44 lines
1.6 KiB
Plaintext
44 lines
1.6 KiB
Plaintext
Prime numbers are prime no matter what base they are represented in.
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A prime number in a base other than 10 may not ''look'' prime at first glance.
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For instance: '''19''' base 10 is '''25''' in base 7.
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Several different prime numbers may be expressed as the "same" string when converted to a different base.
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* '''107''' base '''10''' converted to base '''6''' == '''255'''
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* '''173''' base '''10''' converted to base '''8''' == '''255'''
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* '''353''' base '''10''' converted to base '''12''' == '''255'''
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* '''467''' base '''10''' converted to base '''14''' == '''255'''
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* '''743''' base '''10''' converted to base '''18''' == '''255'''
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* '''1277''' base '''10''' converted to base '''24''' == '''255'''
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* '''1487''' base '''10''' converted to base '''26''' == '''255'''
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* '''2213''' base '''10''' converted to base '''32''' == '''255'''
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;Task
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Restricted to bases '''2''' through '''36'''; find the strings that have the most different bases that evaluate to that string when converting prime numbers to a base.
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Find the conversion string, the amount of bases that evaluate a prime to that string and the enumeration of bases that evaluate a prime to that string.
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Display here, on this page, the string, the count and the list for all of the: '''1''' character, '''2''' character, '''3''' character, and '''4''' character strings that have the '''maximum''' base count that evaluate to that string.
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''Should be no surprise, the string '2' has the largest base count for single character strings.''
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;Stretch goal
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Do the same for the maximum '''5''' character string.
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<br>
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