A089703 -id:A089703 - cp's OEIS frontend

A089702 a(1) = 2 then primes in nondecreasing order such that every concatenation is prime.

2, 3, 3, 3, 3, 23, 43, 59, 67, 83, 199, 239, 421, 569, 613, 1307, 2017, 2129, 2467, 2741, 2953, 3011, 3319, 3413, 3607, 3617, 5449, 6917, 7333, 7529, 8389, 10211, 10357, 12641, 12703, 15077, 17107, 21341, 21799, 22469, 32911, 33587, 33613, 33647

Offset: 0

Amarnath Murthy, Nov 10 2003

			2,23,233,2333,23333,2333323 etc. are primes.

Cf. A089703.

ds:=proc(s) local j: RETURN(add(s[j]*10^(j-1),j=1..nops(s))):end: a:=[2]: k:=1: for n from 1 to 50 do l:=nops(a): for i from k do p:=ithprime(i): if isprime(ds([op(convert(p,base,10)),seq(op(convert(a[l-j],base,10)),j=0..l-1)])) then a:=[op(a),p]: k:=i: break fi od od: op(a); # C. Ronaldo

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004

A158191 Attach the smallest prime to the end of the string a(n-1) so a(n) is also prime.

Original entry on oeis.org

2, 23, 233, 2333, 23333, 2333323, 23333237, 233332373, 23333237353, 2333323735319, 2333323735319149, 2333323735319149571, 23333237353191495713, 23333237353191495713131, 233332373531914957131313

Offset: 1

Sergio Pimentel, Mar 13 2009

a(279) has 1001 digits. - Michael S. Branicky, May 26 2023

			a(6) = 2333323 since a(5) = 23333 (prime) and 233333, 233335, 233337, 2333311, 2333313, 2333317 and 2333319 are all composite.

Michael S. Branicky, Table of n, a(n) for n = 1..278 (terms 1..200 from Harvey P. Dale)

Cf. A048549, A088603, A089703, A065712, A100893.

nxt[n_]:=Module[{k=3},While[CompositeQ[n*10^IntegerLength[k]+k],k = NextPrime[ k]];n*10^IntegerLength[k]+k]; NestList[nxt,2,20] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 13 2019 *)

from itertools import islice
from sympy import isprime, nextprime
def agen(): # generator of terms
    p, s = 2, "2"
    while True:
        yield p
        q = 2
        while not isprime(p:=int(s+str(q))):
            q = nextprime(q)
        s += str(q)
print(list(islice(agen(), 15))) # Michael S. Branicky, May 26 2023

More terms from Sean A. Irvine, Nov 29 2009

cp's OEIS Frontend

A089702 a(1) = 2 then primes in nondecreasing order such that every concatenation is prime.

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A158191 Attach the smallest prime to the end of the string a(n-1) so a(n) is also prime.

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