A prime that cannot be changed into another prime by changing a single digit. more
The first 600 weakly primes :
294001,
505447,
584141,
604171,
971767,
1062599,
1282529,
1524181,
2017963,
2474431,
2690201,
3085553,
3326489,
4393139,
5152507,
5564453,
5575259,
6173731,
6191371,
6236179,
6463267,
6712591,
7204777,
7469789,
7469797,
7858771,
7982543,
8090057,
8353427,
8532761,
8639089,
9016079,
9537371,
9608189,
9931447,
10506191,
10564877,
11124403,
11593019,
12325739,
14075273,
14090887,
14151757,
15973733,
16497121,
17412427,
17412599,
17424721,
18561293,
18953677,
19851991,
20212327,
20414561,
21044557,
21089489,
21281479,
21496661,
21668839,
21717601,
22138349,
22431391,
22480351,
23228479,
23274191,
23462969,
25081361,
25151927,
25475617,
25556941,
25768091,
25872199,
25948847,
26024267,
26521721,
27242179,
27245539,
27425521,
27465103,
27469241,
28046353,
28070047,
28978889,
29136091,
29348797,
29638519,
30791767,
30915637,
30964013,
31240481,
32524313,
33051769,
34302127,
34349969,
34586371,
35009671,
35319367,
35355923,
35673679,
35954509,
36221597,
37074487,
37095427,
37448137,
38178211,
38530123,
39397009,
39689597,
39724417,
40085977,
40432489,
40638727,
40812781,
41745331,
41980441,
42120581,
42145837,
42758917,
43414669,
43432409,
43924399,
43988459,
44617561,
44750351,
45420457,
46031123,
46301219,
46448719,
46591507,
47263001,
47457367,
47744239,
48024359,
48143047,
48341959,
48384977,
48441331,
49259803,
49353841,
49453847,
50030077,
50170513,
50413439,
50456519,
50471857,
50592911,
50729603,
51340909,
52127189,
53355689,
53420963,
53454589,
53751119,
53753587,
53977403,
54048263,
54292081,
54559123,
54868459,
55204889,
55959643,
56485057,
56660599,
56690071,
56743469,
57013823,
57177889,
57375139,
57980963,
58020581,
58091653,
58107953,
58366619,
58572593,
59088739,
59160317,
59704529,
60949807,
61089089,
61552901,
61575539,
61589579,
62324861,
62444033,
62552489,
62725253,
63359161,
64085921,
64087411,
64843237,
65029997,
65040751,
65314439,
65366051,
65702393,
65947213,
66117679,
66640253,
66854549,
67296517,
67489091,
67715653,
67959743,
68030449,
68428379,
68495347,
68970457,
69315427,
69374167,
69505109,
69912431,
70006253,
70078549,
70514141,
70717291,
70850641,
71364053,
71370853,
71756029,
71760109,
72168857,
72418187,
72422393,
72504457,
72519631,
72673213,
72760297,
73022273,
73179193,
73440439,
73644101,
74143801,
74190419,
74543663,
74711779,
75374149,
75448801,
75460849,
76297087,
76456141,
76720291,
76828823,
77250497,
77438461,
77444701,
77511487,
77540017,
77675639,
77844287,
78050209,
78440119,
78562307,
78712681,
78958211,
79477127,
79833133,
80054363,
80286407,
80468587,
81397777,
81434501,
81536501,
81608981,
81811589,
82087813,
82319411,
82542419,
82742243,
82764371,
82817039,
82892633,
82905047,
83127119,
83407327,
83610599,
83880829,
84083011,
84159917,
84255251,
84487439,
84733919,
85415249,
85468223,
85478369,
85637089,
86504879,
86688269,
87055763,
87303817,
87517271,
87615019,
88551439,
88826693,
88903379,
88948439,
89006641,
89146619,
89473777,
89602771,
89819413,
90997241,
92027977,
92305589,
92519951,
92782441,
93573091,
93831383,
94113781,
94874159,
94912583,
95401417,
95517517,
95532289,
95663761,
95992103,
97069493,
97165001,
97283321,
97353379,
97518247,
97551143,
97792117,
97864961,
97994641,
98285017,
98372203,
98451193,
98643439,
98701003,
98750609,
98954621,
99041179,
99157987,
99595919,
99778351,
100447177,
101154751,
101413777,
102871081,
103291453,
104097043,
104908273,
105217711,
106086811,
106371787,
107552111,
108903143,
110548133,
111033269,
111438259,
111522709,
111627713,
111974587,
112602443,
112663181,
113130803,
113290007,
115610399,
116061419,
116297257,
116321323,
117302429,
118121197,
118565423,
118966829,
119050499,
119075857,
119686943,
122047117,
122150891,
122773549,
123892907,
125286191,
126270601,
126445639,
126517543,
126772411,
127311133,
128456557,
128824391,
128885389,
129461279,
130859077,
131022547,
131739043,
132077149,
134143837,
134528677,
135085453,
135272429,
135345391,
135870139,
136003643,
136240781,
136562467,
137083109,
137165071,
137813021,
138583811,
139281463,
139452133,
139806203,
140383207,
141016331,
141017011,
141187097,
141307483,
142095827,
142380013,
142790317,
143561773,
143924173,
144232247,
144442087,
144481273,
144536701,
144988267,
146020961,
146610701,
147826829,
147846253,
148421633,
148974047,
149411569,
149480959,
150175379,
150971243,
151187611,
151753867,
154114031,
154377841,
154467277,
154477891,
155498891,
156148427,
156251789,
156303463,
156394657,
156589987,
156693529,
157018483,
157101907,
157553993,
159290381,
161423527,
162066193,
162123869,
162417733,
162524249,
162630497,
163146457,
163482377,
163655431,
164076173,
164262151,
164787449,
165543479,
165600647,
165613871,
165656159,
165862253,
165994513,
166374487,
167056709,
167637101,
167753561,
168956971,
169567081,
169817047,
170448713,
170880299,
171154673,
171206471,
171310747,
172155173,
172535497,
173011789,
173050477,
173485307,
173854783,
174163679,
174465541,
174615391,
175110097,
175164643,
175489417,
175539191,
175988881,
176582687,
176598493,
176704379,
177704491,
177911983,
178014517,
180044797,
180455519,
180552809,
181475743,
181946617,
182363249,
182386921,
183585973,
183838177,
183855059,
183875191,
184116337,
184972289,
185627177,
185823727,
186000169,
186343193,
187558759,
187750883,
188756171,
189525311,
189895879,
190056833,
190530629,
191139671,
192093787,
192855583,
193837841,
194437163,
194512459,
194846149,
195315619,
196363373,
196389047,
197611483,
197964253,
198129871,
198303601,
198764771,
198873523,
199802621,
200410643,
200875271,
201067729,
201674041,
202172063,
202607243,
204677017,
206375471,
206461007,
206845729,
207091853,
207751811,
207773861,
208017679,
208278557,
209297449,
209538169,
209769991,
210362171,
211848541,
212040557,
212083709,
212470087,
212545831,
213685123,
214374443,
215329753,
215723539,
215962031,
216553829,
216575111,
216826097,
217870921,
217974623,
218730991,
218803751,
219149123,
219172579,
219438257,
219688867,
219972637,
220176029,
220556603,
221147131,
221758003,
221944409,
222626231,
222638237,
222696457,
222883571,
222914941,
223182941,
223404989,
223646447,
224398087,
224455391,
224545759,
224709337,
225113981,
225265883,
225761299,
226122881,
227652493,
228107927,
228661457,
228999007.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 318177 values, from 294001 to 99999446179).
n\r | 0 | 1 |
2 | 0 | 318177 | 2 |
3 | 0 | 159815 | 158362 | 3 |
4 | 0 | 159120 | 0 | 159057 | 4 |
5 | 0 | 80081 | 79092 | 79122 | 79882 | 5 |
6 | 0 | 159815 | 0 | 0 | 0 | 158362 | 6 |
7 | 0 | 55535 | 52312 | 51842 | 50891 | 53804 | 53793 | 7 |
8 | 0 | 79696 | 0 | 79657 | 0 | 79424 | 0 | 79400 | 8 |
9 | 0 | 53529 | 52319 | 0 | 53220 | 53013 | 0 | 53066 | 53030 | 9 |
10 | 0 | 80081 | 0 | 79122 | 0 | 0 | 0 | 79092 | 0 | 79882 | 10 |
11 | 0 | 23474 | 26391 | 46938 | 25318 | 36917 | 37545 | 25325 | 46411 | 26420 | 23438 |
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.