A100607 -id:A100607 - cp's OEIS frontend

A101218 Primes that are a concatenation of 2, 3 and a prime.

233, 2311, 2341, 2347, 2371, 2383, 2389, 23131, 23167, 23173, 23197, 23227, 23251, 23269, 23293, 23311, 23431, 23509, 23557, 23563, 23593, 23599, 23677, 23719, 23743, 23761, 23773, 23827, 23857, 23887, 23911, 23929, 23971, 23977, 231019

Offset: 1

Parthasarathy Nambi, Dec 14 2004

			233 is a prime concatenated from the primes 2,3 and 3
2311 is a prime concatenated from the primes 2,3 and 11

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Peter Alfeld The 10,000 smallest prime numbers.

Cf. A100607, A101219, A101249, A101250, A101251, A101252.

Select[23*10^IntegerLength[#]+#&/@Prime[Range[200]],PrimeQ] (* Harvey P. Dale, Jun 09 2013 *)

Extended by Ray Chandler, Dec 22 2004

A101219 Primes that are a concatenation of 3, 5 and a prime.

Original entry on oeis.org

353, 3511, 3517, 3529, 3541, 3547, 3559, 3571, 3583, 35107, 35149, 35227, 35251, 35257, 35281, 35311, 35317, 35353, 35401, 35419, 35449, 35461, 35491, 35509, 35521, 35569, 35593, 35617, 35677, 35797, 35809, 35839, 35863, 35911, 35977

Offset: 1

Parthasarathy Nambi, Dec 14 2004

			3511 is a prime concatenated from the primes 3, 5 and 11.

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Peter Alfeld The 10,000 smallest prime numbers.

Cf. A100607, A101218, A101249, A101250, A101251, A101252.

Select[35*10^IntegerLength[#]+#&/@Prime[Range[200]],PrimeQ] (* Harvey P. Dale, Jan 23 2019 *)

Extended by Ray Chandler, Dec 22 2004

A101249 Primes that are a concatenation of 5, 7 and a prime.

Original entry on oeis.org

577, 5711, 5717, 5737, 5741, 5743, 5779, 5783, 57107, 57131, 57139, 57149, 57163, 57173, 57179, 57191, 57193, 57223, 57241, 57251, 57269, 57271, 57283, 57331, 57347, 57349, 57367, 57373, 57383, 57389, 57397, 57457, 57467, 57487, 57503

Offset: 1

Parthasarathy Nambi, Dec 16 2004

			5711 is a prime concatenated from the primes 5,7 and 11.

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
Peter Alfeld, The 10,000 smallest prime numbers.

Cf. A100607, A101218, A101219, A101250, A101251, A101252.

Select[ Table[ FromDigits[ Flatten[ IntegerDigits /@ {5, 7, Prime[n]}]], {n, 100}], PrimeQ[ # ] &] (* Robert G. Wilson v, Dec 20 2004 *)

Extended by Ray Chandler and Robert G. Wilson v, Dec 22 2004

A101250 Primes that are a concatenation of 7, 11 and a prime.

Original entry on oeis.org

71119, 71129, 71143, 71147, 71153, 71161, 71167, 71171, 711131, 711163, 711173, 711181, 711223, 711307, 711317, 711353, 711397, 711409, 711463, 711479, 711499, 711509, 711523, 711563, 711577, 711617, 711653, 711691, 711701, 711709, 711727

Offset: 1

Parthasarathy Nambi, Dec 16 2004

			71119 is a prime concatenated from the primes 7, 11 and 19.

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
Peter Alfeld, The 10,000 smallest prime numbers.

Cf. A100607, A101218, A101219, A101249, A101251, A101252.

Select[ Table[ FromDigits[ Flatten[ IntegerDigits /@ {7, 11, Prime[n]}]], {n, 130}], PrimeQ[ # ] &] (* Robert G. Wilson v, Dec 20 2004 *)

Extended by Ray Chandler and Robert G. Wilson v, Dec 22 2004

A100633 Primes that are the decimal concatenation of three separate primes.

Original entry on oeis.org

257, 523, 1123, 1153, 1327, 1373, 1723, 1753, 1973, 2113, 2137, 2237, 2293, 2297, 2311, 2341, 2347, 2357, 2371, 2377, 2383, 2389, 2417, 2437, 2473, 2477, 2531, 2543, 2579, 2593, 2617, 2677, 2711, 2713, 2719, 2729, 2731, 2741, 2753, 2767, 2789, 2797

Offset: 1

Robert G. Wilson v, Dec 03 2004

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

Cf. A100607, A383195.

filter:= proc(n) local m,i,j,ni,nj,np,n3;
 if not isprime(n) then return false fi;
 m:= ilog10(n);
 for i from 1 to m-1 do
   ni:= n mod 10^i;
   if ni < 10^(i-1) or not isprime(ni) then next fi;
   np:= (n-ni)/10^i;
   for j from 1 to m-i do
     nj:= np mod 10^j;
     if nj < 10^(j-1) then next fi;
     n3:= (np-nj)/10^j;
     if nops({ni,nj,n3})=3 and isprime(nj) and isprime(n3) then return true fi;
 od od;
 false
end proc;
select(filter, [seq(i,i=3..10000,2)]); # Robert Israel, Apr 28 2025

(*first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) t = KSubsets[ Prime[ Range[25]], 3]; lst = {}; Do[k = 1; u = Permutations[ t[[n]]]; While[k < 7, v = FromDigits[ Flatten[IntegerDigits /@ u[[k]]]]; If[ PrimeQ[v], AppendTo[lst, v]]; k++ ], {n, Binomial[25, 3]}]; Take[ Union[lst], 42]

Edited by Charles R Greathouse IV, Apr 29 2010

A383195 Primes that are the concatenation of three primes, of which two are equal.

Original entry on oeis.org

223, 227, 233, 277, 337, 353, 373, 557, 577, 727, 733, 757, 773, 1733, 1777, 1933, 2213, 2237, 2243, 2267, 2273, 2297, 2333, 2377, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3413, 3433, 3533, 3593, 3613, 3673, 3733, 3793, 3833, 4133, 4177, 4733, 5333, 5519, 5531, 5573

Offset: 1

Robert Israel, Apr 28 2025

nonn

Complement of A100633 in A100607.

			a(3) = 233 is a term because 233 is prime and is the concatenation of the primes 2, 3 and 3, of which two are equal.

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

Cf. A100607, A100633.

filter:= proc(n) local m, i, j, ni, nj, np, n3;
 if not isprime(n) then return false fi;
 m:= ilog10(n);
 for i from 1 to m-1 do
   ni:= n mod 10^i;
   if ni < 10^(i-1) or not isprime(ni) then next fi;
   np:= (n-ni)/10^i;
   for j from 1 to m-i do
     nj:= np mod 10^j;
     if nj < 10^(j-1) then next fi;
     n3:= (np-nj)/10^j;
     if nops({ni, nj, n3})<3 and isprime(nj) and isprime(n3) then return true fi;
 od od;
 false
end proc:
select(filter, [seq(i,i=3..10000,2)]);

A276803 Semiprimes k such that the concatenation of its prime factors is prime.

Original entry on oeis.org

6, 21, 22, 33, 39, 46, 51, 58, 82, 93, 111, 115, 133, 141, 142, 159, 166, 177, 187, 201, 205, 219, 226, 235, 237, 247, 249, 253, 262, 267, 274, 291, 301, 319, 327, 355, 358, 391, 411, 427, 478, 489, 501, 502, 505, 511, 535, 538, 543, 562, 565, 573, 583, 586, 589

Offset: 1

K. D. Bajpai, Sep 17 2016

Alternatively: Semiprimes p*q, with p

Corresponding primes are at A105184.

			21 is a term because 21 = 3 * 7 that is a semiprime : concatenation of 3 and 7 = 37  which is prime.
142 is a term because 142 = 2 * 71 that is a semiprime : concatenation of 2 and 71 = 271 which is prime.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A000040, A001358, A100607, A105184.

Select[Select[Range[1000], PrimeOmega[#] == 2 &], PrimeQ[FromDigits[Join[IntegerDigits [First@First[FactorInteger[#]]], IntegerDigits[First@Last[FactorInteger[#]]]]]] &]
Select[Range[1000],PrimeOmega[#]==PrimeNu[#]==2&&PrimeQ[FromDigits[ Flatten[ IntegerDigits/@FactorInteger[#][[All,1]]]]]&] (* Harvey P. Dale, Aug 03 2022 *)

list(lim)=my(v=List()); forprime(p=2,lim\2, forprime(q=2, min(p,lim\p), if(isprime(eval(Str(q,p))), listput(v,p*q)))); Set(v) \\ Charles R Greathouse IV, Sep 17 2016

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cp's OEIS Frontend

A101218 Primes that are a concatenation of 2, 3 and a prime.

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A101219 Primes that are a concatenation of 3, 5 and a prime.

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A101249 Primes that are a concatenation of 5, 7 and a prime.

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A101250 Primes that are a concatenation of 7, 11 and a prime.

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A100633 Primes that are the decimal concatenation of three separate primes.

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A383195 Primes that are the concatenation of three primes, of which two are equal.

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Maple

A276803 Semiprimes k such that the concatenation of its prime factors is prime.

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