A pair of prime puzzles May 27, 2006 pm31 3:22 pm
Posted by jd2718 in Puzzles.trackback
1. The difference between two prime numbers is 33. What is their product?
2. Can you create a 3-digit number such that the number and all other numbers formed by premutations of its digits, are prime? (eg, 127 is prime, and 271 is prime, but 172, 217, 721, and 712 are not…) How many such numbers are there?
Hi JD, have you got an email address where you can be reached?
jd2718 at gmail dot com.
I just got a new computer (went over to mac) and can’t figure out why your page looks so different. Mosaic is fine - there’s a fine mosiac museum in Antakya, old Antioch, in the part of Turkey that descends the Mediterranean coast towards Lebanon and that was briefly independent as the Hatay Republic between the world wars, and looks nothing like the fictional desert Hatay Republic that shows up in Raiders of the Lost Ark - {inhale} (Turkey on the brain) - Mosaic is fine, but the side bars have disappeared and I can’t back navigate, and I am sure I dropped some math comments, maybe Peano stuff? in some older posts.
I just checked - your site looks fine on the pc. I’ll figure out the mac mess
Difference of 33? The only way that can happen is if one’s even and one’s odd. The only even prime is 2, which would make the other one 35. Which isn’t prime. What am I missing?
Opps.
You’re not missing a thing. I meant 29. Managed to count the wrong way from 31. Thanks for pointing that out.
[...] Not food. Puzzles. Before I start new puzzles for the fall, I want to clear out the old ones from the Spring. There are three on this site that didn’t have solutions posted. Here they are. I will post solutions next week. A prime puzzle: Can you create a 3-digit number such that the number and all other numbers formed by premutations of its digits, are prime? (eg, 127 is prime, and 271 is prime, but 172, 217, 721, and 712 are not…) How many such numbers are there? (May 27) Photographer Puzzle: photographer takes about 15 seconds to line up a group of people and take their photo. Faced with a group of 4 people, and a little extra time, he decides to take their photo in every arrangement possible (this guy always lines them up in 1 row, and never leaves gaps). How long will it take to take all the photos? Guess before you do the math, always more fun that way. [...]
Easy, if you specify that two digits can repeat (there are about four such numbers.) If they can’t then there is no answer.
Note: might ask if one can “find” a number since they’ve all been “created” for some time now.
Yes, and hmm.
I can write “To be or not to be…” Now, if I claimed to be the first…
Likewise, I can create a number. But I cannot claim that it is a new creation. (I know, I know, I am on shaky ground here).
Was it Dedekind who said: “God created the naturals, all else is man’s creation”?
Correction:
German mathematician Leopold Kronecker (1823–1891) is reported to have said, “God created the natural numbers; all the rest is the work of man.”
You may not be able to create a number, but you can patent one!