20080617, 01:48  #1 
May 2004
New York City
3·17·83 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" primerelated 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 openended puzzle. 
20080617, 02:39  #2 
"Ben"
Feb 2007
2×3^{2}×191 Posts 
135181951414519 is (probably) prime.
mersennes 
20080617, 03:18  #3 
A Sunny Moo
Aug 2007
USA (GMT5)
1869_{16} Posts 

20080617, 03:31  #4 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 

20080617, 03:52  #5 
"Ben"
Feb 2007
2·3^{2}·191 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" primerelated 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 20080617 at 03:54 
20080617, 04:57  #6 
"Richard B. Woods"
Aug 2002
Wisconsin USA
7692_{10} 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 20080617 at 05:54 
20080617, 06:04  #7 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 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 wordnumber 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)? LetterNumber SemiPrime Words? Last fiddled with by cheesehead on 20080617 at 06:24 
20080617, 12:34  #8  
Cranksta Rap Ayatollah
Jul 2003
641_{10} Posts 
Quote:


20080617, 12:57  #9 
May 2004
New York City
3·17·83 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. 
20080617, 16:35  #10  
Oct 2006
100000100_{2} Posts 
Quote:
What about other languages dos = 41519 = prime; seis = 195919 = prime Couldn't find any in the first 20 of German, Italian, French 

20080617, 18:05  #11  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2×7^{2}×109 Posts 
Quote:
Ok, so it's not prime, being 3 * 239383973 but, nonetheless, it's a counterexample to your claim. Paul Last fiddled with by xilman on 20080617 at 18:11 Reason: Added prime factorization. 

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