A136061 -id:A136061 - cp's OEIS frontend

A136066 Mother primes of order 7.

31, 61, 151, 181, 241, 271, 331, 421, 541, 601, 631, 691, 991, 1051, 1171, 1231, 1321, 1531, 1621, 1951, 2221, 2251, 2341, 2671, 2851, 2971, 3331, 3391, 3571, 3931, 4021, 4051, 4201, 4231, 4591, 4651, 4951, 5281, 5581, 5821, 6121, 6271, 6301, 6451, 6481

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest mother primes of order n see A136020 (also definition). For mother primes of order 1 see A091180. For mother primes of order 2 see A136061. For mother primes of order 3 see A136062. For mother primes of order 4 see A136063. For mother primes of order 5 see A136064. For mother primes of order 6 see A136065.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A088878, A091180, A136019, A136020, A136061, A136062, A136063, A136064, A136065, A136067, A136068, A136069, A136070.

n = 7; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A136062 Mother primes of order 3.

Original entry on oeis.org

29, 43, 71, 113, 127, 197, 211, 281, 421, 463, 491, 547, 617, 673, 701, 743, 757, 883, 911, 953, 967, 1051, 1093, 1163, 1373, 1471, 1583, 1597, 1667, 1877, 1933, 2143, 2213, 2311, 2423, 2437, 2647, 2801, 2857, 2927, 3011, 3067, 3137, 3221, 3347, 3557

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest mother primes of order n see A136020 (also definition). For mother primes of order 1 see A091180. For mother primes of order 2 see A136061.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A088878, A091180, A136019, A136020, A136061, A136063, A136064, A136065, A136066, A136067, A136068, A136069, A136070.

n = 3; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A136069 Mother primes of order 10.

Original entry on oeis.org

43, 127, 211, 337, 379, 463, 631, 757, 883, 967, 1093, 1471, 1723, 2017, 2143, 2269, 2647, 2731, 2857, 3109, 3613, 3739, 4159, 4663, 4789, 4999, 5503, 5881, 5923, 6133, 6427, 6553, 6637, 7057, 7309, 7393, 7687, 8317, 8779, 8821, 9199, 9283, 9661, 9787

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest mother primes of order n see A136020 (also definition). For mother primes of order 1 see A091180. For mother primes of order 2 see A136061. For mother primes of order 3 see A136062. For mother primes of order 4 see A136063. For mother primes of order 5 see A136064. For mother primes of order 6 see A136065. For mother primes of order 8 see A136066. For mother primes of order 9 see A136067.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A088878, A091180, A136019, A136020, A136061, A136062, A136063, A136064, A136065, A136066, A136067, A136068, A136070.

n = 10; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A136063 Mother primes of order 4.

Original entry on oeis.org

19, 37, 109, 163, 199, 271, 379, 523, 541, 631, 739, 919, 1009, 1171, 1459, 1549, 1621, 1783, 1999, 2053, 2089, 2143, 2161, 2251, 2521, 2539, 2791, 2971, 3169, 3673, 3889, 3943, 4159, 4483, 4519, 4861, 5059, 5113, 5563, 5779, 5869, 5923, 6211, 6301, 6373

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest mother primes of order n see A136020 (also definition). For mother primes of order 1 see A091180. For mother primes of order 2 see A136061. For mother primes of order 3 see A136062.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A088878, A091180, A136019, A136020, A136061, A136062, A136064, A136065, A136066, A136067, A136068, A136069, A136070.

n = 4; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A136064 Mother primes of order 5.

Original entry on oeis.org

23, 67, 199, 331, 397, 463, 661, 727, 859, 1123, 1783, 2113, 2179, 2311, 2971, 3037, 3433, 3631, 3697, 4027, 4093, 4159, 4357, 4621, 5347, 5479, 5743, 6007, 6271, 6337, 6733, 7393, 7591, 7789, 8053, 8317, 8647, 9043, 9109, 9439, 9967, 10099, 10627

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest mother primes of order n see A136020 (also definition). For mother primes of order 1 see A091180. For mother primes of order 2 see A136061. For mother primes of order 3 see A136062. For mother primes of order 4 see A136063.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A088878, A091180, A136019, A136020, A136061, A136062, A136063, A136065, A136066, A136067, A136068, A136069, A136070.

n = 5; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A136065 Mother primes of order 6.

Original entry on oeis.org

53, 79, 131, 157, 521, 547, 599, 677, 859, 911, 937, 1249, 1301, 1327, 1951, 2029, 2237, 2341, 2549, 2731, 2887, 2939, 3121, 3251, 3329, 3407, 3511, 3797, 4057, 4759, 4967, 5591, 5981, 6007, 6761, 7229, 7307, 7411, 7489, 7879, 8009, 8191, 8581, 8737

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest mother primes of order n see A136020 (also definition). For mother primes of order 1 see A091180. For mother primes of order 2 see A136061. For mother primes of order 3 see A136062. For mother primes of order 4 see A136063. For mother primes of order 5 see A136064.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A088878, A091180, A136019, A136020, A136061, A136062, A136063, A136064, A136066, A136067, A136068, A136069, A136070.

n = 6; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A136067 Mother primes of order 8.

Original entry on oeis.org

103, 307, 613, 1021, 1123, 1327, 2143, 2347, 2551, 3061, 3571, 3877, 4591, 6427, 6733, 7753, 8263, 8467, 9181, 9283, 10303, 10711, 11731, 12037, 12343, 12547, 12853, 15607, 15913, 16831, 17137, 17341, 17851, 18973, 19891, 21013, 21727

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest mother primes of order n see A136020 (also definition). For mother primes of order 1 see A091180. For mother primes of order 2 see A136061. For mother primes of order 3 see A136062. For mother primes of order 4 see A136063. For mother primes of order 5 see A136064. For mother primes of order 6 see A136065. For mother primes of order 8 see A136066.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A088878, A091180, A136019, A136020, A136061, A136062, A136063, A136064, A136065, A136066, A136068, A136069, A136070.

n = 8; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A136068 Mother primes of order 9.

Original entry on oeis.org

191, 229, 419, 571, 761, 1103, 1483, 1559, 1901, 2053, 2129, 2851, 3079, 4219, 4409, 4523, 4561, 4751, 6271, 6689, 6803, 7069, 7753, 8171, 8209, 8513, 8741, 8779, 9311, 9463, 9539, 10831, 11743, 11971, 12161, 12503, 12541, 12959, 14251, 14593, 14669

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest mother primes of order n see A136020 (also definition). For mother primes of order 1 see A091180. For mother primes of order 2 see A136061. For mother primes of order 3 see A136062. For mother primes of order 4 see A136063. For mother primes of order 5 see A136064. For mother primes of order 6 see A136065. For mother primes of order 8 see A136066. For mother primes of order 9 see A136067.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A088878, A091180, A136019, A136020, A136061, A136062, A136063, A136064, A136065, A136066, A136067, A136069, A136070.

n = 9; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A136070 Mother primes of order 11.

Original entry on oeis.org

47, 139, 277, 691, 829, 967, 1381, 1657, 2347, 3727, 4831, 5107, 5521, 6211, 7039, 7177, 7591, 8419, 9109, 9661, 10627, 12007, 12421, 13249, 14767, 16699, 17389, 19597, 20149, 20287, 21529, 24151, 24979, 25117, 26497, 28429, 29671, 29947

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest mother primes of order n see A136020 (also definition). For mother primes of order 1 see A091180. For mother primes of order 2 see A136061. For mother primes of order 3 see A136062. For mother primes of order 4 see A136063. For mother primes of order 5 see A136064. For mother primes of order 6 see A136065. For mother primes of order 8 see A136066. For mother primes of order 9 see A136067. For mother primes of order 10 see A136068.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A088878, A091180, A136019, A136020, A136061, A136062, A136063, A136064, A136065, A136066, A136067, A136068, A136069.

n = 11; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A204592 Primes p such that (p+1)/2, (p+2)/3, (p+3)/4 and (p+4)/5 are also prime.

Original entry on oeis.org

19441, 266401, 423481, 539401, 600601, 663601, 908041, 1113961, 1338241, 1483561, 1657441, 1673401, 2578801, 3109681, 3150841, 3336601, 3613681, 4112761, 4160641, 4798081, 5114881, 5412961, 5516281, 5590201, 5839681, 6078361, 7660801, 8628481, 9362641, 9388801, 9584401, 9733081

Offset: 1

M. F. Hasler, Feb 26 2012

nonn

Equivalently, primes p in A163573 such that p+4 is a semiprime. (Since all p in A163573 are of the form p=120k+1, p+4 is necessarily a multiple of 5. The other prime factor is then (p+4)/5 = 24k+1.)

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

Select[Prime[Range[700000]],AllTrue[{(#+1)/2,(#+2)/3,(#+3)/4,(#+4)/5},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 05 2017 *)

{my(p=1); until(, isprime(p+=120) || next; for( j=2,5, isprime(p\j+1) || next(2)); print1(p","))}

forprime(p=2,1e7,if(p%120==1&&isprime((p+1)/2)&&isprime((p+2)/3)&& isprime((p+3)/4)&&isprime((p+4)/5),print1(p", "))) \\ Charles R Greathouse IV, Feb 26 2012

A204592 = A163573 intersect A136061.

cp's OEIS Frontend

A136066 Mother primes of order 7.

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A136062 Mother primes of order 3.

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A136069 Mother primes of order 10.

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A136063 Mother primes of order 4.

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A136064 Mother primes of order 5.

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A136065 Mother primes of order 6.

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A136067 Mother primes of order 8.

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A136068 Mother primes of order 9.

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A136070 Mother primes of order 11.

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