PARI's commands

[3.14159]

Nevermind. I answered my own question. Okay: I can mess with the params as I wish? Cool.

Wait: Does it use the F/trial division switch?

[3.14159]

Also: Found 268 * 4200! + 1 (13399 digits). A prime with a prime number of digits. Excellent.

[science_man_88]

plength(n) = forstep(x=(10^n)+1,10^(n+1),[2],if(isprime(x),return(x)))

for some reason this isn't working properly. I can get it to work as planned but then it might mess up someone else if they use it.

[science_man_88]

realized why now doh.

[CRGreathouse]

sm: It looks good to me. This is A003617(n+1), right?

Faster would be

plength(n)=nextprime(10^n)

[science_man_88]

Originally Posted by CRGreathouse

sm: It looks good to me.

well it isn't! and I know why.

(15:42) gp > plength(n) = forstep(x=(10^n)+1,10^(n+1),[2],if(isprime(x),return(x)))
%471 = (n)->forstep(x=(10^n)+1,10^(n+1),[2],if(isprime(x),return(x)))
(15:43) gp > plength(3)
%472 = 1009
(15:43) gp >

is the original result

(15:45) gp > plength(n) = forstep(x=(10^(n-1))+1,10^(n),[2],if(isprime(x),return(x)))
%473 = (n)->forstep(x=(10^(n-1))+1,10^(n),[2],if(isprime(x),return(x)))
(15:45) gp > plength(3)
%474 = 101
(15:45) gp >

see the difference the reason the original was working weird is I didn't account for 1-9 so when i put in plength(3) the first on started at 10^3 which already has 4 digits when I compensate I get the correct value.

[science_man_88]

I also did this with your knowledge:

sumdigits(n) = if(n%9!=0,return(n%9),return(n%9+9))

but you might think it's kinda lame.

[science_man_88]

0 1 2 3 4 5 6 7 8 9
1 1 2 3 4 5 6 7 8 9
2 2 4 6 8 1 3 5 7 9
3 3 6 9 3 6 9 3 6 9
4 4 8 3 7 2 6 1 5 9
5 5 1 6 2 7 3 8 4 9
6 6 3 9 6 3 9 6 3 9
7 7 5 3 1 8 6 4 2 9
8 8 7 6 5 4 3 2 1 9
9 9 9 9 9 9 9 9 9 9

if i did my math correct this is the sum of digits multiplication table.

[CRGreathouse]

Originally Posted by science_man_88

I also did this with your knowledge:

sumdigits(n) = if(n%9!=0,return(n%9),return(n%9+9))

but you might think it's kinda lame.

This only works for n < 100. For larger numbers, try

dsum(n,b=10)={
  my(s=0);
  while(n>=b,
    s += n%b;
    n \= b;
  );
  s+n
};
addhelp(dsum, "dsum(n,{b=10}): Sum of the base-b digits of n.");

A more efficient version would work mod 100 or 1000 using a lookup table, and use divrem rather than \ and %. A really efficient version would split the values into two parts of roughly equal length until they became 'small' (say, less than a googol).

[CRGreathouse]

Originally Posted by science_man_88

see the difference the reason the original was working weird is I didn't account for 1-9 so when i put in plength(3) the first on started at 10^3 which already has 4 digits when I compensate I get the correct value.

Because you didn't explain what the function was supposed to do, you didn't have a help message, and the name wasn't self-explanatory, I couldn't tell that this was an error rather than the intended behavior.

[CRGreathouse]

Originally Posted by 3.14159

Also: Found 268 * 4200! + 1 (13399 digits). A prime with a prime number of digits. Excellent.

Primes with a prime number of digits... hmm. I wonder in what sense this has positive density. Of course it has natural density 0, as a subset of the primes; I don't know what its upper logarithmic density would be. If that's not positive, is there a finer measure? I wonder.

The set is 'weird' because it has huge gaps, then lots of relatively densely packed elements: no members (strictly) between 10^114 - 153 and 10^126 + 679, a gap of length ~10^126, but then > 3.44218 * 10^123 members in the next 10^126.