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Old 2020-01-06, 17:10   #1
Stargate38
 
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Question 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 non-Mangammal prime? Any chance someone could give me a definition, or a link to one? All I know is that 97600541752017987211 is a non-Mangammal 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 2020-01-06 at 17:45 Reason: typo
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Old 2020-01-06, 17:45   #2
Fan Ming
 
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Maybe this.
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Old 2020-01-06, 17:49   #3
ATH
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https://mersenneforum.org/showthread.php?t=6440

Mangammal primes: prime numbers which are impossible factors of 3^n-2, i.e. they do not divide 3^n-2 for any value of n.
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Old 2020-01-06, 18:12   #4
Stargate38
 
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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.
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Old 2020-01-06, 19:54   #5
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I think it's a warm-blooded 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.
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Old 2020-01-06, 20:39   #6
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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
A simple Pari script showing the smallest exponent e for which p divides 3^e - 2, for the first few primes p > 3 for which the multiplicative order of 2 (mod p) does divide the multiplicative order of 3 (mod p) is as follows:

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,p-1);m=(p-1)/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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