This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
N:= 20: # to get all terms of up to N digits A:= select(isprime,[seq(seq((10^n-1)/9 - 10^j,j=n-2..1,-1),n=3..N)]); # Robert Israel, Jun 23 2015
f[n_] := Block[{lst = {}, r = (10^(n - 1) - 1)/9}, AppendTo[ lst, Select[ FromDigits[ Permutations[ Append[ IntegerDigits@ r, 0]]], PrimeQ@# && # > 100 &]]; Union@ Flatten@ lst]; Array[f, 18] // Flatten (* Robert G. Wilson v, Jun 22 2015 *)
[p: p in PrimesUpTo(3*10^7) | &*Intseq(p) eq 8]; // Vincenzo Librandi, Jul 27 2016
Union[ Flatten[ Table[ Select[ Sort[ FromDigits /@ Join[ Permutations[ Flatten[{8, Table[1, {n}]}]], Permutations[ Flatten[{2, 4, Table[1, {n - 1}]}]], Permutations[ Flatten[{2, 2, 2, Table[1, {n - 2}]}] ]]], PrimeQ[ # ] & ], {n, 0, 7}]]]
Select[Prime[Range[3 10^6]], Times@@IntegerDigits[#] == 8 &] (* Vincenzo Librandi, Jul 27 2016 *)
[p: p in PrimesUpTo(1000000) | &*Intseq(p) eq 12]; // Vincenzo Librandi, Jul 27 2016
Union[ Flatten[ Table[ Select[ Sort[ FromDigits /@ Join[ Permutations[ Flatten[{2, 6, Table[1, {n - 1}]}]], Permutations[ Flatten[{3, 4, Table[1, {n - 1}]}]], Permutations[ Flatten[{2, 2, 3, Table[1, {n - 2}]}] ]]], PrimeQ[ # ] & ], {n, 0, 5}]]]
Select[Prime[Range[75000]], Times@@IntegerDigits[#] == 12 &] (* Vincenzo Librandi, Jul 27 2016 *)
Array starts
2, 3, 5, 7, 11, 19, 23, ...
13, 17, 31, 37, 71, 73, 79, ...
113, 131, 197, 199, 311, 337, 373, ...
1193, 1931, 3119, 3779, 7793, 7937, 9311, ...
11939, 19391, 19937, 37199, 39119, 71993, 91193, ...
193939, 199933, 319993, 331999, 391939, 393919, 919393, ...
17773937, 39371777, 71777393, 73937177, 77393717, 77739371, 93717773, ...
119139133, 133119139, 139133119, 191391331, 311913913, 331191391, 913311913, ...
...
eva(n) = subst(Pol(n), x, 10)
rot(n) = if(#Str(n)==1, v=vector(1), v=vector(#n-1)); for(i=2, #n, v[i-1]=n[i]); u=vector(#n); for(i=1, #n, u[i]=n[i]); v=concat(v, u[1]); v
count_primes(n) = my(d=digits(n), i=0); while(1, if(ispseudoprime(eva(d)), i++); d=rot(d); if(d==digits(n), return(i)))
row(n, terms) = my(i=0); forprime(p=1, , if(count_primes(p)==n, print1(p, ", "); i++); if(i==terms, print(""); break))
array(rows, cols) = for(x=1, rows, row(x, cols))
array(7, 7) \\ print initial 7 rows and 7 columns of array
Select[Range[1000], PrimeQ[#] && Length[Union[RealDigits[#][[1]]]] <= 2 &] Select[Prime[Range[200]],Count[DigitCount[#],0]>7&] (* Harvey P. Dale, Jul 14 2017 *)
1379 is in the sequence since 379, 179, 139 & 137 are all primes. - _Robert G. Wilson v_, Oct 07 2014
fQ[n_] := Union[ PrimeQ[ Table[ Quotient[n, 10^k]*10^(k - 1) + Mod[n, 10^(k - 1)], {k, 1 + Floor@ Log10@ n}] ]] == {True}; Select[ Range@ 1675, fQ] (* Robert G. Wilson v, Oct 07 2014 *)
ddpnQ[n_]:=With[{id=IntegerDigits[n]},AllTrue[Table[FromDigits[Drop[id,{i}]],{i,Length[id]}],PrimeQ]]; Select[Range[2000],ddpnQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 12 2017 *)
isok(n) = {d = digits(n); for (i=1, #d, nd = []; for (k=1, #d, if (k != i, nd = concat(nd, d[k]));); if (! isprime(subst(Pol(nd), x, 10)), return (0));); return (1);} \\ Michel Marcus, Jul 17 2014
DroppingAnyDigitGivesAPrime(N,b) = {
\\ Property-testing function; returns 1 if true for N, 0 otherwise
\\ Works with any base b. Here usable with b=10.
my(k=b,m); if(N=(k\b), m=(N\k)*(k\b)+(N%(k\b));
if ((m<2)||(!isprime(m)),return(0)); k*=b);
return(1);
} \\ Stanislav Sykora, Jan 14 2016
from sympy import isprime def is_A034895(n): s = str(n) return n>9 and all(isprime(int(s[:i]+s[i+1:])) for i in range(len(s))) # David Radcliffe, Dec 11 2017
import Data.List (permutations, (\\))
a258706 n = a258706_list !! (n-1)
a258706_list = f a000040_list where
f ps'@(p:ps) | any (== 0) (map a010051' dps) = f ps
| otherwise = p : f (ps' \\ dps)
where dps = map read $ permutations $ show p
-- Reinhard Zumkeller, Jun 10 2015
Flatten@{2, 3, 5, 7,
Table[Select[
Table @@
Prepend[Prepend[
Table[{A@k, A[k - 1], 4}, {k, 2, n}], {A[1], 4}],
Unevaluated[
Unevaluated[FromDigits[{1, 3, 7, 9}[[A /@ Range[n]]]]]]] //
Flatten,
Function[L,
And[PrimeQ[#],
And @@ PrimeQ[
FromDigits /@ (Permute[L, #] & /@
RandomPermutation[Length@L, 5])],
And @@ PrimeQ[FromDigits /@ Rest[Permutations[L]]]]]@
IntegerDigits@# &], {n, 2, 33}]}
(* Exhaustively searches thru 33 digits in ~7.5 sec, and up to 69 digits in 5 min, but cannot reach 317 digits. Not helpful in the light of Schroeppel's theorem that it's all repunits past 991. - Bill Gosper, Jan 06 2017 *)
{A=[2,5]; for(n=1, 317, my(D=[1,3,7,9], r=10^n\9); for(a=1,4, for(b=a^(n<3),4, for(j=0, if(b!=a,n-1), ispseudoprime(D[a]*r+(D[b]-D[a])*10^j)||next(2)); A=setunion(A, [r*D[a]+(D[b]-D[a])*10^if(b=n[1] && #select(d->d,n[^1]-n[^-1])<2 && !for(i=1,(#n)^(n[#n]>1), isprime(fromdigits(n=concat(n[^1],n[1])))||return)} \\ By Johnson's theorem and minimality required here, the number must be of the form ab...b or a...ab (=> first difference of digits has at most 1 nonzero component) and then is sufficient to consider rotations of the digits.
\\ M. F. Hasler, Jun 26 2018
t = {}; Do[p=Prime[n]; If[Length[Select[Table[FromDigits[k], {k,Permutations[IntegerDigits[p]]}], PrimeQ]] == 1, AppendTo[t,p]], {n,330}]; t (* Jayanta Basu, May 07 2013 *)
Select[Prime[Range[400]],AllTrue[FromDigits/@Rest[ Permutations[ IntegerDigits[#]]], CompositeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 22 2015 *)
is(n,d=digits(n))={isprime(n)&&!for(i=1,(#d)!, (n=vecextract(d,numtoperm(#d,i)))!=d&& isprime(fromdigits(n))&& return)} \\ Then: select(is,primes(500)) - M. F. Hasler, Jun 28 2018
is(n)={isprime(n)||return; my(d=vecsort(digits(n), (a, b)->if(a-b&& t=bittest(650, a)-bittest(650, b),t,a-b)), p=vector(#d,i,i), N(p,i=2)= while((t=p[i]-1)&& while((setsearch(Set(p[i+1..#p]),t)|| d[t]==d[p[i]])&& t--,); !t, i++>#p&& return); i<#p|| bittest(650, d[t])|| return; concat([setminus(Set(p[1..i]),[t]), t, p[i+1..#p]]), t); #d==1|| !until(!p=N(p),(n!=t=fromdigits(vecextract(d,p)))&& isprime(t)&& return)} \\ Produces only inequivalent permutations which can be prime. - M. F. Hasler, Jun 28 2018
A039986_row(n)={if(n>1, local(D=eval(Vec("0245681379")), u=vectorv(n, i, 10^(n-i)), nextperm()=for(i=2,n,(t=p[i]-1)&& while(setsearch(Set(p[i+1..n]),t)|| d[t]==d[p[i]], t--||break); t|| next; iM. F. Hasler, Jul 01 2018
from itertools import count, islice, combinations_with_replacement from sympy.utilities.iterables import multiset_permutations from sympy import isprime def A039986_gen(): # generator of terms for l in count(1): xlist = [] for p in combinations_with_replacement('0123456789',l): flag = False for q in multiset_permutations(p): if isprime(m:=int(''.join(q))): if flag or q[0]=='0': flag = False break else: flag = True r = m if flag: xlist.append(r) yield from sorted(xlist) A039986_list = list(islice(A039986_gen(),30)) # Chai Wah Wu, Dec 26 2023
[p: p in PrimesUpTo(40000) | Set(Intseq(p)) subset [3, 5, 1]];
Select[Prime[Range[3 10^3]], Complement[IntegerDigits[#], {3, 5, 1}]=={} &]
Select[Flatten[Table[FromDigits/@Tuples[{1,3,5},n],{n,5}]],PrimeQ] (* Harvey P. Dale, Mar 03 2020 *)
from gmpy2 import is_prime, mpz from itertools import product A260224_list = [int(''.join(x)) for n in range(1,10) for x in product('135',repeat=n) if is_prime(mpz(''.join(x)))] # Chai Wah Wu, Jul 21 2015
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