OFFSET
1,1
COMMENTS
This sequence is the subset of primes in A189409.
The sequence A189409 is an extension of Euclid's second theorem about generating infinitely many prime numbers.
The motivation for this sequence is Euclid's second theorem or infinitude of primes theorem. Per this theorem, N = (2*3*5..p) + 1 generates the i-th Euclid number. p = p_i is the i-th prime. This Euclid number is either a prime or product of primes with one of the prime factors greater than p_i.
This is generated as a product of the squares of the first N prime numbers and adding 1 to it. M = ((2*2)*(3*3)*(5*5)*...*(p*p)) + 1. a(8) is a possible prime of 1328 digits.
The next term is about 2.519... * 10^1327. - Amiram Eldar, Nov 23 2018
FORMULA
EXAMPLE
PROG
(Python)
from functools import reduce
import numpy as np
def factors(n):
return reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))
mul=1
for i in range(1, 20):
if len(factors(i))<3:
mul*= i*i
if len(factors(mul+1))< 3:
print(mul+1)
CROSSREFS
KEYWORD
nonn
AUTHOR
Abhiram R Devesh, Jan 23 2013
STATUS
approved