A079652 -id:A079652 - cp's OEIS frontend

A217039 Primes having only {4, 5, 7} as digits.

5, 7, 47, 457, 547, 557, 577, 757, 4447, 4457, 4547, 5477, 5557, 7457, 7477, 7547, 7577, 7757, 44777, 45557, 45757, 47777, 54547, 54577, 55457, 55547, 57457, 57557, 74747, 75557, 75577, 77447, 77477, 77557, 77747, 444547, 444557, 445447, 445477, 445747, 447757

Offset: 1

Jonathan Vos Post, Sep 24 2012

These are the primes in A214584. Primes whose numerals are all written (san serif) with at least one right or acute angle.

Cf. A079651, A079652, A214584.

Cf. A036953, A260044, A260267 - A260271, A199325 - A199329, A061247, A199340 - A199349.

[p: p in PrimesUpTo(450000) | Intseq(p) subset [4,5,7]]; // Bruno Berselli, Sep 25 2012

Select[Flatten[Table[FromDigits/@Tuples[{4,5,7},n],{n,6}]],PrimeQ] (* Bruno Berselli, Sep 25 2012 *)

A217039(n=50,show=0,L=[4,5,7])={for(d=1,1e9, my(t, u=vector(d,i,10^(d-i))~); forvec(v=vector(d,i,[if(i==d&&d>1,3/*must end in 7*/,1), #L]), ispseudoprime(t=vecextract(L, v)*u)||next; show&&print1(t", "); n--||return(t)))} \\ Syntax updated for newer PARI versions by M. F. Hasler, Jul 25 2015

A000040 INTERSECTION A214584.

A034470 Prime numbers using only the curved digits 0, 2, 3, 5, 6, 8 and 9.

Original entry on oeis.org

2, 3, 5, 23, 29, 53, 59, 83, 89, 223, 229, 233, 239, 263, 269, 283, 293, 353, 359, 383, 389, 503, 509, 523, 563, 569, 593, 599, 653, 659, 683, 809, 823, 829, 839, 853, 859, 863, 883, 929, 953, 983, 2003, 2029, 2039, 2053, 2063, 2069, 2083, 2089, 2099, 2203

Offset: 1

Robert G. Wilson v, Jan 24 2003

Intersection of A000040 and A028374. - K. D. Bajpai, Sep 07 2014

			From _K. D. Bajpai_, Sep 07 2014: (Start)
29 is prime and is composed only of the curved digits 2 and 9.
359 is prime and is composed only of the curved digits 3, 5 and 9.
(End)
20235869 is the smallest instance using all curved digits. - _Michel Marcus_, Sep 07 2014

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A028374, A072960, A079652.

N:= 4: # to get all entries with at most N digits
S:= {0,2,3,5,6,8,9}:
T:= S:
for j from 2 to N do
T:= map(t -> seq(10*t+s,s=S),T);
od:
select(isprime,T);
# In Maple 11 and earlier, uncomment the next line:
# sort(convert(%,list)); # Robert Israel, Sep 07 2014

Select[Range[2222], PrimeQ[#] && Union[Join[IntegerDigits[#], {0, 2, 3, 5, 6, 8, 9}]] == {0, 2, 3, 5, 6, 8, 9} &] (* RGWv *)
Select[Prime[Range[500]], Intersection[IntegerDigits[#], {1, 4, 7}] == {} &] (* K. D. Bajpai, Sep 07 2014 *)

A361822 Primes without {2, 5} as digits.

Original entry on oeis.org

3, 7, 11, 13, 17, 19, 31, 37, 41, 43, 47, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 163, 167, 173, 179, 181, 191, 193, 197, 199, 307, 311, 313, 317, 331, 337, 347, 349, 367, 373, 379, 383, 389, 397, 401, 409, 419, 431, 433, 439, 443, 449, 461, 463

Offset: 1

Bernard Schott, Mar 26 2023

Subsequence of primes that are in A361780.

Intersection of A000040 and A361780.
Cf. A079651 (primes with {1, 4, 7}), A079652 (primes with {0, 3, 6, 8, 9}).
Cf. A247052 (primes with {1, 2, 4, 5, 7}), A034470 (primes with {0, 2, 3, 5, 6, 8, 9}).
Cf. A106116, A154761, A386320 - A386358 (primes without two decimal digits).
Cf. A385776.

filter:= proc(n) convert(convert(n,base,10),set) intersect {2,5} = {} end proc:
select(filter, [seq(ithprime(i),i=1..1000)]); # Robert Israel, Mar 26 2023

Select[Prime[Range[100]], AllTrue[IntegerDigits[#], ! MemberQ[{2, 5}, #1] &] &] (* Amiram Eldar, Mar 26 2023 *)

print(list(islice(primes_with("01346789"), 41))) # uses function/imports in A385776. Jason Bard, Jul 20 2025

A217048 Semiprimes using only the curved digits 0, 3, 6, 8 and 9.

Original entry on oeis.org

6, 9, 33, 38, 39, 69, 86, 93, 303, 309, 339, 386, 393, 398, 633, 669, 689, 698, 699, 803, 838, 866, 869, 886, 889, 893, 898, 899, 933, 939, 989, 993, 998, 3039, 3063, 3086, 3093, 3098, 3099, 3309, 3338, 3369, 3383, 3386, 3398, 3603, 3639, 3669, 3683, 3693

Offset: 1

Jonathan Vos Post, Sep 25 2012

This is to A079652 as semiprimes A001358 are to primes A000040.

			a(41) = 3338 = 2 * 1669, the 938th semiprime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A001358, A072960.

IsSemiprime:=func; [n: n in [2..3700] | IsSemiprime(n) and Intseq(n) subset [0,3,6,8,9]]; // Bruno Berselli, Sep 25 2012

R:= [0,3,6,8,9]:
Res:= NULL: count:= 0:
for m from 1 while count < 100 do
  L:= convert(m,base,5);
  n:= add(R[L[i]+1]*10^(i-1),i=1..nops(L));
  if numtheory:-bigomega(n)=2 then Res:= Res, n; count:= count+1 fi
od:
Res; # Robert Israel, Feb 16 2020

A001358 INTERSECTION A072960.

A107291 Numbers k such that 10^k(10^7(-1+10^k)+6083806) + 10^k - 1 is prime.

Original entry on oeis.org

8, 33, 41, 495, 657, 1904, 4497, 9369, 11096, 11465, 12542, 20819

Offset: 1

Jason Earls, May 20 2005

These are palprimes with curved digits, i.e., palindromic primes composed of only 0's, 3s, 6s, 8s, or 9s and they have all been proved prime. No more terms up to 7000. Primality proof for the largest: PFGW Version 20041001.Win_Stable (v1.2 RC1b) [FFT v23.8] Primality testing 10^4497*(10^7*(-1+10^4497)+6083806)+10^4497-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Running N+1 test using discriminant 3, base 3+sqrt(3) Running N+1 test using discriminant 3, base 5+sqrt(3) 10^4497*(10^7*(-1+10^4497)+6083806)+10^4497-1 is prime! (147.0046s+0.0074s)

			8 is a term because 10^8*(10^7*(-1+10^8)+6083806)+10^8-1 = 99999999608380699999999 is prime.

R. Ondrejka, The Top Ten: a Catalogue of Primal Configurations.

Cf. A079652.

is(n)=ispseudoprime(10^n*(10^7*(-1+10^n)+6083806)+10^n-1) \\ Charles R Greathouse IV, Jun 13 2017

a(8)-a(12) from Michael S. Branicky, Sep 21 2024

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A217039 Primes having only {4, 5, 7} as digits.

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A034470 Prime numbers using only the curved digits 0, 2, 3, 5, 6, 8 and 9.

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A361822 Primes without {2, 5} as digits.

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A217048 Semiprimes using only the curved digits 0, 3, 6, 8 and 9.

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A107291 Numbers k such that 10^k*(10^7*(-1+10^k)+6083806) + 10^k - 1 is prime.

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A107291 Numbers k such that 10^k(10^7(-1+10^k)+6083806) + 10^k - 1 is prime.