A248932 -id:A248932 - cp's OEIS frontend

A169685 Decimal expansion of 2^521 - 1.

6, 8, 6, 4, 7, 9, 7, 6, 6, 0, 1, 3, 0, 6, 0, 9, 7, 1, 4, 9, 8, 1, 9, 0, 0, 7, 9, 9, 0, 8, 1, 3, 9, 3, 2, 1, 7, 2, 6, 9, 4, 3, 5, 3, 0, 0, 1, 4, 3, 3, 0, 5, 4, 0, 9, 3, 9, 4, 4, 6, 3, 4, 5, 9, 1, 8, 5, 5, 4, 3, 1, 8, 3, 3, 9, 7, 6, 5, 6, 0, 5, 2, 1, 2, 2, 5, 5, 9, 6, 4, 0, 6, 6, 1, 4, 5, 4, 5, 5

Offset: 157

N. J. A. Sloane, Apr 13 2010

The 13th Mersenne prime, A000668(13); 521 = A000043(13). - M. F. Hasler, Jan 09 2013

			686479766013060971498190079908139321726943530014330540939446345918\
554318339765605212255964066145455497729631139148085803712198799971\
6643812574028291115057151.

Arkadiusz Wesolowski, Table of n, a(n) for n = 157..313
D. H. Lehmer, Recent Discoveries of Large Primes, Mathematics of Computation, vol. 6, No. 37 (1952), p. 61.
Wikipedia, Mersenne prime

Cf. A169684 = A000668(11), A169681 = A000668(12), A204063 = A000668(14), A248931 = A000668(15), A248932 = A000668(16), A248933 = A000668(17), A248934 = A000668(18), A248935 = A000668(19), A248936 = A000668(20).

Reverse(Intseq(2^521-1)); // Arkadiusz Wesolowski, Oct 18 2014

IntegerDigits[2^521-1] (* Paolo Xausa, Oct 07 2023 *)

A169681 Decimal expansion of 2^127-1.

Original entry on oeis.org

1, 7, 0, 1, 4, 1, 1, 8, 3, 4, 6, 0, 4, 6, 9, 2, 3, 1, 7, 3, 1, 6, 8, 7, 3, 0, 3, 7, 1, 5, 8, 8, 4, 1, 0, 5, 7, 2, 7

Offset: 39

Vincenzo Librandi, Apr 12 2010

The 12th Mersenne prime, A000668(12); 127 = A000043(12). Also, the fifth Catalan number A007013(4). - M. F. Hasler, Jan 09 2013

			170141183460469231731687303715884105727.

Wikipedia, Mersenne prime

Cf. A169684 = A000668(11), A169685 = A000668(13), A204063 = A000668(14), A248931 = A000668(15), A248932 = A000668(16), A248933 = A000668(17), A248934 = A000668(18), A248935 = A000668(19), A248936 = A000668(20).

Reverse(Intseq(2^127-1)); // Arkadiusz Wesolowski, Oct 18 2014

IntegerDigits[2^127 - 1] (* Paolo Xausa, Apr 05 2024 *)

2^127-1 = 2^A000043(12)-1 = A000668(12). - M. F. Hasler, Jan 09 2013

Edited by N. J. A. Sloane, Apr 13 2010

A204063 Decimal expansion of 2^607 - 1, the 14th Mersenne prime A000668(14).

Original entry on oeis.org

5, 3, 1, 1, 3, 7, 9, 9, 2, 8, 1, 6, 7, 6, 7, 0, 9, 8, 6, 8, 9, 5, 8, 8, 2, 0, 6, 5, 5, 2, 4, 6, 8, 6, 2, 7, 3, 2, 9, 5, 9, 3, 1, 1, 7, 7, 2, 7, 0, 3, 1, 9, 2, 3, 1, 9, 9, 4, 4, 4, 1, 3, 8, 2, 0, 0, 4, 0, 3, 5, 5, 9, 8, 6, 0, 8, 5, 2, 2, 4, 2, 7, 3, 9, 1, 6, 2, 5, 0, 2, 2, 6, 5, 2, 2, 9, 2, 8, 5, 6, 6, 8, 8, 8, 9

Offset: 183

M. F. Hasler, Jan 09 2013

			2^607-1 = 531 * 10^180 +
137992816767098689588206552468627329593117727031923199444138 * 10^120 +
200403559860852242739162502265229285668889329486246501015346 * 10^60 +
579337652707239409519978766587351943831270835393219031728127.

M. F. Hasler, Table of n, a(n) for n = 183..365
D. H. Lehmer, Recent Discoveries of Large Primes, Mathematics of Computation, vol. 6, No. 37 (1952), p. 61.
Wikipedia, Mersenne prime

Cf. A169684 = A000668(11), A169681 = A000668(12), A169685 = A000668(13), A248931 = A000668(15), A248932 = A000668(16), A248933 = A000668(17), A248934 = A000668(18), A248935 = A000668(19), A248936 = A000668(20).

Reverse(Intseq(2^607-1)); // Arkadiusz Wesolowski, Oct 18 2014

RealDigits[2^607-1,10,120][[1]] (* Harvey P. Dale, Sep 23 2016 *)

digits(2^607-1) \\ Simplified by M. F. Hasler, Oct 19 2019

2^A000043(14)-1.

A248931 Decimal expansion of 2^1279 - 1, the 15th Mersenne prime A000668(15).

Original entry on oeis.org

1, 0, 4, 0, 7, 9, 3, 2, 1, 9, 4, 6, 6, 4, 3, 9, 9, 0, 8, 1, 9, 2, 5, 2, 4, 0, 3, 2, 7, 3, 6, 4, 0, 8, 5, 5, 3, 8, 6, 1, 5, 2, 6, 2, 2, 4, 7, 2, 6, 6, 7, 0, 4, 8, 0, 5, 3, 1, 9, 1, 1, 2, 3, 5, 0, 4, 0, 3, 6, 0, 8, 0, 5, 9, 6, 7, 3, 3, 6, 0, 2, 9, 8, 0, 1, 2, 2, 3, 9, 4, 4, 1, 7, 3, 2, 3, 2, 4, 1, 8, 4, 8, 4, 2, 4

Offset: 386

Arkadiusz Wesolowski, Oct 17 2014

The 13th through the 17th Mersenne primes were found in 1952 by Raphael M. Robinson, using SWAC.

			10407932194664399081925240327364085538615262247266704805319112350403608...

Arkadiusz Wesolowski, Table of n, a(n) for n = 386..771
D. H. Lehmer, A New Mersenne Prime, Mathematics of Computation, vol. 6, No. 39 (1952), p. 205.
Wikipedia, Mersenne prime

Cf. A169684 = A000668(11), A169681 = A000668(12), A169685 = A000668(13), A204063 = A000668(14), A248932 = A000668(16), A248933 = A000668(17), A248934 = A000668(18), A248935 = A000668(19), A248936 = A000668(20).

Magma
```
Reverse(Intseq(2^1279-1));
```

RealDigits[2^1279 - 1, 10, 100][[1]] (* G. C. Greubel, Oct 03 2017 *)

PARI
```
eval(Vec(Str(2^1279-1)))
```

Equals 2^A000043(15) - 1.

A248933 Decimal expansion of 2^2281 - 1, the 17th Mersenne prime A000668(17).

Original entry on oeis.org

4, 4, 6, 0, 8, 7, 5, 5, 7, 1, 8, 3, 7, 5, 8, 4, 2, 9, 5, 7, 1, 1, 5, 1, 7, 0, 6, 4, 0, 2, 1, 0, 1, 8, 0, 9, 8, 8, 6, 2, 0, 8, 6, 3, 2, 4, 1, 2, 8, 5, 9, 9, 0, 1, 1, 1, 1, 9, 9, 1, 2, 1, 9, 9, 6, 3, 4, 0, 4, 6, 8, 5, 7, 9, 2, 8, 2, 0, 4, 7, 3, 3, 6, 9, 1, 1, 2, 5, 4, 5, 2, 6, 9, 0, 0, 3, 9, 8, 9, 0, 2, 6, 1, 5, 3

Offset: 687

Arkadiusz Wesolowski, Oct 17 2014

The 13th through the 17th Mersenne primes were found in 1952 by Raphael M. Robinson, using SWAC.

The digits of this prime were published on page 167 of Nordisk Mathematisk Tidskrift 2 (1954).

			44608755718375842957115170640210180988620863241285990111199121996340468...

Arkadiusz Wesolowski, Table of n, a(n) for n = 687..1373
D. H. Lehmer, Two New Mersenne Primes, Mathematics of Computation, vol. 7, No. 41 (1952), p. 72.
Wikipedia, Mersenne prime

Cf. A169684 = A000668(11), A169681 = A000668(12), A169685 = A000668(13), A204063 = A000668(14), A248931 = A000668(15), A248932 = A000668(16), A248934 = A000668(18), A248935 = A000668(19), A248936 = A000668(20).

Magma
```
Reverse(Intseq(2^2281-1));
```

RealDigits[2^2281 - 1, 10, 100][[1]] (* G. C. Greubel, Oct 03 2017 *)

PARI
```
eval(Vec(Str(2^2281-1)))
```

Equals 2^A000043(17) - 1.

A248934 Decimal expansion of 2^3217 - 1, the 18th Mersenne prime A000668(18).

Original entry on oeis.org

2, 5, 9, 1, 1, 7, 0, 8, 6, 0, 1, 3, 2, 0, 2, 6, 2, 7, 7, 7, 6, 2, 4, 6, 7, 6, 7, 9, 2, 2, 4, 4, 1, 5, 3, 0, 9, 4, 1, 8, 1, 8, 8, 8, 7, 5, 5, 3, 1, 2, 5, 4, 2, 7, 3, 0, 3, 9, 7, 4, 9, 2, 3, 1, 6, 1, 8, 7, 4, 0, 1, 9, 2, 6, 6, 5, 8, 6, 3, 6, 2, 0, 8, 6, 2, 0, 1, 2, 0, 9, 5, 1, 6, 8, 0, 0, 4, 8, 3, 4, 0, 6, 5, 5, 0

Offset: 969

Arkadiusz Wesolowski, Oct 17 2014

The prime was found on September 8, 1957, by Hans Riesel, using BESK.

			25911708601320262777624676792244153094181888755312542730397492316187401...

Arkadiusz Wesolowski, Table of n, a(n) for n = 969..1937
Hans Riesel, A New Mersenne Prime, Mathematics of Computation, vol. 12 (1958), p. 60.
Wikipedia, Mersenne prime

Cf. A169684 = A000668(11), A169681 = A000668(12), A169685 = A000668(13), A204063 = A000668(14), A248931 = A000668(15), A248932 = A000668(16), A248933 = A000668(17), A248935 = A000668(19), A248936 = A000668(20).

Magma
```
Reverse(Intseq(2^3217-1));
```

RealDigits[2^3217 - 1, 10, 100][[1]] (* G. C. Greubel, Oct 03 2017 *)

PARI
```
eval(Vec(Str(2^3217-1)))
```

Equals 2^A000043(18) - 1.

A248935 Decimal expansion of 2^4253 - 1, the 19th Mersenne prime A000668(19).

Original entry on oeis.org

1, 9, 0, 7, 9, 7, 0, 0, 7, 5, 2, 4, 4, 3, 9, 0, 7, 3, 8, 0, 7, 4, 6, 8, 0, 4, 2, 9, 6, 9, 5, 2, 9, 1, 7, 3, 6, 6, 9, 3, 5, 6, 9, 9, 4, 7, 4, 9, 9, 4, 0, 1, 7, 7, 3, 9, 4, 7, 4, 1, 8, 8, 2, 6, 7, 3, 5, 2, 8, 9, 7, 9, 7, 8, 7, 0, 0, 5, 0, 5, 3, 7, 0, 6, 3, 6, 8, 0, 4, 9, 8, 3, 5, 5, 1, 4, 9, 0, 0, 2, 4, 4, 3, 0, 3

Offset: 1281

Arkadiusz Wesolowski, Oct 17 2014

This prime and the 20th Mersenne prime were found in 1961 by Alexander Hurwitz, using IBM 7090.

			19079700752443907380746804296952917366935699474994017739474188267352897...

Arkadiusz Wesolowski, Table of n, a(n) for n = 1281..2561
Alexander Hurwitz, New Mersenne Primes, Mathematics of Computation, vol. 16, No. 78 (1962), pp. 249-251.
Wikipedia, Mersenne prime

Cf. A169684 = A000668(11), A169681 = A000668(12), A169685 = A000668(13), A204063 = A000668(14), A248931 = A000668(15), A248932 = A000668(16), A248933 = A000668(17), A248934 = A000668(18), A248936 = A000668(20).

Magma
```
Reverse(Intseq(2^4253-1));
```

RealDigits[2^4253 - 1, 10, 100][[1]] (* G. C. Greubel, Oct 03 2017 *)

PARI
```
eval(Vec(Str(2^4253-1)))
```

Equals 2^A000043(19) - 1.

A248936 Decimal expansion of 2^4423 - 1, the 20th Mersenne prime A000668(20).

Original entry on oeis.org

2, 8, 5, 5, 4, 2, 5, 4, 2, 2, 2, 8, 2, 7, 9, 6, 1, 3, 9, 0, 1, 5, 6, 3, 5, 6, 6, 1, 0, 2, 1, 6, 4, 0, 0, 8, 3, 2, 6, 1, 6, 4, 2, 3, 8, 6, 4, 4, 7, 0, 2, 8, 8, 9, 1, 9, 9, 2, 4, 7, 4, 5, 6, 6, 0, 2, 2, 8, 4, 4, 0, 0, 3, 9, 0, 6, 0, 0, 6, 5, 3, 8, 7, 5, 9, 5, 4, 5, 7, 1, 5, 0, 5, 5, 3, 9, 8, 4, 3, 2, 3, 9, 7, 5, 4

Offset: 1332

Arkadiusz Wesolowski, Oct 17 2014

The 19th Mersenne prime and this prime were found in 1961 by Alexander Hurwitz, using IBM 7090.

			28554254222827961390156356610216400832616423864470288919924745660228440...

Arkadiusz Wesolowski, Table of n, a(n) for n = 1332..2663
Alexander Hurwitz, New Mersenne Primes, Mathematics of Computation, vol. 16, No. 78 (1962), pp. 249-251.
Wikipedia, Mersenne prime

Cf. A169684 = A000668(11), A169681 = A000668(12), A169685 = A000668(13), A204063 = A000668(14), A248931 = A000668(15), A248932 = A000668(16), A248933 = A000668(17), A248934 = A000668(18), A248935 = A000668(19).

Magma
```
Reverse(Intseq(2^4423-1));
```

RealDigits[2^4423 - 1, 10, 100][[1]] (* G. C. Greubel, Oct 03 2017 *)

PARI
```
eval(Vec(Str(2^4423-1)))
```

Equals 2^A000043(20) - 1.

A169684 Decimal expansion of 2^107 - 1.

Original entry on oeis.org

1, 6, 2, 2, 5, 9, 2, 7, 6, 8, 2, 9, 2, 1, 3, 3, 6, 3, 3, 9, 1, 5, 7, 8, 0, 1, 0, 2, 8, 8, 1, 2, 7

Offset: 33

N. J. A. Sloane, Apr 13 2010

The 11th Mersenne prime A000668(11), see also the formula, and A134731, A169681, A169685 for the next three terms in that sequence. - M. F. Hasler, Jan 09 2013

			162259276829213363391578010288127.

Wikipedia, Mersenne prime

Cf. A169681 = A000668(12), A169685 = A000668(13), A204063 = A000668(14), A248931 = A000668(15), A248932 = A000668(16), A248933 = A000668(17), A248934 = A000668(18), A248935 = A000668(19), A248936 = A000668(20).

Reverse(Intseq(2^107-1)); // Arkadiusz Wesolowski, Oct 18 2014

IntegerDigits[2^107-1] (* Paolo Xausa, Oct 07 2023 *)

eval(Vec(Str(2^107-1))) \\ or simply: digits(2^107-1) in PARI version 2.6+. - M. F. Hasler, Jan 09 2013

2^107 - 1 = 2^A000043(11) - 1 = A000668(11). - M. F. Hasler, Jan 09 2013

A275977 Decimal expansion of 2^9689 - 1, the 21st Mersenne prime A000668(21).

Original entry on oeis.org

4, 7, 8, 2, 2, 0, 2, 7, 8, 8, 0, 5, 4, 6, 1, 2, 0, 2, 9, 5, 2, 8, 3, 9, 2, 9, 8, 6, 6, 0, 0, 0, 5, 9, 0, 9, 7, 4, 1, 4, 9, 7, 1, 7, 2, 4, 0, 2, 2, 3, 6, 5, 0, 0, 8, 5, 1, 3, 3, 4, 5, 1, 0, 9, 9, 1, 8, 3, 7, 8, 9, 5, 0, 9, 4, 2, 6, 6, 2, 9, 7, 0, 2, 7, 8, 9, 2, 7, 6, 8, 6, 1, 1, 2, 7, 0, 7, 8, 9, 4, 5, 8, 6, 8, 2

Offset: 2917

Arkadiusz Wesolowski, Aug 15 2016

			47822027880546120295283929866000590974149717240223650085133451099183789...

Arkadiusz Wesolowski, Table of n, a(n) for n = 2917..5833
Wikipedia, Mersenne prime

Cf. A169684 = A000668(11), A169681 = A000668(12), A169685 = A000668(13), A204063 = A000668(14), A248931 = A000668(15), A248932 = A000688(16), A248933 = A000668(17), A248934 = A000668(18), A248935 = A000668(19), A248936 = A000668(20), A275979 = A000668(22), A275980 = A000668(23), A275981 = A000668(24), A275982 = A000668(25), A275983 = A000668(26), A275984 = A000668(27).

Magma
```
Reverse(Intseq(2^9689-1))[1..105];
```

First@RealDigits@N[2^9689 - 1, 100] (* G. C. Greubel, Aug 15 2016 *)
RealDigits[2^MersennePrimeExponent[21]-1,10,120][[1]] (* Harvey P. Dale, Aug 14 2025 *)

PARI
```
eval(Vec(Str(2^9689-1)))[1..105]
```

2^A000043(21) - 1.

cp's OEIS Frontend

A169685 Decimal expansion of 2^521 - 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

A169681 Decimal expansion of 2^127-1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

Formula

Extensions

A204063 Decimal expansion of 2^607 - 1, the 14th Mersenne prime A000668(14).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A248931 Decimal expansion of 2^1279 - 1, the 15th Mersenne prime A000668(15).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A248933 Decimal expansion of 2^2281 - 1, the 17th Mersenne prime A000668(17).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A248934 Decimal expansion of 2^3217 - 1, the 18th Mersenne prime A000668(18).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A248935 Decimal expansion of 2^4253 - 1, the 19th Mersenne prime A000668(19).

Views

Author

Keywords