cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-19 of 19 results.

A227537 Number of Mersenne primes that have between 10^n and 10^(n+1) - 1 digits.

Original entry on oeis.org

7, 5, 6, 8, 5, 6, 7
Offset: 0

Views

Author

Olivier de Mouzon, Jul 18 2013

Keywords

Comments

The nice property of this sequence is that (at least up to n = 6) there seems to be a rather stable number of Mersenne primes for each digit number group [10^n ... 10^(n+1) - 1].
At the moment (Jul 18 2013), there are already 4 Mersenne primes in the next group (n = 7), the last one was discovered on Jan 25 2013 and has 17425170 digits.
Note that for n = 6, a(n) = 7 still needs full confirmation, as tests for all factors between M42 = M_25964951 and M_44457869 (more than 10^7 digits) have only made once and a double check is needed to confirm a(6) = 7.
If this sequence were to actually be stable, this would mean that the number of Mersenne primes having between 10^n and 10^(n+1) - 1 digits is always around 6, when the number of prime numbers in the same digit number group constantly increases: around 2.3*10^(10^(n+1)-(n+1)). Also the number of Mersenne numbers in the same digit group constantly increases (though much less than the number of prime numbers): 9*10^n/[(n+1)*log(2) + log(log(10)/log(2))*log(2)/log(10)]. So, if a(n) is really rather stable (around 6), Mersenne primes frequency among Mersenne numbers lower than x is converging towards 0 in the magnitude of [log(log(x))]^2/log(x). Hence primes are still around 6*[log(log(x))]^2 more frequent among Mersenne numbers than among numbers.

Examples

			For n = 1, a(n) = 5 Mersenne primes with 10 to 99 digits, which are:
* M8 = M_31 = 2147483647,
* M9 = M_61 = 2305843009213693951,
* M10 = M_89 = 618970019642690137449562111,
* M11 = M_107 = 162259276829213363391578010288127,
* M12 = M_127 = 170141183460469231731687303715884105727.

Links

Crossrefs

Cf. A000043, A000668, A028335.

A233385 Primes that are a concatenations of n-th Mersenne exponent and n-th Mersenne prime.

Original entry on oeis.org

23, 37, 7127, 138191, 19524287
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Dec 08 2013

Keywords

Comments

Primes of the form A000043(n)*10^A028335(n) + A000668(n).

Examples

			a(4) is 138191(prime number) where 13 is 5th Mersenne exponent and 8191 is 5th Mersenne prime.

Crossrefs

Cf. A000043, A000668, A028335.

A371850 Decimal expansion of 2^216091 - 1, the 31st Mersenne prime.

Original entry on oeis.org

7, 4, 6, 0, 9, 3, 1, 0, 3, 0, 6, 4, 6, 6, 1, 3, 4, 3, 6, 8, 7, 3, 3, 9, 5, 7, 9, 4, 0, 0, 5, 1, 1, 4, 8, 9, 5, 4, 0, 2, 2, 8, 7, 5, 4, 0, 8, 4, 9, 7, 7, 3, 2, 8, 8, 0, 5, 1, 1, 3, 3, 0, 4, 9, 7, 7, 7, 9, 3, 6, 6, 2, 7, 2, 5, 2, 7, 0, 9, 6, 8, 7, 8, 0, 6, 6, 4, 3, 9, 5
Offset: 65050

Views

Author

Paolo Xausa, Apr 10 2024

Keywords

Comments

This prime has 65050 decimal digits and was discovered by David Slowinski in 1985.

Examples

			746093103064661343687339579400511489540228754084977...

Links

Crossrefs

Cf. A000043 (exponents), A000668, A028335 (lengths).
Cf. decimal expansion of Mersenne primes: see OEIS Wiki link.

Programs

  • Mathematica
    IntegerDigits[2^216091 - 1][[;;100]]

A371851 Decimal expansion of 2^756839 - 1, the 32nd Mersenne prime.

Original entry on oeis.org

1, 7, 4, 1, 3, 5, 9, 0, 6, 8, 2, 0, 0, 8, 7, 0, 9, 7, 3, 2, 5, 1, 6, 3, 5, 9, 9, 2, 4, 5, 9, 0, 3, 3, 2, 7, 8, 9, 0, 7, 7, 9, 3, 6, 3, 6, 9, 0, 5, 0, 7, 0, 3, 0, 9, 7, 4, 6, 5, 4, 7, 3, 5, 5, 3, 8, 3, 8, 2, 7, 2, 1, 5, 6, 2, 0, 6, 6, 2, 5, 7, 6, 3, 1, 9, 1, 4, 7, 9, 7
Offset: 227832

Views

Author

Paolo Xausa, Apr 10 2024

Keywords

Comments

This prime has 227832 decimal digits and was discovered by David Slowinski and Paul Gage in 1992.

Examples

			174135906820087097325163599245903327890779363690507...

Links

Crossrefs

Cf. A000043 (exponents), A000668, A028335 (lengths).
Cf. decimal expansion of Mersenne primes: see OEIS Wiki link.

Programs

  • Mathematica
    IntegerDigits[2^756839 - 1][[;;100]]

A371852 Decimal expansion of 2^859433 - 1, the 33rd Mersenne prime.

Original entry on oeis.org

1, 2, 9, 4, 9, 8, 1, 2, 5, 6, 0, 4, 2, 0, 7, 6, 4, 9, 6, 6, 6, 5, 3, 3, 4, 8, 5, 2, 5, 5, 5, 6, 2, 0, 7, 3, 3, 8, 4, 1, 6, 2, 0, 1, 9, 9, 1, 7, 4, 1, 6, 5, 6, 9, 3, 7, 0, 1, 9, 0, 6, 6, 2, 6, 7, 5, 6, 7, 8, 1, 4, 7, 2, 4, 0, 8, 4, 9, 5, 2, 9, 6, 9, 1, 9, 8, 9, 3, 1, 9
Offset: 258716

Views

Author

Paolo Xausa, Apr 10 2024

Keywords

Comments

This prime has 258716 decimal digits and was discovered by David Slowinski and Paul Gage in 1994.

Examples

			129498125604207649666533485255562073384162019917416569...

Links

Crossrefs

Cf. A000043 (exponents), A000668, A028335 (lengths).
Cf. decimal expansion of Mersenne primes: see OEIS Wiki link.

Programs

  • Mathematica
    IntegerDigits[2^859433 - 1][[;;100]]

A371853 Decimal expansion of 2^1257787 - 1, the 34th Mersenne prime.

Original entry on oeis.org

4, 1, 2, 2, 4, 5, 7, 7, 3, 6, 2, 1, 4, 2, 8, 6, 7, 4, 7, 2, 5, 3, 2, 3, 2, 1, 8, 4, 6, 6, 9, 7, 8, 9, 6, 0, 0, 5, 2, 7, 8, 7, 1, 8, 5, 6, 5, 4, 6, 5, 9, 4, 6, 9, 3, 8, 0, 4, 1, 3, 2, 0, 4, 8, 9, 5, 8, 0, 4, 0, 5, 5, 4, 4, 5, 0, 5, 6, 1, 1, 4, 0, 3, 1, 3, 1, 9, 1, 5, 5
Offset: 378632

Views

Author

Paolo Xausa, Apr 10 2024

Keywords

Comments

This prime has 378632 decimal digits and was discovered by David Slowinski and Paul Gage in 1996.

Examples

			412245773621428674725323218466978960052787185654659...

Links

Crossrefs

Cf. A000043 (exponents), A000668, A028335 (lengths).
Cf. decimal expansion of Mersenne primes: see OEIS Wiki link.

Programs

  • Mathematica
    IntegerDigits[2^1257787 - 1][[;;100]]

A371874 Decimal expansion of 2^1398269 - 1, the 35th Mersenne prime.

Original entry on oeis.org

8, 1, 4, 7, 1, 7, 5, 6, 4, 4, 1, 2, 5, 7, 3, 0, 7, 5, 1, 4, 2, 6, 7, 7, 2, 6, 4, 3, 8, 9, 1, 3, 5, 4, 2, 6, 0, 1, 5, 3, 1, 3, 7, 8, 3, 0, 8, 5, 0, 2, 2, 2, 7, 1, 0, 3, 2, 1, 1, 4, 5, 1, 0, 4, 8, 4, 6, 9, 9, 3, 8, 0, 3, 0, 8, 9, 9, 6, 1, 6, 0, 8, 3, 4, 0, 9, 8, 0, 2, 3
Offset: 420921

Views

Author

Paolo Xausa, Apr 10 2024

Keywords

Comments

This prime has 420921 decimal digits and was discovered by Joel Armengaud in 1996.

Examples

			81471756441257307514267726438913542601531378308502...

Links

Crossrefs

Cf. A000043 (exponents), A000668, A028335 (lengths).
Cf. decimal expansion of Mersenne primes: see OEIS Wiki link.

Programs

  • Mathematica
    IntegerDigits[2^1398269 - 1][[;;100]]

A371875 Decimal expansion of 2^2976221 - 1, the 36th Mersenne prime.

Original entry on oeis.org

6, 2, 3, 3, 4, 0, 0, 7, 6, 2, 4, 8, 5, 7, 8, 6, 4, 9, 8, 8, 6, 0, 4, 1, 4, 4, 1, 1, 7, 0, 8, 9, 2, 7, 4, 5, 0, 5, 0, 2, 7, 0, 4, 9, 8, 6, 8, 0, 5, 2, 7, 7, 0, 5, 7, 6, 2, 0, 1, 0, 4, 4, 9, 8, 0, 8, 3, 7, 2, 2, 8, 5, 0, 0, 5, 3, 1, 6, 1, 2, 8, 7, 5, 5, 2, 3, 8, 6, 4, 0
Offset: 895932

Views

Author

Paolo Xausa, Apr 10 2024

Keywords

Comments

This prime has 895932 decimal digits and was discovered by Gordon Spence in 1997.

Examples

			6233400762485786498860414411708927450502704986805277...

Links

Crossrefs

Cf. A000043 (exponents), A000668, A028335 (lengths).
Cf. decimal expansion of Mersenne primes: see OEIS Wiki link.

Programs

  • Mathematica
    IntegerDigits[2^2976221 - 1][[;;100]]

A371876 Decimal expansion of 2^3021377 - 1, the 37th Mersenne prime.

Original entry on oeis.org

1, 2, 7, 4, 1, 1, 6, 8, 3, 0, 3, 0, 0, 9, 3, 3, 6, 7, 4, 3, 3, 5, 5, 4, 2, 1, 5, 1, 7, 6, 7, 3, 4, 9, 2, 6, 1, 4, 7, 3, 6, 5, 4, 0, 9, 7, 1, 0, 3, 9, 0, 5, 3, 3, 3, 6, 7, 8, 9, 9, 3, 0, 4, 8, 6, 8, 8, 9, 2, 4, 3, 8, 4, 7, 8, 3, 4, 7, 2, 5, 9, 6, 4, 4, 6, 9, 8, 9, 0, 2
Offset: 909526

Views

Author

Paolo Xausa, Apr 10 2024

Keywords

Comments

This prime has 909526 decimal digits and was discovered by Roland Clarkson in 1998.

Examples

			12741168303009336743355421517673492614736540971039...

Links

Crossrefs

Cf. A000043 (exponents), A000668, A028335 (lengths).
Cf. decimal expansion of Mersenne primes: see OEIS Wiki link

Programs

  • Mathematica
    IntegerDigits[2^3021377 - 1][[;;100]]
Previous Showing 11-19 of 19 results.

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