A177061
Primes p formed from single-digit primes only, each used at most once.
Original entry on oeis.org
2, 3, 5, 7, 23, 37, 53, 73, 257, 523, 2357, 2753, 3257, 3527, 5237, 5273, 7253, 7523
Offset: 1
Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), May 02 2010
3//7 = 37 = prime(12) is the 6th term.
2//3//5//7 = 2357 = prime(350) is the 11th term
p = 7//5//2//3 = 7523 = prime(953) = A033548(59) is the last term.
- E. I. Ignatjew, Mathematische Spielereien, Urania Verlag Leipzig/Jena/Berlin 1982
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Select[FromDigits/@Flatten[Permutations/@Subsets[{2,3,5,7}],1],PrimeQ]// Union (* Harvey P. Dale, Sep 08 2021 *)
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isok(p) = {my(d = digits(p)); if (#d == #Set(d) && vecmin(apply(isprime, d)) == 1, return (1)); return(0);}
lista() = {forprime(p=1, 100000, if (isok(p), print1(p, ", ")););} \\ Michel Marcus, Aug 07 2020
Edited by Assoc. Eds. OEIS, May 09 2010
A172315
Primes of the form 2^i*3^j - 1 with i + j = 13.
Original entry on oeis.org
8191, 27647, 62207, 139967, 314927, 472391, 1062881
Offset: 1
Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Jan 31 2010
8191 = 2^13 - 1 = prime(1028)
27647 = 2^10 x 3^3 - 1 = prime(3016) = prime(2^3 x 13 x 29)
62207 = 2^8 x 3^5 - 1 = prime(6253) = prime(13^ 2 x 37)
139967 = 2^6 x 3^7 - 1 = prime(13005)
314927 = 2^4 x 3^9 - 1 = prime(27191), index is prime(2978)
472391 = 2^3 x 3^10 - 1 = prime(39419), index is prime(4150)
1062881 = 2 x 3^12 - 1 = prime(83024)
- Helmut Kracke, Mathe-musische Knobelisken, Duemmler Bonn, 2. Auflage 1983
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Select[Union[Flatten[{2^#[[1]] 3^#[[2]]-1,2^#[[2]] 3^#[[1]]-1}&/@ Table[ {n,13-n},{n,0,13}]]],PrimeQ] (* Harvey P. Dale, Jan 11 2016 *)
A347612
Semiprimes formed from single-digits primes only, each used at most once.
Original entry on oeis.org
25, 35, 57, 235, 237, 253, 327, 527, 537, 573, 723, 753, 2537, 2573, 2735, 5327, 5723, 7235
Offset: 1
527 is a semiprime and its non-repeating digits are primes.
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Select[FromDigits/@Flatten[Permutations/@Subsets[ {2,3,5,7}],1],PrimeOmega[ #] == 2&]//Union
Showing 1-3 of 3 results.
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