Problems & Puzzles: Puzzles

Puzzle 919. K csc primes without certain ending digit Vic Bold sent the following nice puzzle. From 3779 to 3889 there are 12 prime numbers not ending in digit 9.  Is there a longer list missing one last digit By my side I (CR) found a larger set: from 2462372461 to 2462373707 there are 57 consecutive primes not ending in the digit "3".  Q. Send your largest set.

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Contribution came from Jan van Delden and Giovanni Resta

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Jan wrote:

Starting at 19489355557003 there are 107 primes not ending in 7.

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Giovanni wrote:

I searched the primes up to 2.4 * 10^14.

I found these records for each digit (1, 3, 7, 9)

1-less run starting at 203387773718707 of length 84
3-less run starting at  25051782351877  of length 80
9-less run starting at 215393802984323  of length 85

and
7-less run starting at 19489355557003  of length 107 !

The primes in this run are

19489355500000 +
{57003, 57019, 57033, 57069, 57151, 57159, 57211, 57253, 57283,
57289, 57339, 57363, 57381, 57391, 57403, 57423, 57499, 57513, 57549,
57571, 57589, 57621, 57709, 57723, 57733, 57741, 57751, 57811, 57873,
57879, 57913, 57949, 57951, 57961, 58003, 58021, 58063, 58081, 58111,
58159, 58201, 58209, 58219, 58221, 58423, 58441, 58461, 58483, 58573,
58581, 58663, 58671, 58683, 58809, 58833, 58839, 58863, 58879, 58921,
58989, 58993, 59059, 59061, 59073, 59109, 59131, 59139, 59161, 59173,
59203, 59221, 59253, 59281, 59319, 59343, 59353, 59379, 59419, 59431,
59463, 59469, 59563, 59571, 59593, 59683, 59691, 59719, 59749, 59799,
59803, 59811, 59851, 59871, 59911, 59929, 59941, 60013, 60019, 60093,
60163, 60189, 60193, 60201, 60229, 60249, 60291, 60309},

so the ending digits are:

{3, 9, 3, 9, 1, 9, 1, 3, 3, 9, 9, 3, 1, 1, 3, 3, 9, 3, 9, 1, 9, 1, 9,
3, 3, 1, 1, 1, 3, 9, 3, 9, 1, 1, 3, 1, 3, 1, 1, 9, 1, 9, 9, 1, 3, 1,
1, 3, 3, 1, 3, 1, 3, 9, 3, 9, 3, 9, 1, 9, 3, 9, 1, 3, 9, 1, 9, 1, 3,
3, 1, 3, 1, 9, 3, 3, 9, 9, 1, 3, 9, 3, 1, 3, 3, 1, 9, 9, 9, 3, 1, 1,
1, 1, 9, 1, 3, 9, 3, 3, 9, 3, 1, 9, 9, 1, 9}.

 

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