# Talk:Semiprime

## task clarification

The use of the phrase *natural numbers* (according to Wikipedia)

(quoted from Wikipedia **Natural number**:

There is no universal agreement about whether to include zero in the set of natural numbers: some define the natural numbers to be the positive integers {1, 2, 3, ...}, while for others the term designates the non-negative integers {0, 1, 2, 3, ...}. The former definition is the traditional one, with the latter definition having first appeared in the 19th century.

I personally like *positive integers* or *non-negative integers* for one or the other; that way, there can be no misunderstanding. -- Gerard Schildberger (talk) 01:17, 21 February 2014 (UTC)

Of course, if all program examples would handle both cases, this would be a moot point. -- Gerard Schildberger (talk) 01:17, 21 February 2014 (UTC)

- It doesn't matter
*when taken in this context*. Zero is never taken as prime.

- That was never my point. Unity also isn't a prime. But an
**isPrime**function should be able to test any integer and return a correct result (as to being a prime or not) without giving an error or causing a loop. Same thing with an*isSemiprime*function. It should be able to return a correct result. Understanding that extremely large numbers would be problematic, of course. -- Gerard Schildberger (talk) 08:00, 21 February 2014 (UTC)

- That was never my point. Unity also isn't a prime. But an

- Are you saying that the task description is confusing as it stands? --Paddy3118 (talk) 07:17, 21 February 2014 (UTC)

- Well, maybe not confusing, but it could be clarified. The use of any phrase (or word) that is under contention (disagreement) should never be used in a definition. If not, then we could say that semiprimes are the product of exactly two (possibly equal) primes. The use of a clarifying adjective should be definitive, and not be argumentative (since there is not an agreed-on definition). I like Mathworld's definition better: a semiprime, also called a 2-almost prime, biprime, or
*p q*-number, is a composite number that is the product of two (possible equal) primes. This also has the advantage of introducing other (alias) names for people searching for alternate names. A note about the square of a prime being, by definition, is a semiprime would be a nice addition. -- Gerard Schildberger (talk) 08:00, 21 February 2014 (UTC)

- Well, maybe not confusing, but it could be clarified. The use of any phrase (or word) that is under contention (disagreement) should never be used in a definition. If not, then we could say that semiprimes are the product of exactly two (possibly equal) primes. The use of a clarifying adjective should be definitive, and not be argumentative (since there is not an agreed-on definition). I like Mathworld's definition better: a semiprime, also called a 2-almost prime, biprime, or

## a graphic view of the first 10k semi-primes

For those that are interested, here is the output of my **$CALC** (REXX) program that shows a binary map of the first 10k semiprimes.

The command used was: (extra blanks were used to make the command's arguments easier to read)

$CALC trans{ isSemiPrime[ iota(10k) ], 'fefa'x, 10} ;;; SQUISH GRoup 100

The **isSemiPrime** BIF outputs a **0** (zero) to indicate the number isn't semi-prime, or a **1** (unity) to indicate a semi-prime.

The **translate** BIF converts (for easier perusing) ones and zeroes to ■ and ** · ** [the square bullets are the semi-primes].

The **iota** BIF generates the numbers 1 ──► 10,000 which are passed to the **isSemiPrime** BIF.

The **SQUISH** option removes all blanks from the output (except for the index).

The **GROUP** option groups **100** output items per line.

(Output is shown at ^{2}/_{3} size.)

╔═══════════════════════════════════════════════╗ ║ trans{ isSemiPrime[ iota(10k) ], 'fefa'x, 10} ║ ╚═══════════════════════════════════════════════╝ 1► ···■·■··■■···■■·····■■··■■······■■■··■■······■··■·■···■·■■···■··■···■····■··■····■··■■■···■·■■■····· 101► ·····■····■···■··■■·■■■·····■···■■······■■■·■■········■··■■·■····■··■·······■■····■·■·■······■······ 201► ■■■·■■··■···■■■·■■■·■····■········■·■·········■·■···■■····■··■··■·■······■···■········■·■·■···■··■■· 301► ■■■·■···■····■····■·■·■··■■·■····■■···■·■····■········■··■··■■··■·····■·····■···■■···■····■·■■■··■·· 401► ··■···■···■·■·■·■····■····■·········■·······■■■···■·■■···■·······■··■·■·■····■··■■··■···■···■···■··· 501► ■■··■·····■··■■·■·■······■■·■···■·■·■■···■■·■·····■·■■····■··■··■■······■·····■·■·■··■··■·■·····■··· 601► ··········■··■·······■■··■··■···■■■·············■·····■······■····■·■·■··■····■·■···■·■·■····■■·■■■· 701► ··■··■■·····■···■■··■·■·······■··■··■·······■■··■···■·■··■····■··■■···■······■■·■···■···■·■·■■····■· 801► ·■■···■·····■·■·■■············■···■··■··■■■·····■·■··········■··■■··■·■······■■······■··■···■·■··■■· 901► ■···■·······■■··■···■■■··■······■■····■···■·····■·■···■··■■·■···■·······■■····■··■··■···■···■·■··■·· 1001► ··■··■■···■······■········■·········■···■■■··■■·······■·■·■·······■·····■···■·■·■■···········■····■· 1101► ■·········■··■■···■·■····■······■·■·■■■·■■··■·■·■····■··■·■·····■·■·■····■··■········■··■·■···■··■■· 1201► ·■■·■·■···■··■····■······■■······■···■··■·■···■·····■·■·■···■■■···■···■·■········■··■■······■■····■· 1301► ·····■······■·■·■■···■······■···■···■·■···■·■■■·■·■··■■·■·····■··■··■·■·······■··■■·■·■·■·■·■···■··· 1401► ■■■·■·····■···■·■■··················■■··■············■··■···■···■■··■···■···■■·······■··········■··· 1501► ■■····■·■···■■··■····■····■·■·····■·■■··■····■········■·····■·■·■···■····■··■·······■···■·■··■······ 1601► ··■··············■···■■·······■·■·····■·■■■··■··■·■··■■··■··■·········■·■····■■·■···■·■·■·■········· 1701► ··■··■■···■·■■··■■·······■■···■···■···■·····■·····■··■··■···■■■·■■··■····■····■·■···········■·■·■·■· 1801► ··■···■······■··■·■·■■······■·····■·■■■·■·■·····■·■·■···■■······■········■·······■■·······■·■■■·■··· 1901► ··■··■··■·····■···■·■·■···■·■····■··■·■·■■■·■········■··■·■·■·■··■■·■·······■···■■■·■·····■··■······ 2001► ····■············■■·■····■····■·■····■··■■··■·■·■·■·······■··■···■····■·■···■■················■··■·· 2101► ■■■·■···········■·■··■■··■■··········■········■·■·····■·■·■·····■·■···■·■■··■···■■■··■··■·■··■■···■· 2201► ■····■··■·····■·■■■·······■·■·■··■··········■■··■···■···■■····■·······■·······■···■·■·····■········· 2301► ·■··■■■·······■·■·■·■·■··■■·■·····■······■··········■·····■·■■■·····■····■···········■····■···■····· 2401► ·■····■·····■·····■······■■·■···■■■·······■··■··■···■·■··■··■■■·····■·■··■····■·■·■···■·■·■···■·■■·· 2501► ■·····■·■···■·■·■■■·············■···■·······■········■···■■·■·■··■■·■·■·■···■■··■■····■·■····■····■· 2601► ·■■·■■····■··■■·······■···■·■·■······■··■■■·····■·■·■■······■·······■···········■··················· 2701► ■···■···············■■■·········■■■·······■··■■·········■·■·■■········■·■·····■·····■·■··········■·· 2801► ······■·■·■·■·■··■····■···■···■·······■·■···■■·······■■··■■···■··■■·■········■··■···■·······■■····■· 2901► ■■···■····■·■····■··■·■·····■·■·■·■·····■■····■·■·■·······■··■··■■······■■··■■··■·■··■■···■·■·■··■·· 3001► ····■·■·····■···■····■····■·■·■···■···■···■··■■·····■···■····■■·■·····■·■···■·······■■····■·■·■·■■■· 3101► ■·■··■■·····■···■■········■···■·■■····■··■■···■·■·■·■·■··■··■····■······■·········■·····■···■■··■·■· 3201► ·■··■·■······■■··■····■··■■·····■·■··■■·■■····■······■······■·■·■···■···■■··■·■·■·····■···■·■·■····· 3301► ····■···■····■··■········■■······■··■■··■·······■·■·■···········■···■·······■·■···■·■■■······■··■■·· 3401► ■·■·····■·····■··■■·■·····■···■·····■·■··■■··■······■·■···■······■······■·······■■····■·■···■■··■··· 3501► ··■·■■······■····■··■·■···················■·■·····■··■······■·■··■··■····■···■■·······■·■·····■···■· 3601► ■■■·······■··········■······■·····■···■·■····■■·■·■·■·······■■··■·■·■·········■···■···■·····■■■····· 3701► ······■···■·■·■·····■■···········■··■····■■··■■·■····■■··■····■·············■■··■···■·■···■·······■· 3801► ·■··■···■·■··■··■········■■·■·■·····■·■·■···■···■·········■··■··■■■·■···■·········■·······■·■····■■· 3901► ■■■·····■···········■·············■·■···■····■··■···■···■■■·■·■·········■■··■·■·■·■·■■····■··■··■■·· 4001► ·····■··■············■········■·■■··■·■···■·■········■■··■··■·■·····■········■····■···■·········■··· 4101► ■·■·■■··■·····■·■·■·■····■········■··■··■·■·■·····■··········■■··■··■·■··■···■··■·■···■·■···■·■·■■·· 4201► ······■·····■········■■··■■·········■·········■·■········■···■··■·■·■····■····■·■■··■■■···■···■···■· 4301► ··■··■■·■···■·■·■·■·■■········■·■·······■·■·······■·■····■■·······■·■·······■·■·■···■·■·····■·····■· 4401► ····■■····■·■■■·■········■■·■·····■···■··■■·····■···■·······■·····■·■·■··■···■■······■■·■·······■·■· 4501► ■■········■·················■·■·■■■·■■··■····■······■·■···■··■······■·■·■■··■·■······■··■···■■■····· 4601► ■·····■·■···■····■■··■····■·■·■·■···········■·■···········■·■····■■·········■■··■■··■·■······■····■· 4701► ■■··■···■·■·■■··■·········■·······■·■·■·■■····■·■····■··■····■■·■■··■·■·····■■··■····■····■······■·· 4801► ··■·······■·······■·■■····■·■····■■·■·■·■·■··■■·■···■·■·■·■···■···■·····■■······■■■·■·····■··■··■··· 4901► ······■···■···■··■········■······■····■······■·······■■·······■·······■·······■·■···■···■·······■··· 5001► ■····■■·········■·········■·■···■·······■■··■·······■···■····■■·■···■·■······■■······■··■·■·■·■·■■·· 5101► ·■··■·····■··■········■···■·■·■·····■···■·■·····■·····■··■··■·■·■···■···■···■····■■··■····■···■···■· 5201► ■·····■·····■····■■·■·■··········■······■■··■···■·■···■·■·■···■··■■·■·······■·········■·····■■····■· 5301► ····■·····■··■■·■■··■····■■·■·■·······■··■··■···■···■■··■·■·■·■··■■···■··■··■■····■··■··■········■·· 5401► ■·■·······■··■·······■···■··■···■·■··■········■·······■··■■·■■··■···■···■········■··■···■···■···■■·· 5501► ·····■··■···■·■·················■■····■·■·■·■···■····■······■·····■··········■■··■■·■·■······■··■·■· 5601► ■■■··■··■·■·■·■·■·■·······■·■·■·■···■■······■·················■··■■···■··■··■········■············■· 5701► ·■■···■·····■■······■■■·····■·■·······■·······■·····■·■··■■·■···■·■···■·■■··■···········■···■■····■· 5801► ··■··■··■·····■··■··············■■··■·········■·····■■■·················■····■············■·■·····■· 5901► ····■■··■·■··■··■·■·■····■······■·■·■■··■■····■···■·······■·■·■·■···■·■·····■·■···■·····■·■·■···■■■· 6001► ■■··■···■···■···■·■··■■·······■·■····■··■····■··■·■·······■·····■·····■··■··■···■■··■·■··········■·· 6101► ··■···■·■·····■·■·■··■····■······■····■·····■·········■·■■■·■····■■·■········■■·■···■·■·■·■·■······· 6201► 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··········■·■■■·■■····■·······■·■·■·····■■■·■·■·■···■···■····■··■■■·■·■·······■·■·■··■········■·■·■· 7201► ■············■··■·····■··■····■·■■■·····■····■··■·■···■·····■■··■···■·■·■■··■·■······■··■·■···■····· 7301► ··■·······■·■····■■···■···■···········■·■■■··■·······■■·■···■·■···■·····■···■·■··■····■···■··■··■··· 7401► ■■■·■···■·····■··■■·■·■···■···■···■··■■·■···■·■·····■■········■·■■····■······■····■·········■·■····· 7501► ■·······■···■·····■··■········■··■···■····■···········■··■····■·······■··············■······■■··■··· 7601► ■····■··■···■·■·■·■·······■·■·■·■···■····■···■■···■·■·■·····■·■··■····■·······■··············■··■··· 7701► ·■···■··■·■···■·····■····■··■·······■·■·····■·■···■··■·······■■·■···■·■·■····■■·■·■···■·······■···■· 7801► ■·····■···■·■■····■··■····■···■··■■·■■·······■··■·■···■··■■·■■■·······■··············■····■··■■·■·■· 7901► ··■·····■···■·■·····■············■····■·■···············■···■·····■·■·■·····■■■·■···■···■·■·····■·■· 8001► ·■■·■■······■■······■·■··■■···■·■·■··■···■··■·■·■·■··■··■···■·■·■·■···■·····■·■···■···········■·■■·· 8101► ·■··■········■····■·■·······■·■·■·■·■·■·■·■··■··■···■···■■■·············■········■··■■■·■···■···■■·· 8201► ■·■···■·····■········■■···■···················■·■·■··■··■■■·■····■■··········■■·····■·············■· 8301► ■····■··■····■■··■··■·····■···■·■·■···■·■···■·■···■··■··■·■·······■···■·■·········■·······■·······■· 8401► ■■■···■·■·■·■···■····■···········■···■··■···········■···■■■··■··■·····■·■·····■··■■·■■··■·■···■·■·■· 8501► ··■··■■·■·■······■■··■······■·■··········■··■■··■·■·■···■···■····■■···■······■■···■···■·····■■······ 8601► ··■·■·····■···■·■···■···········■···■·■···········■·■■··■·■·■···■········■···■····■·······■······■·· 8701► ····■···■·■··■··■········■■·······■·······■··■··■·■·······■·····■·■·····■···■···■■········■··■■·■··· 8801► ■·······■···■···■■·······················■■··■····■·····■·■···········■·■·····■·■■··■···■·■··■····■· 8901► ·■■···■·■···■■■·■···■····■■·······■···■·····■·■·····■········■···■··········■···■·■··■··■·······■··· 9001► ··■·■········■··■·■···■··■····■·■■··■■·······■■·····■·■·■···········■·■·■···■·■···■·····■····■··■■·· 9101► ■·····■···■·■·■···■·■■■·······■··■········■···■·■·····■··········■■·■·········■··■■·········■■··■··· 9201► ■····■····■·····■·····■·····■···■·■·■····■····■·■···■·····■···■···■···■··■···■·······■■·■········■■· 9301► ■■··■·■·····■■···········■■·■·····■··········■■·····■·■·■■····■·■·············■··■■·■···■·····■····· 9401► ·····■■·■·■···············■··············■··■■··■·■······■·······■··■···········■·····■·■···■······· 9501► ■■··■·■·■·······■■····■···■·■·····■·······■·········■···■···■·■·■■··■·■·■■··■■·······■··■···■····■■· 9601► ·■····■·■·■·····■········■■······■··■···■·····■···■···■···■··■■·■·■···■·■·········■···■···■········· 9701► ■·■···■·····■········■····■···■··········■··■·······■■■·■·■·■·■·······■·■···■■··············■···■·■· 9801► 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