A007053 -id:A007053 - cp's OEIS frontend

A073514 Number of primes less than 10^n with initial digit 4.

0, 3, 20, 139, 1069, 8747, 74114, 641594, 5661135, 50653546, 458352691, 4185483176, 38510936699, 356622729564, 3320632228693, 31067060521057, 291869049531878, 2752144407792176, 26035873192178041, 247025281876786013, 2349914303292170310, 22407593754131275705

Offset: 1

Shyam Sunder Gupta, Aug 14 2002

			a(2)=3 because there are 3 primes up to 10^2 whose initial digit is 4 (namely 41, 43 and 47).

Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A073509 to A073517, their sum is A006880.

For primes with initial digit d (1 <= d <= 9) see A045707, A045708, A045709, A045710, A045711, A045712, A045713, A045714, A045715; A073517, A073516, A073515, A073514, A073513, A073512, A073511, A073510, A073509

f[n_] := f[n] = PrimePi[5*10^n] - PrimePi[4*10^n] + f[n - 1]; f[0] = 0; Table[ f[n], {n, 0, 13}]

Edited and extended by Robert G. Wilson v, Aug 29 2002

a(20)-a(22) added by David Baugh, Mar 22 2015

A073515 Number of primes less than 10^n with initial digit 3.

Original entry on oeis.org

1, 3, 19, 139, 1097, 8960, 75290, 651085, 5735086, 51247361, 463196868, 4225763390, 38851672813, 359541975662, 3345924530873, 31288310624754, 293820812588401, 2769490109678920, 26191046215879444, 248421640738371325, 2362546444095790527, 22522418647770393663

Offset: 1

Shyam Sunder Gupta, Aug 14 2002

			a(2)=3 because there are 3 primes up to 10^2 whose initial digit is 3 (namely 3, 31 and 37).

Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A073509 to A073517, their sum is A006880.

For primes with initial digit d (1 <= d <= 9) see A045707, A045708, A045709, A045710, A045711, A045712, A045713, A045714, A045715; A073517, A073516, A073515, A073514, A073513, A073512, A073511, A073510, A073509

f[n_] := f[n] = PrimePi[4*10^n] - PrimePi[3*10^n] + f[n - 1]; f[0] = 1; Table[ f[n], {n, 0, 12}]

Edited and extended by Robert G. Wilson v, Aug 29 2002

a(21)-a(22) added by David Baugh, Mar 22 2015

A073516 Number of primes less than 10^n with initial digit 2.

Original entry on oeis.org

1, 3, 19, 146, 1129, 9142, 77025, 664277, 5837665, 52064915, 469864125, 4281198201, 39319600765, 363545360347, 3380562309312, 31590949437540, 296487794277035, 2793170342851930, 26402713858800478, 250324979315879678, 2379753569255122805, 22678735843184786383

Offset: 1

Shyam Sunder Gupta, Aug 14 2002

			a(2)=3 because there are 3 primes up to 10^2 whose initial digit is 2 (namely 2, 23 and 29).

Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A073509 to A073517, their sum is A006880.

For primes with initial digit d (1 <= d <= 9) see A045707, A045708, A045709, A045710, A045711, A045712, A045713, A045714, A045715; A073517, A073516, A073515, A073514, A073513, A073512, A073511, A073510, A073509

f[n_] := f[n] = PrimePi[3*10^n] - PrimePi[2*10^n] + f[n - 1]; f[0] = 1; Table[ f[n], {n, 0, 13}]

Edited and extended by Robert G. Wilson v, Aug 29 2002

a(21)-a(22) added by David Baugh, Mar 21 2015

A038812 Number of primes less than 1000n.

Original entry on oeis.org

168, 303, 430, 550, 669, 783, 900, 1007, 1117, 1229, 1335, 1438, 1547, 1652, 1754, 1862, 1960, 2064, 2158, 2262, 2360, 2464, 2564, 2668, 2762, 2860, 2961, 3055, 3153, 3245, 3340, 3432, 3538, 3638, 3732, 3824, 3923, 4017, 4107, 4203, 4291, 4392, 4494

Offset: 1

Jeff Burch

nonn

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Andrew R. Booker, The Nth Prime Page
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A038801, A028505, A038813, A038814, A038815, A038816, A038817, A038818, A038819, A038820, A038821, A080122, A080123, A080124, A080125, A080126, A080127, A080128, A080129.

Mathematica
```
Table[ PrimePi[ n*1000 ], {n, 1, 45}]
```

a(n)=primepi(1000*n) \\ Charles R Greathouse IV, Apr 29 2015

Edited and extended by Robert G. Wilson v, Jan 29 2003

A038813 Number of primes less than 10000n.

Original entry on oeis.org

1229, 2262, 3245, 4203, 5133, 6057, 6935, 7837, 8713, 9592, 10453, 11301, 12159, 13010, 13848, 14683, 15497, 16342, 17170, 17984, 18807, 19618, 20437, 21221, 22044, 22837, 23642, 24432, 25224, 25997, 26800, 27608, 28404, 29182, 29977

Offset: 1

Jeff Burch

nonn

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Andrew R. Booker, The Nth Prime Page
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A038801, A028505, A038812, A038814, A038815, A038816, A038817, A038818, A038819, A038820, A038821, A080122, A080123, A080124, A080125, A080126, A080127, A080128, A080129.

Mathematica
```
Table[ PrimePi[ n*10^4 ], {n, 1, 30}]
```

a(n)=primepi(10000*n) \\ Charles R Greathouse IV, Apr 29 2015

Edited and extended by Robert G. Wilson v, Jan 29 2003

A038814 Number of primes less than 100000n.

Original entry on oeis.org

9592, 17984, 25997, 33860, 41538, 49098, 56543, 63951, 71274, 78498, 85714, 92938, 100021, 107126, 114155, 121127, 128141, 135072, 142029, 148933, 155805, 162662, 169511, 176302, 183072, 189880, 196645, 203362, 210109, 216816, 223492, 230209

Offset: 1

Jeff Burch

nonn

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Andrew R. Booker, The Nth Prime Page
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A038801, A028505, A038812, A038813, A038815, A038816, A038817, A038818, A038819, A038820, A038821, A080122, A080123, A080124, A080125, A080126, A080127, A080128, A080129.

Mathematica
```
Table[ PrimePi[ n*10^5 ], {n, 1, 30}]
```

a(n)=primepi(10^5*n) \\ Charles R Greathouse IV, Apr 29 2015

Edited and extended by Robert G. Wilson v, Jan 29 2003

A038815 Number of primes less than n*10^6.

Original entry on oeis.org

78498, 148933, 216816, 283146, 348513, 412849, 476648, 539777, 602489, 664579, 726517, 788060, 849252, 910077, 970704, 1031130, 1091314, 1151367, 1211050, 1270607, 1329943, 1389261, 1448221, 1507122, 1565927, 1624527, 1683065

Offset: 1

Jeff Burch

nonn

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Andrew R. Booker, The Nth Prime Page
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A038801, A028505, A038812, A038813, A038814, A038816, A038817, A038818, A038819, A038820, A038821, A080122, A080123, A080124, A080125, A080126, A080127, A080128, A080129.

Mathematica
```
Table[ PrimePi[ n*10^6 ], {n, 1, 30}]
```

a(n)=primepi(10^6*n) \\ Charles R Greathouse IV, Apr 29 2015

Edited and extended by Robert G. Wilson v, Jan 29 2003

A038816 Number of primes less than n*10^7.

Original entry on oeis.org

664579, 1270607, 1857859, 2433654, 3001134, 3562115, 4118064, 4669382, 5216954, 5761455, 6303309, 6841648, 7378187, 7912199, 8444396, 8974458, 9503083, 10030385, 10555473, 11078937, 11601626, 12122540, 12642573

Offset: 1

Jeff Burch

nonn

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Andrew R. Booker, The Nth Prime Page
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A038801, A028505, A038812, A038813, A038814, A038815, A038817, A038818, A038819, A038820, A038821, A080122, A080123, A080124, A080125, A080126, A080127, A080128, A080129.

Mathematica
```
Table[ PrimePi[ n*10^7 ], {n, 1, 30} ]
```

a(n)=primepi(10^7*n) \\ Charles R Greathouse IV, Apr 29 2015

More terms from Robert G. Wilson v, Aug 27 2001

Edited and extended by Robert G. Wilson v, Jan 29 2003

A038817 Number of primes less than n*10^8.

Original entry on oeis.org

5761455, 11078937, 16252325, 21336326, 26355867, 31324703, 36252931, 41146179, 46009215, 50847534, 55662470, 60454705, 65228333, 69985473, 74726528, 79451833, 84163019, 88862422, 93547928, 98222287, 102886526, 107540122

Offset: 1

Jeff Burch

nonn

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Andrew R. Booker, The Nth Prime Page
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A038801, A028505, A038812, A038813, A038814, A038815, A038816, A038818, A038819, A038820, A038821, A080122, A080123, A080124, A080125, A080126, A080127, A080128, A080129.

Mathematica
```
Table[ PrimePi[ n*10^8 ], {n, 1, 22}]
```

a(n)=primepi(10^8*n) \\ Charles R Greathouse IV, Apr 29 2015

Edited and extended by Robert G. Wilson v, Jan 29 2003

A038818 Number of primes less than n*10^9.

Original entry on oeis.org

50847534, 98222287, 144449537, 189961812, 234954223, 279545368, 323804352, 367783654, 411523195, 455052511, 498388617, 541555851, 584570200, 627440336, 670180516, 712799821, 755305935, 797703398, 840000027, 882206716, 924324489

Offset: 1

Jeff Burch

nonn

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Andrew R. Booker, The Nth Prime Page
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A038801, A028505, A038812, A038813, A038814, A038815, A038816, A038817, A038819, A038820, A038821, A080122, A080123, A080124, A080125, A080126, A080127, A080128, A080129.

Mathematica
```
Table[ PrimePi[ n*10^9 ], {n, 1, 22}]
```

a(n)=primepi(10^9*n) \\ Charles R Greathouse IV, Apr 29 2015

Edited and extended by Robert G. Wilson v, Jan 29 2003

cp's OEIS Frontend

A073514 Number of primes less than 10^n with initial digit 4.

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A073515 Number of primes less than 10^n with initial digit 3.

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A073516 Number of primes less than 10^n with initial digit 2.

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A038812 Number of primes less than 1000n.

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Mathematica

PARI

Extensions

A038813 Number of primes less than 10000n.

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Author

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Crossrefs

Programs

Mathematica

PARI

Extensions

A038814 Number of primes less than 100000n.

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A038815 Number of primes less than n*10^6.

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A038816 Number of primes less than n*10^7.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI