Find number property and write RPL program (HP-49G,G+, HP 50g)

[Thomas Ritschel]

(10-12-2014 12:50 PM)Gerson W. Barbosa Wrote:  Nice find! Twin primes are more rare than Sophie Germain primes. The one you've found belongs to both sets!

Well, actually they should be of similar "rarity", with the twin primes slightly less rare than the Sophie Germains (e.g. from the prime number theorem it should follow a slightly higher chance for p+2 being prime than for 2p+1). Also compare the numbers given at the Top5000 primes pages:

http://primes.utm.edu/top20/page.php?id=1
http://primes.utm.edu/top20/page.php?id=2

But a number belonging to both sets is indeed even more rare!

So, what comes next? A Cunningham chain of 2nd kind, e.g. p and 2p-1 both prime, or, perhaps, a chain with more than two members? Let's check our wallets again...

BTW.: That's a nice article on Brun's constant and it's computation!