A024785 Left-truncatable primes: every suffix is prime and no digits are zero.
2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 113, 137, 167, 173, 197, 223, 283, 313, 317, 337, 347, 353, 367, 373, 383, 397, 443, 467, 523, 547, 613, 617, 643, 647, 653, 673, 683, 743, 773, 797, 823, 853, 883, 937, 947, 953, 967, 983, 997, 1223
Offset: 1
References
- James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 113.
Links
- N. J. A. Sloane, Table of n, a(n) for n = 1..4260 (The full list, based on the De Geest web site)
- I. O. Angell and H. J. Godwin, On Truncatable Primes, Math. Comput. 31, 265-267, 1977.
- Patrick De Geest, The list of 4260 left-truncatable primes
- James Grime and Brady Haran, 357686312646216567629137, Numberphile video (2018).
- Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
- Rosetta Code, Programs for finding truncatable primes
- Eric Weisstein's World of Mathematics, Truncatable Prime
- Chai Wah Wu, On a conjecture regarding primality of numbers constructed from prepending and appending identical digits, arXiv:1503.08883 [math.NT], 2015.
- Index entries for sequences related to truncatable primes
Crossrefs
Programs
-
Haskell
import Data.List (tails) a024785 n = a024785_list !! (n-1) a024785_list = filter (\x -> all (== 1) $ map (a010051 . read) $ init $ tails $ show x) a038618_list -- Reinhard Zumkeller, Nov 01 2011
-
Maple
a:=[[2],[3],[5],[7]]: l1:=1: l2:=4: for n from 1 to 3 do for k from 1 to 9 do for j from l1 to l2 do d:=[op(a[j]),k]: if(isprime(op(convert(d,base,10,10^nops(d)))))then a:=[op(a), d]: fi: od: od: l1:=l2+1: l2:=nops(a): if(l1>l2)then break: fi: od: seq(op(convert(a[j],base,10,10^nops(a[j]))),j=1..nops(a)); # Nathaniel Johnston, Jun 21 2011 # second Maple program: T:= proc(n) option remember; `if`(n=0, "", sort(select(isprime, map(x-> seq(parse(cat(j, x)), j=1..9), [T(n-1)])))[]) end: seq(T(n), n=1..4); # Alois P. Heinz, Sep 01 2021
-
Mathematica
max = 2000; truncate[p_] := If[id = IntegerDigits[p]; FreeQ[id, 0] && (Last[id] == 3 || Last[id] == 7) && PrimeQ[q = FromDigits[ Rest[id]]], q, p]; ok[n_] := FixedPoint[ truncate, n] < 10;p = 5; A024785 = {2, 3, 5}; While[(p = NextPrime[p]) < max, If[ok[p], AppendTo[A024785, p]]]; A024785 (* Jean-François Alcover, Nov 09 2011 *) d[n_]:=IntegerDigits[n]; ltrQ[n_]:=And@@PrimeQ[NestList[FromDigits[Drop[d[#],1]]&,n,Length[d[n]]-1]]; Select[Range[1225],ltrQ[#]&] (* Jayanta Basu, May 29 2013 *) FullList=Sort[Flatten[Table[FixedPointList[Select[Flatten[Table[Range[9]*10^Length@IntegerDigits[#[[1]]] + #[[i]], {i, Length[#]}]], PrimeQ] &, {i}], {i, {2, 3, 5, 7}}]]] (* Fabrice Laussy, Nov 10 2019 *)
-
PARI
v=vector(4260);v[1]=2;v[2]=3;v[3]=5;v[4]=7;i=0;j=4; until(i>=j,i++;p=v[i];P10=10^(1+log(p)\log(10)); for(k=1,9,z=k*P10+p;if(isprime(z),j++;v[j]=z;))); s=vector(4260);s=vecsort(v);for(i=1,j,write("b024785.txt",i," ",s[i]);); \\ -
PARI
is_A024785(n,t=1)={until(t>10*p,isprime(p=n%t*=10)||return);n==p} \\ M. F. Hasler, Apr 17 2014
-
PARI
A024785=vector(25,n,p=vecsort(concat(apply(p->select(isprime, vector(9,i, i*10^(n-1)+p)),if(n>1,p))))); \\ Yields the list of rows (n-digit terms, n = 1..25). Use concat(%) to flatten. There are faster variants using matrices (vectorv(9,i,1)*p+[1..9]~*10^(n-1)*vector(#p,i,1)) and/or predefined vectors, but they are less concise and this takes less than 0.1 sec. - M. F. Hasler, Nov 07 2018
-
Python
from sympy import isprime def alst(): primes, alst = [2, 3, 5, 7], [] while len(primes) > 0: alst += sorted(primes) candidates = set(int(d+str(p)) for p in primes for d in "123456789") primes = [c for c in candidates if isprime(c)] return alst print(alst()) # Michael S. Branicky, Apr 11 2021
Comments