A prime whose prefixes or suffixes are all prime. more
The first 600 truncatable primes :
2,
3,
5,
7,
13,
17,
23,
29,
31,
37,
43,
47,
53,
59,
67,
71,
73,
79,
83,
97,
113,
137,
167,
173,
197,
223,
233,
239,
283,
293,
311,
313,
317,
337,
347,
353,
367,
373,
379,
383,
397,
443,
467,
523,
547,
593,
599,
613,
617,
643,
647,
653,
673,
683,
719,
733,
739,
743,
773,
797,
823,
853,
883,
937,
947,
953,
967,
983,
997,
1223,
1283,
1367,
1373,
1523,
1613,
1823,
1997,
2113,
2137,
2333,
2339,
2347,
2383,
2393,
2399,
2467,
2617,
2647,
2683,
2797,
2939,
2953,
3119,
3137,
3167,
3313,
3347,
3373,
3467,
3547,
3613,
3617,
3643,
3673,
3733,
3739,
3793,
3797,
3823,
3853,
3947,
3967,
4283,
4337,
4373,
4397,
4523,
4547,
4643,
4673,
4937,
4967,
5113,
5167,
5197,
5347,
5443,
5647,
5653,
5683,
5743,
5939,
5953,
6113,
6173,
6197,
6317,
6337,
6353,
6367,
6373,
6397,
6547,
6653,
6673,
6823,
6883,
6947,
6967,
6983,
6997,
7193,
7283,
7331,
7333,
7393,
7523,
7547,
7643,
7673,
7823,
7853,
7883,
7937,
8167,
8317,
8353,
8443,
8467,
8647,
9137,
9173,
9283,
9337,
9397,
9467,
9547,
9613,
9643,
9743,
9883,
9967,
12113,
12347,
12647,
12953,
13313,
13613,
13967,
15443,
15647,
15683,
16547,
16673,
16823,
16883,
18353,
18443,
21283,
21523,
21613,
21997,
23167,
23333,
23339,
23399,
23993,
24337,
24373,
24547,
24967,
26113,
26317,
26947,
27283,
27673,
27823,
27883,
29137,
29173,
29399,
31193,
31223,
31379,
32467,
32647,
32797,
33347,
33547,
33613,
33617,
33797,
33967,
34283,
34337,
34673,
36353,
36373,
36653,
36947,
36997,
37337,
37339,
37397,
37547,
37643,
37853,
38167,
38317,
39397,
39883,
42467,
42683,
42797,
42953,
43313,
43613,
43853,
45197,
45953,
46337,
46997,
48353,
48647,
49547,
49613,
51283,
51613,
53617,
54547,
54673,
56113,
56197,
56983,
57283,
57853,
59393,
59399,
59467,
59743,
61223,
61283,
61613,
62137,
62347,
62383,
62467,
62617,
62683,
63313,
63347,
63467,
63617,
63823,
63853,
64283,
64373,
64937,
65167,
65647,
66173,
66337,
66373,
66653,
66883,
66947,
67523,
67547,
67853,
67883,
68443,
69337,
69467,
71933,
72383,
72467,
72617,
72647,
72797,
72953,
73331,
73547,
73613,
73643,
73673,
73823,
73939,
75167,
75347,
75653,
75683,
75743,
76367,
76673,
76883,
78167,
78317,
78467,
79283,
79337,
79397,
79613,
79967,
81223,
81283,
81373,
83137,
83617,
84523,
84673,
84967,
86113,
86197,
86353,
87523,
87547,
87643,
87853,
89137,
91283,
91367,
91373,
91823,
91997,
92347,
92383,
92467,
92647,
92683,
93967,
94397,
94547,
95443,
96337,
96353,
96823,
96997,
97283,
97523,
97547,
97673,
97883,
98317,
98443,
98467,
99137,
99173,
99397,
99643,
121283,
121523,
121997,
124337,
126317,
132647,
133967,
136373,
139397,
139883,
162683,
163853,
181283,
184523,
184967,
186113,
187547,
192347,
192383,
195443,
196337,
213613,
215443,
231223,
233347,
233617,
233993,
234673,
236653,
236947,
237547,
239933,
242467,
242797,
243613,
261223,
264283,
266947,
267523,
272383,
273613,
273643,
275167,
276673,
276883,
279337,
279397,
279613,
279967,
291367,
291373,
291997,
293999,
294397,
296353,
297523,
299137,
313613,
318443,
326113,
326947,
327673,
327823,
332467,
336353,
336373,
336653,
336997,
337853,
338167,
342467,
343313,
345953,
346337,
348353,
356113,
356197,
357283,
361223,
362137,
362347,
363313,
364373,
364937,
366173,
367547,
367853,
367883,
368443,
372797,
373379,
373393,
373613,
373823,
375743,
378167,
378317,
378467,
379283,
379397,
381223,
381373,
384673,
387853,
391283,
391367,
391373,
391823,
392347,
392383,
392467,
392647,
395443,
396353,
396997,
397283,
397547,
397673,
398467,
399137,
399173,
399643,
421997,
424547,
424967,
427283,
427883,
429137,
432797,
433967,
439883,
453617,
454547,
454673,
459467,
462467,
463313,
463823,
465167,
466373,
481373,
492467,
492647,
493967,
496997,
498467,
499397,
513313,
516673,
516883,
534283,
536353,
536947,
537547,
537853,
542467,
542683,
542797,
543313,
543853,
549547,
563467,
564373,
564937,
566173,
566653,
566947,
567883,
573673,
576883,
578167,
578317,
578467,
579283,
579613,
579967,
593933,
593993,
594397,
597523,
597673,
612113,
613967,
616547,
616673,
621997,
626113,
626317,
626947,
627673,
629137,
631223,
632647,
633613,
633797,
633967,
636353,
636653,
636947,
636997,
638317,
642683,
642797,
642953,
649613,
653617,
656113,
659467,
661613,
662617,
663823.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 4158 values, from 2 to 999769267986197).
n\r | 0 | 1 |
2 | 1 | 4157 | 2 |
3 | 1 | 2042 | 2115 | 3 |
4 | 0 | 2080 | 1 | 2077 | 4 |
5 | 1 | 7 | 2007 | 2113 | 30 | 5 |
6 | 0 | 2042 | 1 | 1 | 0 | 2114 | 6 |
7 | 1 | 679 | 693 | 682 | 719 | 709 | 675 | 7 |
8 | 0 | 756 | 1 | 1490 | 0 | 1324 | 0 | 587 | 8 |
9 | 0 | 689 | 699 | 1 | 689 | 716 | 0 | 664 | 700 | 9 |
10 | 0 | 7 | 1 | 2113 | 0 | 1 | 0 | 2006 | 0 | 30 | 10 |
11 | 0 | 419 | 410 | 402 | 419 | 409 | 414 | 423 | 435 | 393 | 434 |
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.