Prime Words

davar55 · 2008-06-17, 01:48

Start by numbering the letters of the alphabet, so that
A=1,B=2,...,Y=25,Z=26.

For a given word or name or sentence (or any sequence of letters)
form the concatenation of the numerical values.

For example, "PRIME" becomes 16189135, which is of course composite.
So PRIME is not a prime word.

The puzzle is to find "interesting" prime-related words,
e.g. the longest prime word, words which factor into other words,
a meaningful sentence that is prime, words whose reversal is prime,
or something more interesting than what I've suggested.

I won't given any examples, I just thought this might be interesting
as an open-ended puzzle.

bsquared · 2008-06-17, 02:39

135181951414519 is (probably) prime.

mersennes

mdettweiler · 2008-06-17, 03:18

Quote:

Originally Posted by bsquared

135181951414519 is (probably) prime.

mersennes

Proven prime with Pari/GP.

Mini-Geek · 2008-06-17, 03:31

http://rumkin.com/tools/cipher/numbers.php

bsquared · 2008-06-17, 03:52

This puzzle is pretty neat... so I got to writting some code.

I found a cool word list site for raw input: http://wordlist.sourceforge.net/

fed the words (skipping those with apostrophes) into my prime checker and tracked a few things...

found 15404 prime words out of 414540
the biggest was counterrevolutionaries
= 3152114205181852215122120915141189519

checking the prime words for "interesting" prime-related words is harder to do... much less forming meaningful interesting sentences. That'll be a neat challenge.

- ben.

[edit]
I can post the list of prime words, if anyone wants them to build from...

cheesehead · 2008-06-17, 04:57

Subproblem:

Find a set of multiple distinct words that are all represented by the same (prime, preferably) numerical value. This is possible because of ambiguity in coding: e.g., the substring "15" can represent either "O" or "AE"; "23" can represent either "BC" or "W".

Substrings:

11 = "AA" or "K"

12 = "AB" or "L"

13 = "AC" or "M"

14 = "AD" or "N"

15 = "AE" or "O"

16 = "AF" or "P"

17 = "AG" or "Q"

18 = "AH" or "R"

19 = "AI" or "S"

21 = "BA" or "U"

22 = "BB" or "V"

23 = "BC" or "W"

24 = "BD" or "X"

25 = "BE" or "Y"

26 = "BF" or "Z"

- - - - -

Words:

22120 = BUT or VAT

25520 = BEET or YET

18152251819 = ROBBERS or ROVERS (http://rumkin.com/tools/cipher/numbers.php doesn't decode this correctly unless you include helper hyphens)

But none of those is prime. (Prime words of more than one letter can end only in "A", "C", "G", "I", "K", "M", "Q", "S", "U" or "W".)

cheesehead · 2008-06-17, 06:04

Hmm...

My 18152251819 from the preceding post isn't prime within the standard integers, but it can't be decomposed into factors each of which are legitimate coded word values. 18152251819 = 13 * 1396327063 (http://wims.unice.fr/wims/wims.cgi), but the largest factor can't be a legitimate coded word value because it contains a zero that's not following a 1 or a 2.

OTOH, the entire number can be decoded into more than one word, which makes it a sort of "composite" within the group of word-number pairs using this coding.

So, what's a good term for this case (or the case in which the entire number is prime within the integers)?

Letter-Number Semi-Prime Words?

Orgasmic Troll · 2008-06-17, 12:34

Quote:

Originally Posted by cheesehead

Hmm...

My 18152251819 from the preceding post isn't prime within the standard integers, but it can't be decomposed into factors each of which are legitimate coded word values. 18152251819 = 13 * 1396327063 (http://wims.unice.fr/wims/wims.cgi), but the largest factor can't be a legitimate coded word value because it contains a zero that's not following a 1 or a 2.

OTOH, the entire number can be decoded into more than one word, which makes it a sort of "composite" within the group of word-number pairs using this coding.

So, what's a good term for this case (or the case in which the entire number is prime within the integers)?

Letter-Number Semi-Prime Words?

too long, I suggest "Cheesehead Words"

davar55 · 2008-06-17, 12:57

Here's a negative result:
NO NUMBERS ARE PRIME! (at least not in English).
None of their names end in A,C,G,I,K,M,Q,S,U, or W.

roger · 2008-06-17, 16:35

Quote:

Here's a negative result:
NO NUMBERS ARE PRIME! (at least not in English).
None of their names end in A,C,G,I,K,M,Q,S,U, or W.

What about other languages
dos = 41519 = prime; seis = 195919 = prime
Couldn't find any in the first 20 of German, Italian, French

xilman · 2008-06-17, 18:05

Quote:

Originally Posted by davar55

Here's a negative result:
NO NUMBERS ARE PRIME! (at least not in English).
None of their names end in A,C,G,I,K,M,Q,S,U, or W.

Gross?

Ok, so it's not prime, being 3 * 239383973 but, nonetheless, it's a counterexample to your claim.

Paul

2008-06-17, 01:48	#1
davar55 May 2004 New York City 10212₈ Posts	Prime Words Start by numbering the letters of the alphabet, so that A=1,B=2,...,Y=25,Z=26. For a given word or name or sentence (or any sequence of letters) form the concatenation of the numerical values. For example, "PRIME" becomes 16189135, which is of course composite. So PRIME is not a prime word. The puzzle is to find "interesting" prime-related words, e.g. the longest prime word, words which factor into other words, a meaningful sentence that is prime, words whose reversal is prime, or something more interesting than what I've suggested. I won't given any examples, I just thought this might be interesting as an open-ended puzzle.

2008-06-17, 03:52	#5
bsquared "Ben" Feb 2007 3×1,171 Posts	This puzzle is pretty neat... so I got to writting some code. I found a cool word list site for raw input: http://wordlist.sourceforge.net/ fed the words (skipping those with apostrophes) into my prime checker and tracked a few things... found 15404 prime words out of 414540 the biggest was counterrevolutionaries = 3152114205181852215122120915141189519 checking the prime words for "interesting" prime-related words is harder to do... much less forming meaningful interesting sentences. That'll be a neat challenge. - ben. [edit] I can post the list of prime words, if anyone wants them to build from... Last fiddled with by bsquared on 2008-06-17 at 03:54

2008-06-17, 04:57	#6
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 1111000001100₂ Posts	Subproblem: Find a set of multiple distinct words that are all represented by the same (prime, preferably) numerical value. This is possible because of ambiguity in coding: e.g., the substring "15" can represent either "O" or "AE"; "23" can represent either "BC" or "W". Substrings: 11 = "AA" or "K" 12 = "AB" or "L" 13 = "AC" or "M" 14 = "AD" or "N" 15 = "AE" or "O" 16 = "AF" or "P" 17 = "AG" or "Q" 18 = "AH" or "R" 19 = "AI" or "S" 21 = "BA" or "U" 22 = "BB" or "V" 23 = "BC" or "W" 24 = "BD" or "X" 25 = "BE" or "Y" 26 = "BF" or "Z" - - - - - Words: 22120 = BUT or VAT 25520 = BEET or YET 18152251819 = ROBBERS or ROVERS (http://rumkin.com/tools/cipher/numbers.php doesn't decode this correctly unless you include helper hyphens) But none of those is prime. (Prime words of more than one letter can end only in "A", "C", "G", "I", "K", "M", "Q", "S", "U" or "W".) Last fiddled with by cheesehead on 2008-06-17 at 05:54

2008-06-17, 06:04	#7
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 17014₈ Posts	Hmm... My 18152251819 from the preceding post isn't prime within the standard integers, but it can't be decomposed into factors each of which are legitimate coded word values. 18152251819 = 13 * 1396327063 (http://wims.unice.fr/wims/wims.cgi), but the largest factor can't be a legitimate coded word value because it contains a zero that's not following a 1 or a 2. OTOH, the entire number can be decoded into more than one word, which makes it a sort of "composite" within the group of word-number pairs using this coding. So, what's a good term for this case (or the case in which the entire number is prime within the integers)? Letter-Number Semi-Prime Words? Last fiddled with by cheesehead on 2008-06-17 at 06:24

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2008-06-17, 02:39	#2
bsquared "Ben" Feb 2007 3×1,171 Posts	135181951414519 is (probably) prime. mersennes

2008-06-17, 03:31	#4
Mini-Geek Account Deleted "Tim Sorbera" Aug 2006 San Antonio, TX USA 17×251 Posts	http://rumkin.com/tools/cipher/numbers.php

2008-06-17, 12:57	#9
davar55 May 2004 New York City 2×29×73 Posts	Here's a negative result: NO NUMBERS ARE PRIME! (at least not in English). None of their names end in A,C,G,I,K,M,Q,S,U, or W.