20221112, 00:48  #1 
Jul 2021
2·19 Posts 
Prime 'anagrams'
Take a prime number and rearrange the digits to get another prime number. This is difficult for small numbers, but gets easier as the primes get larger. Therefore the question becomes: What is that largest prime that has no anagrams? ie. no other primes can be made by reordering it's digits. It might seem trivial for a number like 22222222222222221 to make the last digit even, but is such a number prime in the first place? (I haven't checked this example LOL)
I wrote a little Python script to check these, so far the largest I've found with zero anagrams is 33343 (it's a slow program ) Can anyone find larger ones? 
20221112, 02:17  #2 
Jun 2003
2×2,719 Posts 
99949999 appears to be the largest 8digit one

20221112, 02:27  #3 
Jul 2021
2·19 Posts 

20221112, 02:30  #4 
Jun 2003
2×2,719 Posts 
List of nearrepdigit primes/PRPs (https://stdkmd.net/nrr/prime/primesize.txt) might be a good place to look

20221112, 02:35  #5 
Jun 2003
5438_{10} Posts 
Not by looking at all the anagrams for a prime, for sure
I looped thru all primes < 10^8, converted them into a "canonical" form and checked if that has been seen before. Any canonical form seen only once means, it has no anagrams. Of course, you get to know that only after entire range of ndigit primes have been scanned. 
20221112, 03:01  #6 
Jul 2021
100110_{2} Posts 
I deduped my lists, so having all the same digits doesn't really count (or at least not in the spirit of the task )
EDIT: i think i responded the the wrong msg, no matter Last fiddled with by raresaturn on 20221112 at 03:02 
20221112, 04:17  #7 
Einyen
Dec 2003
Denmark
19·181 Posts 
As you pointed out any prime with all even numbers or 5's and just the last digit 1,3,7 or 9 are trivial candidates for this.
Nontrivial ones: Largest below 10^{6}: 999499 Largest below 10^{7}: 9999991 Largest below 10^{8}: 99949999 Largest below 10^{9}: 999499999 There are "only" 350 of them from 11 to 10^{9} including the trivial ones. Count of them including trivials starting from 11: 10^{1}  10^{2}: 13 10^{2}  10^{3}: 34 10^{3}  10^{4}: 45 10^{4}  10^{5}: 68 10^{5}  10^{6}: 67 10^{6}  10^{7}: 47 10^{7}  10^{8}: 36 10^{8}  10^{9}: 40 
20221112, 05:22  #8 
Jul 2021
100110_{2} Posts 
That's really interesting...I wonder if we can just keep adding 9's to the end eg: 99949999999999999999999999999 (and will it always be a prime?)
Last fiddled with by raresaturn on 20221112 at 05:27 
20221112, 10:09  #9 
Romulan Interpreter
"name field"
Jun 2011
Thailand
3×23×149 Posts 
Nope.

20221112, 11:41  #10  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
3^{4}·7·13 Posts 
Quote:
Trimming away a 2 at a time, I didn't encounter a prime until 2221. 

20221112, 13:29  #11 
"Forget I exist"
Jul 2009
Dartmouth NS
2×3×23×61 Posts 
Code:
forperm(digits(randomprime(10^9)),x,print(x)) 
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