A165292 -id:A165292 - cp's OEIS frontend

A165555 Primes obtained from other primes by prefixing a 5.

53, 523, 541, 547, 571, 5101, 5107, 5113, 5167, 5179, 5197, 5227, 5233, 5281, 5347, 5419, 5431, 5443, 5449, 5479, 5503, 5521, 5557, 5563, 5569, 5641, 5647, 5653, 5659, 5683, 5701, 5743, 5821, 5827, 5839, 5857, 5881, 5953, 51031, 51061, 51109, 51151, 51193, 51217

Offset: 1

Parthasarathy Nambi, Sep 21 2009

The primes are considered in increasing order. Primes with the same number of digits, the difference between adjacent terms seems to be a multiple of 3.

			5479 is a prime obtained by prefixing a 5 to the prime 479.

K. D. Bajpai, Table of n, a(n) for n = 1..10000
Chris Caldwell, The First 10,000 Primes

Cf. A000040, A165243, A165292, A165444.

[k : p in PrimesUpTo (2000) | IsPrime (k) where k is Seqint (Intseq (p) cat Intseq (5))]; // K. D. Bajpai, Jul 14 2017

A165555:= n-> (parse(cat(5,ithprime(n)))): select(isprime, [seq((A165555(n), n=1..1000))]); # K. D. Bajpai, Jul 14 2017

Select[Table[FromDigits[Join[IntegerDigits[5], IntegerDigits[Prime[n]]]], {n, 500}], PrimeQ] (*K. D. Bajpai, Jul 14 2017 *)
Select[5*10^IntegerLength[#]+#&/@Prime[Range[200]],PrimeQ] (* Harvey P. Dale, Sep 29 2024 *)

lista(nn) = forprime(p=2, nn, if (isprime(q=eval(concat(5, Str(p)))), print1(q, ", "))); \\ Michel Marcus, Jul 29 2017

More terms from Vincenzo Librandi, Dec 02 2010

Missing term 5449 inserted by K. D. Bajpai, Jul 14 2017

A167187 Primes obtained from other primes by prefixing a 7.

Original entry on oeis.org

73, 719, 743, 761, 773, 797, 7103, 7109, 7127, 7151, 7193, 7211, 7229, 7283, 7307, 7331, 7349, 7433, 7457, 7487, 7499, 7523, 7541, 7547, 7577, 7607, 7643, 7673, 7691, 7727, 7757, 7823, 7829, 7853, 7877, 7883, 7907, 7919, 7937, 71039, 71069, 71129, 71153

Offset: 1

Parthasarathy Nambi, Oct 29 2009

			7151 is a prime obtained by prefixing a 7 to the prime 151.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000040, A165243, A165292, A165444

Select[FromDigits[Join[{7},IntegerDigits[#]]]&/@Prime[Range[250]],PrimeQ] (* Harvey P. Dale, Aug 08 2014 *)

a(11)-a(42) from Vincenzo Librandi, Nov 01 2009

Corrected (a(15)=7307 inserted) by Harvey P. Dale, Aug 08 2014

A165444 Primes obtained from other primes by prefixing a 4.

Original entry on oeis.org

43, 47, 419, 431, 443, 461, 467, 479, 4127, 4139, 4157, 4211, 4229, 4241, 4271, 4283, 4337, 4349, 4373, 4397, 4409, 4421, 4457, 4463, 4523, 4547, 4643, 4673, 4691, 4733, 4751, 4787, 4877, 4919, 4937, 4967, 41039, 41051, 41117, 41201, 41213, 41231, 41381, 41399

Offset: 1

Parthasarathy Nambi, Sep 19 2009

			4547 is a prime obtained by prefixing a 4 to the prime 547.

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Chris Caldwell, The First 10,000 Primes

Cf. A000040, A165243, A165292

Select[4*10^IntegerLength[#]+#&/@Prime[Range[300]],PrimeQ] (* Harvey P. Dale, Mar 25 2016 *)

More terms from Vincenzo Librandi, Sep 20 2009

A289866 Primes obtained from other primes by prefixing a 1.

Original entry on oeis.org

13, 17, 113, 131, 137, 167, 173, 179, 197, 1103, 1109, 1151, 1163, 1181, 1193, 1223, 1229, 1277, 1283, 1307, 1367, 1373, 1409, 1433, 1439, 1487, 1499, 1523, 1571, 1601, 1607, 1613, 1619, 1709, 1733, 1787, 1811, 1823, 1877, 1907, 1997, 11069, 11087, 11093

Offset: 1

Vincenzo Librandi, Jul 14 2017

			131 is a term because it is a prime obtained by prefixing a 1 to the prime 31.
1409 is a term because it is a prime obtained by prefixing a 1 to the prime 409.

Vincenzo Librandi, Table of n, a(n) for n = 1..2170

Cf. A039790 (primes prefixed by 1).

Cf. primes obtained from other primes by prefixing a k: this sequence (k=1), A165243 (k=2), A165292 (k=3), A165444 (k=4), A165555 (k=5), A289867 (k=6), A167187 (k=7), A290407 (k=8).

[k: p in PrimesUpTo(1500) | IsPrime(k) where k is Seqint(Intseq(p) cat [1])];

Select[Table[FromDigits[Join[IntegerDigits[1], IntegerDigits[Prime[n]]]], {n, 300}], PrimeQ]
Select[Table[10^IntegerLength[p]+p,{p,Prime[Range[200]]}],PrimeQ] (* Harvey P. Dale, Oct 17 2021 *)

A327918 The 16 pure prime dates of each non-leap year of the form concatenate(month,day) with month and day also prime numbers.

Original entry on oeis.org

23, 211, 223, 37, 311, 313, 317, 331, 53, 523, 73, 719, 113, 1117, 1123, 1129

Offset: 1

Wolfdieter Lang, Oct 08 2019

For the numbers for leap years see A327919.
Only the months February (2), March (3), May (5), July (7) and November (11) qualify. The qualifying prime days are for month m=2: 3, 5, 7, 11, 13, 17, 19, 23; for month m = 11: 3, 5, 7, 11, 13, 17, 19, 23, 29 and for months m = 3, 5, and 7: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31.
The months m = 2, 3, 5, 7, 11 contribute 3, 5, 2, 2, 4 days, respectively, adding to 16.

Cf. A165243 (first three terms), A165292 (first five terms), A165555 (first two terms), A167187 (first two terms), A327348 (m and d nonprime allowed), A327914 (with 0 before d = 1..9), A327919 (leap year), A327920 (pure prime dates of d.m form).

A327919 The 17 pure prime dates of each leap year of the form concatenate(month,day) with month and day also prime numbers.

Original entry on oeis.org

23, 211, 223, 229, 37, 311, 313, 317, 331, 53, 523, 73, 719, 113, 1117, 1123, 1129

Offset: 1

Wolfdieter Lang, Oct 08 2019

For the non-leap case see A327918.

The months m = 2, 3, 5, 7, 11 contribute 4, 5, 2, 2, 4 days, respectively, adding to 17.

Cf. A165243 (first four terms), A165292 (first five terms), A165555 (first two terms), A167187 (first two terms), A327349 (m and d nonprime allowed), A327915 (with 0 before d = 1..9), A327918 (non-leap year case), A327920 (pure prime dates of d.m form).

cp's OEIS Frontend

A165555 Primes obtained from other primes by prefixing a 5.

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A167187 Primes obtained from other primes by prefixing a 7.

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A165444 Primes obtained from other primes by prefixing a 4.

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A289866 Primes obtained from other primes by prefixing a 1.

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A327918 The 16 pure prime dates of each non-leap year of the form concatenate(month,day) with month and day also prime numbers.

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A327919 The 17 pure prime dates of each leap year of the form concatenate(month,day) with month and day also prime numbers.

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