
86243,
87013,
87071,
87121,
87151,
88007,
88661,
89833,
90163,
90173,
90469,
90647,
91009,
91019,
91571,
91583,
92251,
92347,
92461,
92627,
92791,
92861,
93097,
94033,
94063,
94151,
94219,
94229,
94327,
95111,
95219,
96043,
96053,
96443,
96553,
97103,
97151,
97231,
97241,
97711,
98911,
99041,
100279,
100549,
100559,
100957,
101869,
101929,
101939,
102359,
102397,
102829,
103619,
103969,
103979,
105031,
105331,
106031,
106621,
106903,
108037,
109103,
109133,
109321,
109331,
110119,
110129,
110273,
110813,
110923,
111053,
111229,
111347,
111443,
111491,
112153,
112163,
112927,
113027,
113327,
113357,
113417,
113591,
113891,
114451,
114809,
115561,
115571,
115601,
115631,
115853,
116089,
116159,
116189,
116257,
117503,
118411,
120181,
120473,
120511,
120709,
120943,
122471,
122503,
122533,
123091,
123217,
123701,
123733,
123821,
124153,
124183,
124193,
124363,
124429,
124459,
125029,
125117,
125383,
125423,
125453,
125627,
126013,
126143,
126271,
126517,
126653,
126691,
127051,
127423,
127681,
127733,
127763,
129113,
129221,
130087,
130183,
131009,
131213,
131371,
131381,
132233,
132283,
132313,
132383,
132541,
132607,
132721,
132751,
132763,
133153,
133213,
133241,
133261,
133271,
133451,
133801,
133811,
133831,
134731,
134741,
135731,
136139,
136177,
136207,
136217,
136237,
136247,
136277,
136337,
136531,
136621,
137437,
138113,
138241,
138319,
139123,
139133,
139201,
139409,
139703,
139831,
140143,
140411,
140423,
140453,
141161,
141241,
141301,
141623,
142231,
142403,
143291,
143357,
143443,
143483,
144307,
145063,
145121,
145207,
145441,
145451,
145513,
145543,
145603,
145661,
145721,
145771,
146323,
147047,
149113,
149173,
149183,
149251,
150197,
150287,
151337,
151537,
151597,
151609,
152003,
152123,
152851,
154073,
154211,
154321,
155017,
155027,
155203,
156127,
156253,
156361.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 1478015 values, from 131 to 999843421).
n\r | 0 | 1 |
2 | 0 | 1478015 | 2 |
3 | 0 | 739402 | 738613 | 3 |
4 | 0 | 737174 | 0 | 740841 | 4 |
5 | 0 | 452116 | 328347 | 421923 | 275629 | 5 |
6 | 0 | 739402 | 0 | 0 | 0 | 738613 | 6 |
7 | 0 | 246207 | 246220 | 245781 | 246684 | 246588 | 246535 | 7 |
8 | 0 | 370172 | 0 | 370561 | 0 | 367002 | 0 | 370280 | 8 |
9 | 0 | 246284 | 245786 | 0 | 246949 | 246075 | 0 | 246169 | 246752 | 9 |
10 | 0 | 452116 | 0 | 421923 | 0 | 0 | 0 | 328347 | 0 | 275629 | 10 |
11 | 0 | 147788 | 148000 | 148237 | 147287 | 147967 | 148084 | 147628 | 147457 | 147852 | 147715 |
A pictorial representation of the table above
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.