20101213, 03:52  #122 
May 2004
New York City
2×2,099 Posts 
While this is current, any other mathematicians here want
to comment on whether this sequence is provably infinite? Perhaps by a density heuristic argument? 
20101213, 04:45  #123 
Aug 2006
5938_{10} Posts 
It's heuristically infinite with the nth term about 2.3n * 10^n. I doubt it can be proven infinite with present technology, but a conditional proof on the ktuple conjecture seems plausible (though it would give bounds wildly out of proportion with the true size of the terms).

20101213, 13:15  #124  
"Forget I exist"
Jul 2009
Dumbassville
8369_{10} Posts 
Quote:
Code:
a=0;for(n=1,100,a=a+prime(n)^prime(n);print(a%(10^n))) 

20101213, 13:50  #125 
May 2004
New York City
2·2,099 Posts 
The next step would be to filter out to only values = 0.
But I think you need a double loop. 
20101213, 14:51  #126 
"Forget I exist"
Jul 2009
Dumbassville
8,369 Posts 

20101213, 16:09  #127  
Jun 2003
17·281 Posts 
Quote:
11, 751, 1129, 361649, 361649, 12462809, 12462809. 

20101213, 16:41  #128 
"Forget I exist"
Jul 2009
Dumbassville
8,369 Posts 
with an outer loop I got 11 661 for the start.

20101213, 23:57  #129 
Aug 2006
1011100110010_{2} Posts 

20101214, 00:56  #130  
"Forget I exist"
Jul 2009
Dumbassville
8,369 Posts 
Quote:
1) isn't always faster 2) results of our codes don't line up so why improve performance of something that gives wrong supposedly inaccurate results 3) I'm already in a bad mood as my sister just called to ask for any mail for here then told me to goto the end of our driveway to check any newer mail and it's almost 9 at night then got mad when i said do I have to, because they technically shouldn't be sending anything here for her or the thing they have planned for my mom.so I'm kinda not in the caring mood. 

20101214, 04:37  #131  
Aug 2006
13462_{8} Posts 
Quote:
It's pretty much faster in all cases. prime() is very inefficient, it typically just goes through the primes until it hits the right one. for(n=1,10,prime(n)) goes through numbers in this order: 2, 2, 3, 2, 3, 5, 2, 3, 5, 7, 2, 3, 5, 7, 11, 2, 3, 5, 7, 11, 13, 2, 3, 5, 7, 11, 13, 17, 2, 3, 5, 7, 11, 13, 17, 19, 2, 3, 5, 7, 11, 13, 17, 19, 23, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 for a total of 10(10+1)/2 = 55 numbers. forprime(p=2,29,p) goes straight through: 2, 3, 5, 7, 11, 13, 17, 19, 23. forprime(p=2, prime(10), p) goes through the primes once to discover the tenth prime, then again for the actual loop. Quote:
Code:
forprime(p=2,prime(floor(N)), f(p)) Code:
for(n=1,N, f(prime(n)))


20101214, 09:18  #132 
"Nathan"
Jul 2008
Maryland, USA
3×7×53 Posts 
p^2 or p^p?
Isn't this the sum of P^2 for p prime, NOT p^p? This thread has me confused...

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