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 A077390 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. 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS T. D. Noe, Table of n, a(n) for n = 1..12975 C. Rivera, Problem 950: Bi-truncatable primes, The Prime Puzzles & Problems Connection. EXAMPLE 21313 is a member as 21313, 131 and 3 all are primes. MATHEMATICA 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 *) CROSSREFS cf. A024770 (right-truncatable primes), A024785 (left-truncatable primes), A137812 (left-or-right truncatable primes). Sequence in context: A030475 A069676 A062353 * A069677 A069678 A069679 Adjacent sequences:  A077387 A077388 A077389 * A077391 A077392 A077393 KEYWORD base,fini,nonn AUTHOR Amarnath Murthy, Nov 07 2002 EXTENSIONS Corrected and extended by T. D. Noe, Apr 19 2011 Crossref text fixed by Karl W. Heuer, Jan 31 2013 STATUS approved

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Last modified May 26 13:49 EDT 2020. Contains 334626 sequences. (Running on oeis4.)