24 lines
928 B
Plaintext
24 lines
928 B
Plaintext
;Definition
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A positive integer '''n''' is a '''Blum integer''' if ''n = p x q'' is a semi-prime for which ''p'' and ''q'' are distinct primes congruent to 3 mod 4. In other words, ''p'' and ''q'' must be of the form 4''t'' + 3 where ''t'' is some non-negative integer.
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<br>
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;Example
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21 is a Blum integer because it has two prime factors: 3 (= 4 x 0 + 3) and 7 (= 4 x 1 + 3).
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;Task
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Find and show on this page the first '''50''' Blum integers.
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Also show the '''26,828'''th.
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<br>
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;Stretch
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Find and show the '''100,000'''th, '''200,000'''th, '''300,000'''th and '''400,000'''th Blum integers.
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For the first '''400,000''' Blum integers, show the percentage distribution by final decimal digit (to 3 decimal places). Clearly, such integers can only end in 1, 3, 7 or 9.
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;Related task
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* [[Semiprime]]
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;References
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* Wikipedia article [[wp:Blum_integer|Blum integer]]
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* OEIS sequence [[oeis:A016105|A016105: Blum integers]]
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<br>
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