20200106, 17:10  #1 
"Daniel Jackson"
May 2011
14285714285714285714
3·5·43 Posts 
What is a Mangammal prime?
I searched for the second prime in Kriesel's link on this post, and found this thread.
Exactly what is a Mangammal prime or, conversely, a nonMangammal prime? Any chance someone could give me a definition, or a link to one? All I know is that 97600541752017987211 is a nonMangammal prime, but I can't find proof of it. I googled "Mangammal prime" (without the quotes; quotes resulted in no results at all), but all the results were about Rani Mangammal. No matter how I word it, I can't find a definition anywhere. EDIT: I found this, but the URL it gives (http://planetmath.org/MangammalPrime) is broken, and the Wayback Machine only archived 404 errors: https://planetmath.org/ShanthaPrime Last fiddled with by Stargate38 on 20200106 at 17:45 Reason: typo 
20200106, 17:49  #3 
Einyen
Dec 2003
Denmark
3,037 Posts 
https://mersenneforum.org/showthread.php?t=6440
Mangammal primes: prime numbers which are impossible factors of 3^n2, i.e. they do not divide 3^n2 for any value of n. 
20200106, 18:12  #4 
"Daniel Jackson"
May 2011
14285714285714285714
3·5·43 Posts 
Thanks. I didn't know if the name was official or not. Maybe someone with editing privileges should add that to the OEIS entry, to prevent any more confusion.

20200106, 19:54  #5 
∂^{2}ω=0
Sep 2002
República de California
2·3^{3}·5·43 Posts 
I think it's a warmblooded vertebrate prime of a class that is distinguished by the possession of hair or fur, the secretion of milk by females for the nourishment of the young primelets, and (typically) the birth of live young.

20200106, 20:39  #6 
Feb 2017
Nowhere
43·101 Posts 
It may be related to the percussive musical primes from Indonesia.
I was unable to find any references outside this Forum directly indicating a definition of the term. I did find a couple of posts indicating it was a prime that did not divide 3^k  2 for any positive integer k. Such primes p > 3 are characterized by the property that the multiplicative order of 2 (mod p) does not divide the multiplicative order of 3 (mod p). A simple Pari script exhibiting the first few is as follows: Code:
? forprime(p=5,100,o2=znorder(Mod(2,p));o3=znorder(Mod(3,p));if(o3%o2<>0,print(p))) 11 13 37 41 59 61 67 73 83 Code:
? forprime(p=5,100,o2=znorder(Mod(2,p));o3=znorder(Mod(3,p));if(o3%o2==0,g=znprimroot(p);l2=znlog(2,g);l3=znlog(3,g);d=gcd(l3,p1);m=(p1)/d;e=lift(Mod(l2/l3,m));print(p" "e))) 5 3 7 2 17 14 19 7 23 7 29 17 31 24 43 27 47 17 53 49 71 11 79 4 89 16 97 43 
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