A069689 -id:A069689 - cp's OEIS frontend

A069687 Primes that yield another prime on placing a 1 on both sides (as leading and trailing digits).

3, 5, 17, 23, 29, 47, 53, 83, 107, 113, 131, 149, 173, 197, 239, 251, 317, 359, 383, 401, 443, 503, 509, 599, 641, 683, 701, 719, 743, 797, 821, 947, 953, 1031, 1049, 1103, 1109, 1187, 1229, 1277, 1283, 1301, 1373, 1583, 1613, 1619, 1637, 1733, 1847, 1889

Offset: 1

Amarnath Murthy, Apr 06 2002

			239 belongs to this sequence as 12391 is also a prime.
947 and 19471 are both primes ==> 947 is in the sequence. [From _José María Grau Ribas_, Jan 22 2012]

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A069688, A069689 & A069690.

a:= proc(n) option remember; local p;
      p:= `if`(n=1, 1, a(n-1));
      do p:= nextprime(p);
         if isprime(parse(cat(1, p, 1))) then break fi
      od; p
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, May 18 2012

Select[ Range[2000], PrimeQ[ # ] && PrimeQ[ FromDigits[ Insert[ IntegerDigits[ # ], 1, {{1}, {-1}}]]] &]
san[i_]:=1+Prime[i]*10+10^(Floor@Log[10,Prime[i]]+2); Prime@Select[Range[1000],PrimeQ@san[#]&]  (* From José María Grau Ribas, Jan 22 2012 *)
Select[Prime[Range[300]],PrimeQ[FromDigits[Join[{1},IntegerDigits[#],{1}]]]&]  (* Harvey P. Dale, May 18 2012 *)

forprime( p=1,9999, isprime(10^#Str(p*10)+p*10+1) & print1(p",")) \\ M. F. Hasler, May 18 2012

A069687_vec(Nmax=10^4)=my(p,d=1);vector(Nmax,i,until(isprime((d+p)*10+1), d<(p=nextprime(p+1))&d*=10);p)  \\ M. F. Hasler, May 19 2012

Edited and extended by Robert G. Wilson v, May 03 2002

Corrected and edited following suggestions by H. P. Dale and others by M. F. Hasler, May 18 2012

A069688 Primes that yield another prime on placing a 3 on both sides (as leading and trailing digits).

Original entry on oeis.org

5, 7, 31, 37, 41, 43, 53, 59, 61, 67, 73, 79, 83, 101, 103, 139, 151, 157, 179, 197, 223, 241, 257, 263, 269, 271, 283, 293, 307, 311, 349, 353, 389, 421, 431, 461, 467, 491, 557, 593, 599, 601, 607, 631, 643, 647, 683, 691, 701, 727, 757, 769, 811, 827, 839

Offset: 1

Amarnath Murthy, Apr 06 2002

			139 is a member as 31393 is also a prime.

Harvey P. Dale, Table of n, a(n) for n = 1..10000

Cf. A069687, A069689, A069690.

Select[ Range[1000], PrimeQ[ # ] && PrimeQ[ FromDigits[ Insert[ IntegerDigits[ # ], 3, {{1}, {-1}}]]] &]
Select[Prime[Range[200]],PrimeQ[FromDigits[Join[{3},IntegerDigits[#],{3}]]]&] (* Harvey P. Dale, Oct 24 2011 *)

Edited and extended by Robert G. Wilson v, May 03 2002

A069690 Primes that yield another prime on placing a 9 on both sides (as leading and trailing digits).

Original entry on oeis.org

2, 19, 23, 31, 41, 43, 47, 53, 61, 67, 71, 73, 83, 101, 107, 109, 113, 149, 163, 193, 211, 239, 241, 263, 269, 277, 313, 317, 331, 347, 373, 397, 409, 421, 439, 443, 499, 521, 523, 541, 547, 607, 617, 619, 641, 647, 673, 677, 757, 787, 829, 863, 877, 907, 911

Offset: 1

Amarnath Murthy, Apr 06 2002

			241 belongs to this sequence as 92419 is also a prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A069687, A069688, A069689.

filter:= proc(n) isprime(9+10*n+9*10^(2+ilog10(n))) end proc:
select(filter, [seq(ithprime(i),i=1..1000)]); # Robert Israel, Feb 02 2021

Select[ Range[2000], PrimeQ[ # ] && PrimeQ[ FromDigits[ Insert[ IntegerDigits[ # ], 9, {{1}, {-1}}]]] &]
Select[Prime[Range[200]],PrimeQ[FromDigits[Join[{9},IntegerDigits[#],{9}]]]&] (* Harvey P. Dale, Nov 07 2022 *)

from sympy import isprime, primerange
def ok(p): return isprime(int('9'+str(p)+'9'))
def aupto(lim): return [p for p in primerange(2, lim+1) if ok(p)]
print(aupto(911)) # Michael S. Branicky, Feb 19 2021

Edited and extended by Robert G. Wilson v, May 03 2002

A059694 Primes p such that 1p1, 3p3, 7p7 and 9p9 are all primes.

Original entry on oeis.org

53, 2477, 4547, 5009, 7499, 8831, 9839, 11027, 24821, 26393, 29921, 36833, 46073, 46769, 47711, 49307, 53069, 59621, 64283, 66041, 79901, 84017, 93263, 115679, 133103, 151121, 169523, 197651, 207017, 236807, 239231, 255191, 259949, 265271, 270071, 300431, 330047

Offset: 1

Patrick De Geest, Feb 07 2001

All terms == 1 (mod 6). The sequence is apparently infinite. There are 16486 terms up to 10^9. - Zak Seidov, Jan 17 2014

Intersection of A069687, A069688, A069689, and A069690. - Zak Seidov, Jan 17 2014

			53 is a term because 1531, 3533, 7537 and 9539 are primes.

Zak Seidov, Table of n, a(n) for n = 1..10000

Cf. A059677, A032682, A059693.

from sympy import isprime, nextprime
from itertools import islice
def agen(): # generator of terms
    p = 2
    while True:
        sp = str(p)
        if all(isprime(int(d+sp+d)) for d in "1379"):
            yield p
        p = nextprime(p)
print(list(islice(agen(), 40))) # Michael S. Branicky, Feb 23 2023

A341017 Primes p such that placing digit i at both ends of p produces another prime for at least two of i = [1,3,7, 9].

Original entry on oeis.org

2, 5, 17, 23, 29, 31, 41, 43, 47, 53, 61, 67, 71, 73, 83, 101, 107, 113, 131, 149, 197, 239, 241, 257, 263, 269, 293, 317, 347, 359, 389, 401, 421, 431, 443, 503, 521, 557, 593, 599, 607, 641, 647, 677, 683, 701, 757, 797, 827, 887, 911, 953, 1031, 1103, 1109, 1117, 1171, 1181, 1187, 1223, 1277

Offset: 1

J. M. Bergot and Robert Israel, Feb 02 2021

Numbers that are in at least two of A069687, A069688, A069689 and A069690.

			a(3) = 17 is a term because 17 is in A069687 and A069689, i.e. 1171 and 7177 are prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A069687, A069688, A069689, A069690.

filter:= proc(n) local i; isprime(n) and numboccur(true,[seq(isprime(i+10*n+i*10^(2+ilog10(n))),i=[1,3,7,9])]) >= 2 end proc:
select(filter, [2,seq(i,i=3..1000)]);

from sympy import isprime, nextprime
def ok(p): return sum(isprime(int(c+str(p)+c)) for c in "1379") >= 2
def aupto(limit): # only test primes
  alst, p = [], 2
  while p <= limit:
    if ok(p): alst.append(p)
    p = nextprime(p)
  return alst
print(aupto(1277)) #Michael S. Branicky, Feb 02 2021

A360781 Primes p such that at least one number remains prime when p is bracketed by a single digit d; that is, at least one instance of d//p//d is prime where // means concatenation.

Original entry on oeis.org

2, 3, 5, 7, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 101, 103, 107, 109, 113, 131, 139, 149, 151, 157, 163, 173, 179, 191, 193, 197, 211, 223, 227, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331

Offset: 1

Harvey P. Dale, Feb 20 2023

The bracketing digit d must be 1, 3, 7, or 9.

			263 is included because 263 is a prime and 32633 (and also 92639) is a prime.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A000040, A059694, A069687, A069688, A069689, A069690.

q:= p-> ormap(isprime, map(d-> parse(cat(d, p, d)), [1, 3, 7, 9])):
select(q, [ithprime(i)$i=1..67])[];  # Alois P. Heinz, Feb 22 2023

brkQ[p_]:=AnyTrue[Table[FromDigits[Join[{d},IntegerDigits[p],{d}]],{d,{1,3,7,9}}],PrimeQ]; Select[Prime[Range[100]],brkQ]

is(p) = my(d=digits(p)); forstep(k=1, 9, 2, if (isprime(fromdigits(concat(k, concat(d,k)))), return(1)));
isok(p) = if (isprime(p), is(p)); \\ Michel Marcus, Feb 20 2023

from sympy import isprime, nextprime
from itertools import islice
def agen(): # generator of terms
    p = 2
    while True:
        sp = str(p)
        if any(isprime(int(d+sp+d)) for d in "1379"):
            yield p
        p = nextprime(p)
print(list(islice(agen(), 57))) # Michael S. Branicky, Feb 20 2023

Union of A069687, A069688, A069689, A069690. - Alois P. Heinz, Feb 22 2023

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A069687 Primes that yield another prime on placing a 1 on both sides (as leading and trailing digits).

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A069688 Primes that yield another prime on placing a 3 on both sides (as leading and trailing digits).

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A069690 Primes that yield another prime on placing a 9 on both sides (as leading and trailing digits).

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A059694 Primes p such that 1p1, 3p3, 7p7 and 9p9 are all primes.

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A341017 Primes p such that placing digit i at both ends of p produces another prime for at least two of i = [1,3,7, 9].

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A360781 Primes p such that at least one number remains prime when p is bracketed by a single digit d; that is, at least one instance of d//p//d is prime where // means concatenation.

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