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 Prime times (Posted on 2011-03-18)
3:53 is a prime time because 353 is prime.
1. How many prime times are there in 12 hours?
2. How many prime times are there in 24 hours?

 See The Solution Submitted by Math Man Rating: 4.0000 (1 votes)

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 computer solution Comment 1 of 1

ct=0
for h=1 to 12
for m=0 to 59
{
n=h*100+m
if isPrime[n]
{
print["\$n "]
ct=ct+1
}
}
println[]
println[ct]
println[]

ct=0
for h=0 to 23
for m=0 to 59
{
n=h*100+m
if n>1
if isPrime[n]
{
print["\$n "]
ct=ct+1
}
}
println[]
println[ct]
println[]

finds

101 103 107 109 113 127 131 137 139 149 151 157 211 223 227 229 233 239 241 251 257 307 311 313 317 331 337 347 349 353 359 401 409 419 421 431 433 439 443 449 457 503 509 521 523 541 547 557 601 607 613 617 619 631 641 643 647 653 659 701 709 719 727 733 739 743 751 757 809 811 821 823 827 829 839 853 857 859 907 911 919 929 937 941 947 953 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
111

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 101 103 107 109 113 127 131 137 139 149 151 157 211 223 227 229 233 239 241 251 257 307 311 313 317 331 337 347 349 353 359 401 409 419 421 431 433 439 443 449 457 503 509 521 523 541 547 557 601 607 613 617 619 631 641 643 647 653 659 701 709 719 727 733 739 743 751 757 809 811 821 823 827 829 839 853 857 859 907 911 919 929 937 941 947 953 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
211

that is, 111 in the 12-hour case, where the times are 1:00 to 12:59, and 211 in the 24-hour case, where the times are 0:00 to 23:59. The times are listed above the counts, without the colon, and without leading zero--that is, just as the prime number involved.

 Posted by Charlie on 2011-03-18 12:55:09
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