30 lines
1.2 KiB
Plaintext
30 lines
1.2 KiB
Plaintext
;Definitions
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A '''circular prime''' is a prime number with the property that the number generated at each intermediate step when cyclically permuting its (base 10) digits will also be prime.
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For example:
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'''1193''' is a circular prime, since '''1931''', '''9311''' and '''3119''' are all also prime.
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Note that a number which is a cyclic permutation of a smaller circular prime is not considered to be itself a circular prime. So '''13''' is a circular prime, but '''31''' is not.
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A '''repunit''' (denoted by R) is a number whose base 10 representation contains only the digit '''1'''.
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For example:
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R(2) = 11 and R(5) = 11111 are repunits.
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;Task
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* Find the first 19 circular primes.
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* If your language has access to arbitrary precision integer arithmetic, given that they are all repunits, find the next 4 circular primes.
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* (Stretch) Determine which of the following repunits are probably circular primes: R(5003), R(9887), R(15073), R(25031), R(35317) and R(49081). The larger ones may take a long time to process so just do as many as you reasonably can.
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;See also
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* [[wp:Circular_prime|Wikipedia article - Circular primes]].
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* [[wp:Repunit|Wikipedia article - Repunit]].
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* [[oeis:A016114|OEIS sequence A016114 - Circular primes]].
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