A prime number p such that the next prime number can be obtained adding p to its sum of digits. more
The first 600 a-pointer primes :
11,
13,
101,
103,
181,
293,
631,
701,
811,
1153,
1171,
1409,
1801,
1933,
2017,
2039,
2053,
2143,
2213,
2521,
2633,
3041,
3089,
3221,
3373,
3391,
3469,
3643,
3739,
4057,
4231,
5153,
5281,
5333,
5449,
5623,
5717,
6053,
6121,
6301,
7043,
7333,
8101,
8543,
9241,
10151,
10313,
10463,
10667,
11161,
11321,
11657,
12203,
12241,
12401,
12553,
12601,
13381,
13523,
13633,
13729,
14087,
14177,
14207,
15017,
15107,
15121,
15413,
15473,
17011,
17123,
17761,
18061,
18313,
18461,
18919,
19141,
20129,
20369,
20431,
21023,
21601,
21713,
21803,
22093,
22453,
22501,
22921,
23003,
23117,
23173,
23311,
23719,
24181,
24923,
25423,
25771,
27043,
29311,
29641,
30119,
30203,
30469,
30713,
31019,
31547,
32203,
32401,
33013,
33091,
33301,
33413,
33811,
33941,
35291,
36319,
36353,
36607,
37123,
37253,
37321,
38351,
39521,
39581,
40543,
41117,
41131,
41203,
41243,
41737,
41911,
42307,
43003,
43117,
43207,
43223,
43913,
44071,
44101,
44389,
44657,
45061,
45139,
46703,
46831,
47221,
47317,
48541,
49081,
49957,
50023,
50111,
50207,
50311,
50513,
50599,
50627,
51691,
51871,
52223,
52267,
53381,
53507,
53527,
54001,
54331,
54421,
54601,
54881,
55127,
55291,
56401,
56999,
57529,
58337,
60413,
60703,
61153,
62327,
63113,
63443,
64189,
64303,
66271,
66763,
68611,
70207,
70249,
71039,
71671,
71741,
72139,
72229,
72623,
73433,
73651,
74027,
74531,
75583,
75941,
76261,
76441,
77291,
77813,
79907,
80491,
80963,
81049,
81773,
82051,
82507,
82729,
83117,
83177,
83357,
83663,
84143,
84349,
84761,
85061,
88301,
89021,
89533,
90203,
91163,
91309,
91433,
92153,
92203,
92269,
93503,
99053,
100193,
100333,
100403,
100649,
100801,
100913,
101141,
101183,
101323,
101363,
101383,
101411,
101503,
101723,
101749,
102023,
102061,
102241,
102481,
102913,
103217,
103291,
103529,
104513,
104597,
104623,
105541,
106993,
107123,
107323,
107903,
108023,
108139,
108649,
109721,
109961,
110051,
110237,
110251,
110543,
111467,
111623,
111751,
112103,
112121,
112213,
112459,
112543,
112741,
113041,
113467,
114031,
114143,
114451,
114691,
115201,
115223,
117023,
117223,
117731,
118127,
118471,
119513,
120209,
120223,
121453,
121507,
121967,
122041,
122117,
122719,
123017,
123127,
123169,
123239,
123457,
123503,
123527,
123833,
124067,
124513,
126001,
126047,
126241,
127219,
127343,
127507,
127781,
128221,
128629,
130099,
130183,
131203,
131221,
131591,
132383,
133283,
133403,
133519,
133999,
134417,
135241,
135979,
136013,
136277,
137089,
139313,
140207,
140281,
140533,
140689,
141079,
141107,
141121,
144139,
144791,
145361,
145549,
146449,
147031,
148171,
148207,
149033,
150413,
150503,
151357,
151397,
151609,
151939,
153287,
153379,
154213,
154459,
154523,
155027,
155047,
155171,
155423,
155627,
156019,
156749,
157061,
157081,
157841,
160001,
160603,
160841,
161017,
161071,
161123,
161611,
162229,
162391,
163367,
163697,
164023,
164209,
164627,
165181,
165479,
165673,
166043,
166429,
166571,
167051,
169501,
170101,
170213,
170299,
170927,
171007,
172127,
172721,
173023,
173573,
174121,
174169,
175081,
175573,
175601,
176651,
177511,
177601,
178039,
180007,
180391,
180751,
181039,
181141,
181253,
181639,
184133,
185189,
185491,
185651,
186317,
187141,
188801,
190613,
192013,
192347,
193261,
194543,
196051,
196927,
197713,
198503,
198859,
198901,
199049,
199153,
200033,
200257,
200341,
201287,
201403,
201557,
202343,
202529,
202639,
204301,
204563,
204679,
204947,
205081,
205171,
205201,
205223,
207199,
207241,
207593,
208963,
209861,
210131,
210173,
210193,
210263,
210283,
210407,
210643,
210739,
211051,
211231,
211349,
211543,
211619,
212131,
212353,
212423,
213097,
214021,
214243,
215329,
216023,
216133,
216289,
216919,
218047,
218171,
218191,
218401,
219103,
220411,
221401,
222679,
223339,
225023,
225241,
226013,
227131,
227951,
228383,
229283,
229351,
230063,
230203,
230663,
230779,
231031,
231053,
231923,
232171,
232571,
232643,
233143,
233251,
233297,
234511,
235369,
236407,
237581,
237707,
239297,
240073,
240101,
240743,
240769,
241229,
241517,
241711,
242309,
242419,
242747,
243931,
244507,
244639,
245593,
245683,
246251,
247553,
247913,
247957,
248141,
248543,
250153,
251297,
253613,
254119,
255217,
256661,
256771,
257141,
257921,
259277,
260419,
260651,
260893,
260921,
261043,
261281,
261407,
262909,
262981,
264013,
264697,
264839,
265021,
265313,
269351,
270379,
270421,
271367,
271501,
271703,
272933,
273233,
273569,
274403,
274751,
275741,
276151,
277961,
279451,
280561,
281207,
281807,
282349,
285317,
286831,
287191,
287821,
287939,
288109,
288433,
289067,
291299,
291619,
291701.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 4481260 values, from 11 to 9999993463).
n\r | 0 | 1 |
2 | 0 | 4481260 | 2 |
3 | 0 | 2307979 | 2173281 | 3 |
4 | 0 | 2246016 | 0 | 2235244 | 4 |
5 | 0 | 1290983 | 970059 | 1339277 | 880941 | 5 |
6 | 0 | 2307979 | 0 | 0 | 0 | 2173281 | 6 |
7 | 0 | 828831 | 683288 | 726639 | 708139 | 787500 | 746863 | 7 |
8 | 0 | 1126480 | 0 | 1121697 | 0 | 1119536 | 0 | 1113547 | 8 |
9 | 0 | 777071 | 724920 | 0 | 868788 | 702644 | 0 | 662120 | 745717 | 9 |
10 | 0 | 1290983 | 0 | 1339277 | 0 | 0 | 0 | 970059 | 0 | 880941 | 10 |
11 | 1 | 423773 | 489935 | 471921 | 421792 | 440133 | 401817 | 468487 | 466108 | 473564 | 423729 |
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.