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truncatable primes
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 
214157 2 
3120422115 3 
40208012077 4 
5172007211330 5 
6020421102114 6 
71679693682719709675 7 
8075611490013240587 8 
9068969916897160664700 9 
1007121130102006030 10 
110419410402419409414423435393434

A pictorial representation of the table above
motab
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.