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In number theory, a left-truncatable prime is a prime number which, in a given base, contains no 0, and if the leading ("left") digit is successively removed, then all resulting numbers are prime. For example, 7817, since 7817, 817, 17 and 7 are all prime.

right-truncatable prime is a prime which remains prime when the last ("right") digit is successively removed. 575E is an example of a right-truncatable prime, since 575E, 575, 57 and 5 are all prime.

Lists of truncatable primes Edit

There are known to be 824E1 left-truncatable primes:

2, 3, 5, 7, E, 15, 17, 1E, 25, 27, 35, 37, 3E, 45, 4E, 57, 5E, 67, 6E, 75, 85, 87, 8E, 95, X7, XE, E5, E7, 117, 11E, 125, 13E, 145, 157, 167, 16E, 175, 18E, 195, 1X7, 1E5, 1E7, 217, 21E, 225, 237, 24E, 25E, 267, 285, 295, 2XE, 315, 325, 327, 33E, 34E, 357, 35E, 375, 3XE, 3E5, 3E7, 415, 41E, 427, 435, 437, 457, 45E, 46E, 485, 48E, 517, 51E, 527, 535, 545, 557, 575, 585, 587, 58E, 5E5, 5E7, 615, 617, 61E, 637, 63E, 66E, 675, 687, 68E, 695, 6X7, 71E, 727, 735, 737, 745, 767, 76E, 775, 785, 817, 825, 835, 85E, 867, 88E, 8X7, 8XE, 8E5, 8E7, 91E, 927, 95E, 987, 995, 9X7, 9XE, 9E5, X17, X27, X35, X37, X3E, X45, X4E, X5E, X6E, X87, X95, XX7, XXE, XE7, E15, E1E, E25, E37, E45, E67, E6E, E95, EE5, EE7, ...

The largest is the 28-digit 471X34X164259EX16E324XE8X32E7817.

There are 12E right-truncatable primes:

2, 3, 5, 7, E, 25, 27, 31, 35, 37, 3E, 51, 57, 5E, 75, E5, E7, 251, 255, 25E, 271, 277, 27E, 315, 357, 35E, 375, 377, 3E5, 3E7, 511, 517, 51E, 575, 577, 5E1, 5E5, 5E7, 5EE, 751, E71, 2555, 2557, 2715, 2717, 2771, 27E1, 27E7, 3155, 315E, 35E1, 35E7, 35EE, 3755, 375E, 3771, 377E, 3E51, 3E55, 3E75, 3E7E, 5117, 511E, 51E7, 575E, 5771, 5777, 577E, 5E17, 5E1E, 5E55, 5E75, 5EE1, 7511, E711, 25551, 25577, 27151, 27155, 2715E, 27E17, 27E77, 31551, 315E5, 375E5, 375EE, 37715, 3E515, 3E557, 3E55E, 3E7E5, 511E7, 51E71, 575EE, 57711, 57717, 577E7, 577EE, 5E175, 5E1E7, 5E55E, 5E751, 5EE17, 75111, 75115, E7111, E7115, 255515, 255775, 271555, 2715E1, 27E177, 27E17E, 27E771, 375E55, 375EE5, 377151, 3E5155, 3E5157, 3E515E, 3E5571, 3E557E, 3E55E7, 3E7E5E, 511E77, 51E717, 575EEE, 577117, 577175, 577E75, 5E55E1, 5E55EE, 5EE171, 751115, E71157, ...

The largest is the X-digit 375EE5E515.