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A077390
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Primes which leave primes at every step if most significant digit and least significant digit are deleted until a one digit or two digit prime is obtained.
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7
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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 127, 131, 137, 139, 151, 157, 173, 179, 223, 227, 229, 233, 239, 251, 257, 271, 277, 331, 337, 353, 359, 373, 379, 421, 431, 433, 439, 457, 479, 521, 523, 557, 571, 577, 631, 653, 659
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OFFSET
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1,1
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COMMENTS
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There are exactly 920720315 such primes, the largest being 9161759674286961988443272139114537477768682563429152377117139 1111313737919133977331737137933773713713973. - Karl W. Heuer, Apr 19 2011
There are exactly 331780864 odd length primes and 588939451 even length primes, the largest odd length prime being
7228828176786792552781668926755667258635743361825711373791931117197999133917737137399993737111177. - Seth A. Troisi, May 07 2019
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LINKS
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EXAMPLE
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21313 is a member as 21313, 131 and 3 all are primes.
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MATHEMATICA
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msd={1, 2, 3, 4, 5, 6, 7, 8, 9}; lsd={1, 3, 7, 9}; Clear[p]; p[1]={2, 3, 5, 7}; p[2]={11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}; p[digits_] := p[digits] = Select[Flatten[Outer[Plus, 10^(digits-1)*msd, 10*p[digits-2], lsd]], PrimeQ]; t={}; k=0; While[Length[t] < 100, k++; t=Join[t, p[k]]]; t (* T. D. Noe, Apr 19 2011 *)
paesQ[n_]:=AllTrue[NestWhileList[FromDigits[Most[Rest[ IntegerDigits[ #]]]]&, n, #>99&], PrimeQ]; Select[Prime[Range[150]], paesQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 01 2015 *)
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PROG
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(Python)
from itertools import count, islice
from sympy import isprime, primerange
def agen(): # generator of terms
odds, evens, digits = [2, 3, 5, 7], list(primerange(10, 100)), 3
yield from odds + evens
while len(odds) > 0 or len(evens) > 0:
new = []
old = odds if digits%2 == 1 else evens
for first in "123456789":
for p in old:
mid = str(p)
for last in "1379":
t = int(first + mid + last)
if isprime(t):
yield t
new.append(t)
old = new
if digits%2: odds = old
else: evens = old
print("...", digits, time()-time0)
digits += 1
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CROSSREFS
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cf. A024770 (right-truncatable primes), A024785 (left-truncatable primes), A137812 (left-or-right truncatable primes).
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KEYWORD
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base,fini,nonn
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AUTHOR
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EXTENSIONS
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Corrected and extended by T. D. Noe, Apr 19 2011
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STATUS
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approved
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