Problems & Puzzles: Puzzles

Puzzle 19.- Primes on a clock

1. How many primes are in a clock if you can read the numbers around the circle clockwise and counterclockwise (the primes should have no more than 15 digits) ?
2. How many prime numbers are in a digital clock ?

Solution part 2.

Patrick De Geest (28/12/98) has found that in a digital clock we can see 211 primes. Here are all of them:

>0002 0003 0005 0007 0011 0013 0017 0019 0023 0029
>0031 0037 0041 0043 0047 0053 0059 0101 0103 0107
>0109 0113 0127 0131 0137 0139 0149 0151 0157 0211
>0223 0227 0229 0233 0239 0241 0251 0257 0307 0311
>0313 0317 0331 0337 0347 0349 0353 0359 0401 0409
>0419 0421 0431 0433 0439 0443 0449 0457 0503 0509
>0521 0523 0541 0547 0557 0601 0607 0613 0617 0619
>0631 0641 0643 0647 0653 0659 0701 0709 0719 0727
>0733 0739 0743 0751 0757 0809 0811 0821 0823 0827
>0829 0839 0853 0857 0859 0907 0911 0919 0929 0937
>0941 0947 0953 1009 1013 1019 1021 1031 1033 1039
>1049 1051 1103 1109 1117 1123 1129 1151 1153 1201
>1213 1217 1223 1229 1231 1237 1249 1259 1301 1303
>1307 1319 1321 1327 1409 1423 1427 1429 1433 1439
>1447 1451 1453 1459 1511 1523 1531 1543 1549 1553
>1559 1601 1607 1609 1613 1619 1621 1627 1637 1657
>1709 1721 1723 1733 1741 1747 1753 1759 1801 1811
>1823 1831 1847 1901 1907 1913 1931 1933 1949 1951
>2003 2011 2017 2027 2029 2039 2053 2111 2113 2129
>2131 2137 2141 2143 2153 2203 2207 2213 2221 2237
>2239 2243 2251 2309 2311 2333 2339 2341 2347 2351
>2357

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Tiziano Mosconi has solved (13/8/2001) the question 2:

Primes Clockwise:

{2, 3, 5, 7, 11, 23, 67, 89, 101, 4567, 10111, 67891, 89101, 789101, 4567891, 23456789, 56789101, 1234567891, 45678910111, 12345678910111}

They are twenty.

Primes Clockwise:

{2, 3, 5, 7, 11, 19, 43, 101, 211, 1019, 1987, 2111, 21211, 76543, 101987, 432121, 4321211, 12111019, 6543212111, 9876543212111}

They are twenty.

As you can see, there are some primes that appear both in the clockwise and in the counterclockwise case, so the total number of primes that appear in a clock is less than 20+20... They are 34

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