OFFSET
1,1
COMMENTS
Leading zeros of the prime within the concatenation are not admitted. Example: 449^2=201601 is a square of a prime which is 2 concatenated with a zero-padded prime 1601. 449 is not in the sequence. - R. J. Mathar, Apr 06 2009
REFERENCES
Wladyslaw Narkiewicz, The development of prime number theory. From Euclid to Hardy and Littlewood. Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2000.
I. Niven, H. S. Zuckerman and H. L. Montgomery, An Introduction to the Theory of Numbers (5th ed.). Wiley Text Books, 1991.
Paulo Ribenboim, The New Book of Prime Number Records. Springer, 1996.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
i) The prime 47 has the square 47^2=2209, but 209=11*19 is not prime, so 47 is not in the sequence.
ii) If we attach 2 to the prime p=401 we get 2401=49^2, but 49=7^2 is not a prime, so there is no contribution to the sequence.
iii) The square of the prime 53 is 2809, i.e., 2 followed by the prime 809, so 53 is in the sequence.
MAPLE
count:= 0: N:= 100: Res:= NULL:
for d from 1 while count < N do
p:= floor(sqrt(2*10^d+10^(d-1)));
while count < N do
p:= nextprime(p);
if p^2 >= 3*10^d then break fi;
q:= p^2 - 2*10^d;
if isprime(q) then
count:= count+1;
Res:= Res, p;
fi
od od:
Res; # Robert Israel, Mar 06 2018
MATHEMATICA
okQ[n_]:=Module[{idn=IntegerDigits[n^2]}, First[idn]==2&& idn[[2]]!=0 && PrimeQ[FromDigits[Rest[idn]]]]; Select[Prime[Range[750]], okQ] (* Harvey P. Dale, Jul 22 2011 *)
PROG
(Python)
from sympy import isprime, primerange
def ok(p):
s = str(p*p); return s[0] == '2' and s[1] != '0' and isprime(int(s[1:]))
print(list(filter(ok, primerange(2, 5298)))) # Michael S. Branicky, May 17 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 29 2009
EXTENSIONS
1451 inserted, and sequence extended beyond 4673, by R. J. Mathar, Apr 01 2009
Edited by R. J. Mathar, Apr 06 2009
STATUS
approved