# EL PROBLEMA DE LOS NUMEROS PRIMOS (TODOS LOS IMPARES SON PRIMOS)

Several students were asked the following problem: Prove that all odd integers higher than 2 are prime.

• Mathematician: 3 is prime, 5 is prime, 7 is prime, and by induction, we have that all the odd integers are prime.
• Statistician: 100% of the sample 5, 13, 37, 41 and 53 is prime, so all odd numbers must be prime.
• Measure nontheorist: there are exactly as many odd numbers as primes (Euclid, Cantor), and exactly one even prime (namely 2), so there must be exactly one odd nonprime (namely 1).
• Physicist: 3 is prime, 5 is prime, 7 is prime, 9 is ... uh, 9 is an experimental error, 11 is prime, 13 is prime...  Well, it seems that you're right.
• Wouldn't a modern physicist employ something like renormalization?
3 is prime, 5 is prime, 7 is prime, 9 is ...
9/3 is prime
11 is prime, 13 is prime, 15 is ...
15/3 is prime
17 is prime, 19 is prime, 21 is ...
21/3 is prime
• Quantum Physicist: All numbers are equally prime and non-prime until observed.
• Chemist: 3 is prime, 5 is prime, 7 is prime.. that's enough.
• Chemist: 1 prime, 3 prime, 5 prime...hey, let's publish!
• Cosmologist: 3 is prime, yes it is true....
• Engineer: 3 is prime, 5 is prime, 7 is prime, 9 is ..., 9 is..., well if you approximate, 9 is prime, 11 is prime, 13 is prime... Well, it does seem right."
• Engineer: 3 is prime, 5 is prime, 7 is prime, 9 is not working, fetch toolbox.
• Engineer: 3 is prime, 5 is prime, 7 is prime, 9 is prime, 11 is prime... [Continue until told to go home by others]
• Professor: 3 is prime, 5 is prime, 7 is prime, and the rest are left as an exercise for the student.
• Computer scientist: I've just whipped up a program to REALLY go and prove it..."  He goes over to his terminal and runs his program.  Reading the output on the screen he says, "1 is prime, 1 is prime, 1 is prime, 1 is prime...."
• Computer scientist using Unix: 3's a prime, 5's a prime, 7's a prime, segmentation fault. core dumped.
• GNU program:
% prime
usage: prime [-nV] [--quiet] [--silent] [--version] [-e script]
--catenate --concatenate | c --create | d
--diff --compare | r --append | t --list | u --update |  x
-extract --get [ --atime-preserve ] [ -b, --block-size N ]
[ -B, --read-full-blocks ]  [  -C,  --directory  DIR  ]  [
--checkpoint     ]  [ -f, --file [HOSTNAME:]F ] [ --force-
local   ] [ -F, --info-script F --new-volume-script F ]  [
-G,  --incremental  ] [ -g, --listed-incremental F ] [ -h,
--dereference ] [ -i, --ignore-zeros ] [  --ignore-failed-
read  ] [ -k, --keep-old-files ] [ -K, --starting-file F ]
[ -l, --one-file-system ] [ -L, --tape-length N  ]  [  -m,
--modification-time   ]  [  -M,  --multi-volume  ]  [  -N,
--after-date DATE, --newer DATE  ]  [  -o,  --old-archive,
--portability   ]  [  -O,  --to-stdout  ]  [  -p,  --same-
permissions, --preserve-permissions ]  [  -P,  --absolute-
paths  ]  [  --preserve       ]  [ -R, --record-number ] [
[-f script-file] [--expression=script] [--file=script-file]
[file...]
prime: you must specify exactly one of the r, c, t, x, or d options
• Computer Scientist: 3 is prime, 5 is prime, 7 is prime, 7 is prime, 7 is prime, 7 is prime...  Bus error. Core dumped.
• The computer programmer method is:

"3 is prime, 5 is prime, 7 is prime, 9 is prime, 9 is prime, 9 is prime, 9 is ..."

Opps, let's try that again:

"3 is prime, 5 is prime, 7 is prime, 9 is ... 3 is prime, 5 is prime, 7 is prime, 9 is ... 3 is ..."

"3 is not prime, 5 is not prime, 7 is not prime, 9 is not prime..."

So much for the beta releases.  Ship this:

"3 is prime, 5 is prime, 7 is prime, 9 is a feature, 11 is prime..."

and put on the cover "More prime numbers than anyone else in the industry!"
Coming soon:

"3 is a prime, 4 is a feature, 5 is a prime, 6 is a feature, 7 is a prime, 8 is not yet implemented, 9 is our backwards compatibilty module, ..."

• Computer Scientist: 10 prime, 11 prime, 101 prime...
• Programmer: 3 is prime, 5 is prime, 7 is prime, 9 will be fixed in the next release, ...
• C programmer: 03 is prime, 05 is prime, 07 is prime, 09 is really 011, which everyone knows is prime, ...
• BASIC programmer: What's a prime?
• COBOL programmer: What's an odd number?
• Windows programmer: 1 is prime. Wait.
• Mac programmer: Now why would anyone want to know about that?  That's not user friendly. You don't worry about it, we'll take care of it for you.
• Bill Gates: 1. No one will ever need any more then 1.
• TRS-80 Computer Programmer: One is prime, Two is prime, Three is prime, Out of Memory.
• Computer Scientist with a Pentium: 3 is prime, 5 is prime, 6.9999978 is prime...
• Software tech support operator:  Well, we haven't had any reports of composite odd numbers... do you have the latest version of ZFC?
• Logician:
Hypothesis: All odd numbers are prime
Proof:
1) If a proof exists, then the hypothesis must be true
2) The proof exists; you're reading it now.
From 1 and 2 follows that all odd numbers are prime
• Confused Undergraduate:  Yes, it's true.  Proof:  Let p be any prime number larger than 2.  Then p is not divisible by 2, so p is odd.  QED
• Linguist: 3 is prime, 5 is prime, 7 is prime, 9 aaah. I can make 9 a prime.
• Linguist: are you lot going to shut up and buy me a beer or not?
• Computational linguist: 3 is an odd prime, 5 is an odd prime, 7 is an odd prime, 9 is a very odd prime, ...
• Philosopher: why don't we just call all the odd numbers prime and call all the prime numbers odd, that way all the odd numbers would be prime
• Philosopher: 3 is prime. Hum, thats an interesting statment, I'll get one of my research students to look into that.
• Economist: "Assume 9 is prime..."
• Economist: 2 is a prime, 4 is a prime.
• Economist: 2 is even, 4 is even, 6 is even...
• Economist: 3 is prime, 5 is prime, 7 is prime, 9 is not prime. Look the prime rate is dropping.
• English Major: 1 is prime, 2 is prime, 3 is prime, 4 is prime... Any fool could prove that the above is wrong... After all, no English major can count that high! ;-)
P.S. And I should know...I've done^H^H^H^H spent time in the English army!
• Theologian: 3 is prime and that's good enough for me!
• Theologian: No after all before God all numbers even, odd and prime are created equal.
• Christian: I'm sure the Bible says that all odd numbers are prime.
• Pope: 9 is prime. If you think otherwise, prepare to be damned
• Psychiatrist: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is prime but trying to supress it, 11 is prime......
• Shrink: 3 is prime, 5 is prime etc... And how could one specify "prime" anyway?
• Psychologists: Do _they_ want to be?
• Sociologist: 3 is a number, 3 is prime, all numbers are prime.
• Sociologist: is it right to call numbers odd?
• Sociologist: 3 is a number, 3 is prime, all numbers are prime.
• Multiculturalist:   Pfui!  There you go, classifying numbers into categories.
• Lawyer: 3 is prime, yet 5 could be anything, taking into account, but not limited to, the fact that 4 may or may not be prime, depending on the witnesses' testimonies and the written evidence furnished.
• Lawyer: According to Maths v Logic, 9 was judicially declared prime
• Lawyer: one is prime, three is prime, five is prime, seven is prime, although there appears to be prima facie evidence that nine is not prime, there exists substantial precedent to indicate that nine should be considered prime.  The following brief presents the case for nine's primeness ...
• Accountant: 3 is prime, 5 is prime, 7 is prime, 9 is prime, deducing 10%
•     tax and 5% other obligations.
• Accountant: What would you like it to be?
• Politician: 3 is prime, 5 is prime, 7 is prime, 9 is composite, 11 is prime -- we can ignore 9 because the primes have a majority.
• Corrupt Politician: For a sufficent donation, 9 can be reclassified
• Politician: Do you want them to be?
• George Bush: What's nine got against being prime?  I'll bet it won't allow the pledge of allegiance to be said in our schools either
• Richard Nixon: Put nine on the enemies list.  I'm gonna get that number.
• Liberals: The fact that nine is not prime indicates a deprived cultural environment which can only be remedied by
•         a federally funded cultural enrichment program.
• Manager: 3 yes, 5 yes, 7 YES, 9 Now let's take a positive attitude here
• QA: 1 is not proven, 2 no and reported, 3 not proven, 4 no and reported,...
• Butcher: Prime? What do numbers have to do with meat?
• Rec.humor poster: one is prime, one is prime, one is prime, one is prime
• Crank: 9 IS PRIME! NOW WHERE IS THE CAPS UNLOCK?
• New Yorker: 3 is prime, 5 is prime, 7 is prime, 9 is ... NONE OF YOUR DAMN BUSINESS!