This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Select[FromDigits/@Permutations[{2,3,5,7}],PrimeQ] (* Harvey P. Dale, Jul 04 2013 *)
a(1)=1: 2; a(2)=1: 23; a(3)=1, 523;
a(4)=8: {2357,2753,3257,3527,5237,5273,7253,7523};
a(5)=20: {112573, 115237,...,735211, 751123}, see A177275;
a(6)=112: {11132357,11132753,...,75231113,75311213}, see links;
a(7)=608: {1113257317,1113321757,...,7523131711,7523171311}, see links;
a(8)= 4436: {111317193257,111317193527,...,753191321117,753217131911}, see links;
a(9)= 34843: {11131719223357,11131719235237,...,75323217191113,75323219131117}
a(10)=0 because sum of digits of first 10 primes (2+3+5+7+(1+1)+(1+3)+(1+7)+(1+9)+(2+3)+(2+9))=57 is multiple of 3.
The only prime concatenations of the first n primes for n = 1..3 are a(1)=2, a(2)=23, and a(3)=523. For n=4, the only prime concatenations of 2, 3, 5, and 7 are 2357, 2753, 3257, 3527, 5237, 5273, 7253, 7523; the largest of these is a(4) = 7523.
from sympy import sieve, isprime
from itertools import permutations
for n in range(1, 14):
sieve.extend_to_no(n)
p = list(map(str, list(sieve._list)))[:n]
mint = 0
for i in permutations(p, len(p)):
t = int(''.join(i))
if t > mint and isprime(t):
mint = t
print(mint, end = ', ') # Gleb Ivanov, Dec 05 2021
The only prime concatenations of the first n primes for n = 1..3 are a(1)=2, a(2)=23, and a(3)=523. For n=4, the only prime concatenations of 2, 3, 5, and 7 are 2357, 2753, 3257, 3527, 5237, 5273, 7253, 7523; the smallest of these is a(4) = 2357.
from sympy import sieve, isprime
from itertools import permutations
for n in range(1, 20):
sieve.extend_to_no(n)
p = list(map(str, list(sieve._list)))[:n]
mint = 10**1000
for i in permutations(p, len(p)):
t = int(''.join(i))
if t < mint and isprime(t):
mint = t
if mint == 10**1000:
print(0, end = ', ')
else:
print(mint, end = ', ') # Gleb Ivanov, Dec 04 2021
Comments