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

1,1

Comments

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

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

Links

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

Example

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A070854, A070847.

Sequence in context: A113629 A034180 A076460 * A346499 A245495 A097726

Adjacent sequences: A379147 A379148 A379149 * A379151 A379152 A379153

Keyword

nonn,base

Author

James S. DeArmon, Dec 16 2024

Extensions

More terms from Michael S. Branicky, Dec 16 2024

Status

approved