A379150 Smallest prime ending in "3", with n preceding "0" digits.

103, 2003, 70003, 100003, 1000003, 20000003, 500000003, 40000000003, 40000000003, 100000000003, 2000000000003, 230000000000003, 3100000000000003, 11000000000000003, 20000000000000003, 100000000000000003, 1000000000000000003, 310000000000000000003, 500000000000000000003

Offset: 1

Author

James S. DeArmon, Dec 16 2024

Keywords

• nonn
• base

Comments

Leading zeros are not allowed, e.g., "03".

a(997) has 1001 digits. - Michael S. Branicky, Dec 16 2024

Examples

			a(1) = 103, is the smallest prime ending in "03";
a(2) = 2003, is the smallest prime ending in "003".
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..996

Crossrefs

Cf. A070854, A070847.

Programs

Mathematica

Table[i=1;While[!PrimeQ[m=FromDigits[Join[IntegerDigits[i],Table[0,n],{3}]]],i++];m,{n,19}] (* James C. McMahon, Dec 23 2024 *)

PARI

a(n)=for(i=1, oo, if(isprime(i*10^(n+1)+3), return(i*10^(n+1)+3))) \\ Johann Peters, Dec 27 2024

Python

import sympy
def prime3_finder():
  outVec = []
  power = 2
  for n in range(100,999999999):
      if not n & 3 == 3: continue # speed-up over simple MOD operation
      if not n % 10**power == 3: continue
      if not sympy.isprime(n): continue
      outVec.append(n)
      power += 1
  return outVec
outvec = prime3_finder()
print(outvec)

Python

from sympy import isprime
from itertools import count
def a(n): return next(i for i in count(10**(n+1)+3, 10**(n+1)) if isprime(i))
print([a(n) for n in range(1, 20)]) # Michael S. Branicky, Dec 16 2024

Extensions

More terms from Michael S. Branicky, Dec 16 2024