70 lines
2.0 KiB
Plaintext
70 lines
2.0 KiB
Plaintext
When calculating prime numbers > 2, the difference between adjacent primes is always an even number. This difference, also referred to as the gap, varies in an random pattern; at least, no pattern has ever been discovered, and it is strongly conjectured that no pattern exists. However, it is also conjectured that between some two adjacent primes will be a gap corresponding to every positive even integer.
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<div style="float:left;padding-left:2em;padding-right:3em;">
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{|class="wikitable"
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!gap!!minimal<br>starting<br>prime!!ending<br>prime
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|2||3||5
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|4||7||11
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|6||23||29
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|8||89||97
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|10||139||149
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|12||199||211
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|14||113||127
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|16||1831||1847
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|18||523||541
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|20||887||907
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|22||1129||1151
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|24||1669||1693
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|26||2477||2503
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|28||2971||2999
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|30||4297||4327
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|}
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</div>
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This task involves locating the minimal primes corresponding to those gaps.
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Though every gap value exists, they don't seem to come in any particular order. For example, this table shows the gaps and minimum starting value primes for 2 through 30:
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For the purposes of this task, considering only primes greater than 2, consider prime gaps that differ by exactly two to be adjacent.
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;Task
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For each order of magnitude '''m''' from '''10¹''' through '''10⁶''':
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* Find the first two sets of minimum adjacent prime gaps where the absolute value of the difference between the prime gap start values is greater than '''m'''.
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;E.G.
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For an '''m''' of '''10¹''';
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The start value of gap 2 is 3, the start value of gap 4 is 7, the difference is 7 - 3 or 4. 4 < '''10¹''' so keep going.
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The start value of gap 4 is 7, the start value of gap 6 is 23, the difference is 23 - 7, or 16. 16 > '''10¹''' so this the earliest adjacent gap difference > '''10¹'''.
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;Stretch goal
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* Do the same for '''10⁷''' and '''10⁸''' (and higher?) orders of magnitude
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Note: the earliest value found for each order of magnitude may not be unique, in fact, ''is'' not unique; also, with the gaps in ascending order, the minimal starting values are not strictly ascending.
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