aarjaneiro/planetmath huggingface dataset:
Skewes’ number

Skewes’ number

Skewes’ number

is the smallest number

n

for which

π

⁢

(

n

)

>

li

⁡

(

n

)

, where

π

⁢

(

x

)

is the

prime counting function

and

li

⁡

(

x

)

is the

logarithmic integral

. The logarithmic integral is a good estimate for the prime counting function, but in the range of

prime numbers

for which we know all smaller primes, the logarithmic integral is an overestimate. Thus, Skewes’ number is the smallest number for which

li

⁡

(

x

)

“goes from being an overestimate to being an underestimate.” (Wells, 1986)

The exact value of Skewes’ number is not currently known. Stanley Skewes in 1933 gave the

lower bound

e

e

e

79

, approximately

10

10

10

34

. He assumed the

Riemann hypothesis

to be true. Others have proven smaller bounds to as low as about

1.4

×

10

316

.

In the 1930s, Skewes’ number was the largest that had ever been used in a serious mathematical proof. It has since then been significantly dwarfed by Graham’s number. It still is the second largest number with its own entry in Wells’

The Penguin Dictionary of Curious and Interesting Numbers

, appearing on the penultimate page of the main text.

References

1

Bays, C. & Hudson, R. H. “A new bound for the smallest

x

with

π

⁢

(

x

)

>

li

⁡

(

x

)

.”

Math. Comput.

69

(2000): 1285 - 1296

2

Wells, D.

The Penguin Dictionary of Curious and Interesting Numbers

London: Penguin Group. (1986): 209

Title

Skewes’ number

Canonical name

SkewesNumber

Date of creation

2013-03-22 17:02:58

Last modified on

2013-03-22 17:02:58

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 11A41

Synonym

Skewes’s number

Synonym

Skewes number

Generated on Fri Feb 9 15:18:06 2018 by

LaTeXML
Smarandache constant

Smarandache constant

The

Smarandache constant

is the minimal solution

x

min

of the generalized Andrica equation:

p

n

+

1

x

-

p

n

x

=

1

where

p

n

is the n

th

prime number

, and

x

∈

ℝ

. The exact value of the Smarandache constant and whether it exists is currently unknown, however according to the

generalized Andrica conjecture

proposed by

Florentin Smarandache

the value of the Smarandache constant is

x

min

≈

0.5671481302

⁢

…

The Smarandache constant should not be confused with a list of sixteen Smarandache constants

s

1

-

s

16

defined as limits of different

convergent series

involving the

Smarandache function

.

Title

Smarandache constant

Canonical

name

SmarandacheConstant

Date of creation

2013-03-22 17:17:49

Last modified on

2013-03-22 17:17:49

Owner

dankomed (17058)

Last modified by

dankomed (17058)

Numerical id

17

Author

dankomed (17058)

Entry type

Conjecture

Classification

msc 11A41

Related topic

FlorentinSmarandache

Generated on Fri Feb 9 15:18:08 2018 by

LaTeXML
Sophie Germain prime

Sophie Germain prime

A

prime number

p

is called

Sophie Germain prime

if

2

⁢

p

+

1

is also prime.

The first few Sophie Germain primes are:

2

,

3

,

5

,

11

,

23

,

29

,

41

,

53

,

83

,

89

,

113

,

131

,

173

,

179

,

191

,

233

,

…

It is conjectured that there are infinitely many Sophie Germain primes,
but (like the

Twin Prime Conjecture

) this has not been proven.
A heuristic estimate for the number of Sophie Germain primes less than

n

is

2

⁢

c

⁢

n

ln

2

⁡

n

, where

c

is the twin prime constant.

Title

Sophie Germain prime

Canonical name

SophieGermainPrime

Date of creation

2013-03-22 14:34:23

Last modified on

2013-03-22 14:34:23

Owner

yark (2760)

Last modified by

yark (2760)

Numerical id

8

Author

yark (2760)

Entry type

Definition

Classification

msc 11A41

Synonym

Germain prime

Generated on Fri Feb 9 15:18:13 2018 by

LaTeXML
strong law of small numbers

strong law of small numbers

The

Strong Law of Small numbers

: There aren’t enough small numbers to the many demands made of them.
This has been formulated
by the mathematician Richard K. Guy.

References

1

Richard K. Guy, The American Mathematical Monthly, vol 95, (1988), pages 697-712.

Title

strong law of small numbers

Canonical

name

StrongLawOfSmallNumbers

Date of creation

2013-03-22 16:10:56

Last modified on

2013-03-22 16:10:56

Owner

Mathprof (13753)

Last modified by

Mathprof (13753)

Numerical id

4

Author

Mathprof (13753)

Entry type

Definition

Classification

msc 11A41

Generated on Fri Feb 9 15:18:15 2018 by

LaTeXML
strong prime

strong prime

In

number theory

, if for the given

n

th prime

p

n

the

inequality

p

n

>

1

3

⁢

∑

i

=

n

-

1

n

+

1

p

i

is true, then

p

n

is said to be a

strong prime

. That is, the

arithmetic mean

of the given prime, the prime immediately below and the one immediately above, is less than the middle prime. The first few are 11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, listed in A051634 of Sloane’s OEIS.

For example, 17 is the seventh prime. The sixth and eighth primes, 13 and 19, add up to 32, and half that is 16. That is less than 17, thus 17 is a strong prime.

Given a

twin prime

p

,

p

+

2

, the lesser prime of the two,

p

, will almost certainly be a strong prime. The only twin prime pairs

p

,

p

+

2

for which

p

is not a strong prime are 3, 5 and 5, 7.

There is a different meaning in

cryptography

, where the term

strong prime

is sometimes used to refer to a prime that can’t be cracked by Pollard’s

p

-

1

algorithm

in a reasonable amount of time because

p

±

1

=

2

⁢

q

⁢

r

, where

q

and

r

are sufficiently large primes. Some of these primes might be vulnerable to Lenstra elliptic curve factorization, however.

It is possible for a prime to be a strong prime both in the cryptographic sense and the number theoretic sense. For the sake of illustration, 439351292910452432574786963588089477522344331 is a strong prime in the number theoretic sense because the arithmetic mean of its two neighboring primes is 62 less. Without the aid of a computer, this number would be a strong prime in the cryptographic sense because 439351292910452432574786963588089477522344330 has the large prime factor 1747822896920092227343 (and in turn the number one less than that has the large prime factor 1683837087591611009), 439351292910452432574786963588089477522344332 has the large prime factor 864608136454559457049 (and in turn the number one less than that has the large prime factor 105646155480762397). Even using algorithms more advanced than

trial division

, these numbers would be difficult to factor by hand. For a modern

computer algebra system

, these numbers can be factored almost instantaneously. A cryptographically strong prime has to be much larger than this example.

Title

strong prime

Canonical name

StrongPrime

Date of creation

2013-03-22 16:34:39

Last modified on

2013-03-22 16:34:39

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

7

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 11A41

Related topic

BalancedPrime

Related topic

WeakPrime

Generated on Fri Feb 9 15:18:16 2018 by

LaTeXML
table of factors of small Mersenne numbers

table of factors of small Mersenne numbers

The following table lists the

prime factors

for some small

Mersenne numbers

, specifically, numbers of the form

2

p

-

1

where

p

is a prime in the range

1

<

p

<

200

and

2

p

-

1

is

composite

. Thus, the following values of

p

have been left off the table: 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127 and all primes greater than 199 (see

table of Mersenne primes

). The numbers get quite large, and correspondingly, so do their factors. All these numbers are

squarefree

(given the Möbius function,

μ

⁢

(

2

p

-

1

)

≠

0

). Their factors are all of the form

2

⁢

m

⁢

p

+

1

, with

m

in the range

0

<

m

<

2

p

-

1

.

p

Factors of

2

p

-

1

11

23, 89

23

47, 178481

29

233, 1103, 2089

37

223, 616318177

41

13367, 164511353

43

431, 9719, 2099863

47

2351, 4513, 13264529

53

6361, 69431, 20394401

59

179951, 3203431780337

67

193707721, 761838257287

71

228479, 48544121, 212885833

73

439, 2298041, 9361973132609

79

2687, 202029703, 1113491139767

83

167, 57912614113275649087721

97

11447, 13842607235828485645766393

101

7432339208719, 341117531003194129

103

2550183799, 3976656429941438590393

109

745988807, 870035986098720987332873

113

3391, 23279, 65993, 1868569, 1066818132868207

131

263, 10350794431055162386718619237468234569

137

32032215596496435569, 5439042183600204290159

139

5625767248687, 123876132205208335762278423601

149

86656268566282183151, 8235109336690846723986161

151

18121, 55871, 165799, 2332951, 7289088383388253664437433

157

852133201, 60726444167, 1654058017289, 2134387368610417

163

150287, 704161, 110211473, 27669118297, 36230454570129675721

167

2349023, 79638304766856507377778616296087448490695649

173

730753, 1505447, 70084436712553223, 155285743288572277679887

179

359, 1433, 1489459109360039866456940197095433721664951999121

181

43441, 1164193, 7648337, 7923871097285295625344647665764672671

191

383, 7068569257, 39940132241, 332584516519201, 87274497124602996457

193

13821503, 61654440233248340616559, 14732265321145317331353282383

197

7487, 26828803997912886929710867041891989490486893845712448833

199

164504919713, 4884164093883941177660049098586324302977543600799

Title

table of factors of small Mersenne numbers

Canonical name

TableOfFactorsOfSmallMersenneNumbers

Date of creation

2013-03-22 18:05:55

Last modified on

2013-03-22 18:05:55

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 11A41

Generated on Fri Feb 9 15:18:18 2018 by

LaTeXML
test for primality of Mersenne numbers

test for primality of Mersenne numbers

Suppose

p

is an

odd prime

, and define a

sequence

L

n

recursively as

L

0

=

4

,

L

n

+

1

=

(

L

n

2

-

2

)

mod

(

2

p

-

1

)

.

The number

2

p

-

1

is prime if and only if

L

p

-

2

=

0

.

References

1

Donald E. Knuth.

The Art of Computer Programming

, volume 2.

Addison-Wesley, 1969.

Title

test for primality of Mersenne numbers

Canonical name

TestForPrimalityOfMersenneNumbers

Date of creation

2013-03-22 13:39:48

Last modified on

2013-03-22 13:39:48

Owner

bbukh (348)

Last modified by

bbukh (348)

Numerical id

8

Author

bbukh (348)

Entry type

Algorithm

Classification

msc 11A41

Classification

msc 11Y11

Classification

msc 11A51

Generated on Fri Feb 9 15:18:50 2018 by

LaTeXML
Thue’s lemma

Thue’s lemma

Let

p

be a

prime number

of the form

4

⁢

k

+

1

. Then there are two unique

integers

a

and

b

with

0

<

a

<

b

such that

p

=

a

2

+

b

2

. Additionally, if a number

p

can be written in as the

sum of two squares

in 2 different ways (i.e.

p

=

a

2

+

b

2

and

p

=

c

2

+

d

2

with the two sums being different), then the number

p

is

composite

.

Title

Thue’s lemma

Canonical name

ThuesLemma

Date of creation

2013-03-22 13:19:05

Last modified on

2013-03-22 13:19:05

Owner

mathcam (2727)

Last modified by

mathcam (2727)

Numerical id

8

Author

mathcam (2727)

Entry type

Theorem

Classification

msc 11A41

Related topic

RepresentingPrimesAsX2ny2

Generated on Fri Feb 9 15:18:51 2018 by

LaTeXML
Ulam spiral

Ulam spiral

The

Ulam spiral

(or

Ulam cloth

) consists of

integers

, starting from a given

n

at the center, written in a spiral with the

prime numbers

highlighted or emphasized in some way. For example, writing a spiral with 42 at the center,

90

67

68

69

70

71

72

89

66

51

52

53

54

73

88

65

50

43

44

55

74

87

64

49

42

45

56

75

86

63

48

47

46

57

76

85

62

61

60

59

58

77

84

83

82

81

80

79

78

and then simply blanking the

composites

, we obtain

67

71

89

53

73

43

47

61

59

83

79

Carrying on this process in more layers will show that most of the primes tend to fall on certain diagonals and not others.

This formation was first pondered by Stanisław Ulam with 1 at the center. He tried carrying out the process much further, and also tried different center values, but in each case the primes would

cluster

on certain diagonals and sparsely populate others. Because almost all primes are odd, it is easy to explain why they would tend to form diagonals, but much more difficult to explain why they fall on certain diagonals.

References

1

Gardner, M. “Mathematical Recreations: The Remarkable Lore of the Prime Number”

Scientific American

210

3: 120 - 128

Title

Ulam spiral

Canonical

name

UlamSpiral

Date of creation

2013-03-22 16:45:41

Last modified on

2013-03-22 16:45:41

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 11A41

Synonym

Ulam cloth

Synonym

Ulam spiral

Generated on Fri Feb 9 15:18:55 2018 by

LaTeXML
Ultrafactorial

Ultrafactorial

Factorials

raised to the power of themselves are called

ultrafactorials

. The first few ultrafactorials are 1, 1, 4, 46656 … (

Sequence

A046882 of OEIS). According to the website cnki.com, functions like ultrafactorial and duplicate exponents are used to rectify the

systematic errors

in increasing load forecasting by

linear regression

. Hence they are helpful in forecasting annual electricity. Similarly

ultraprimorials

can also be defined as

primorials

raised to the power of themselves. The first few ultraprimorials 1, 4, 46656, … (Sequence A165812 of OEIS).

Title

Ultrafactorial

Canonical name

Ultrafactorial

Date of creation

2013-03-22 19:20:49

Last modified on

2013-03-22 19:20:49

Owner

Kausthub (26471)

Last modified by

Kausthub (26471)

Numerical id

4

Author

Kausthub (26471)

Entry type

Definition

Classification

msc 11A41

Generated on Fri Feb 9 15:18:57 2018 by

LaTeXML
upper bound on ϑ⁢(n)

upper bound on

ϑ

⁢

(

n

)

Theorem

.

Let

ϑ

⁢

(

n

)

be the

Chebyshev function

ϑ

⁢

(

n

)

=

∑

p

≤

n

p

⁢

prime

log

⁡

p

.

Then

ϑ

⁢

(

n

)

≤

n

⁢

log

⁡

4

for all

n

≥

1

.

Proof.

By

induction

.

The cases for

n

=

1

and

n

=

2

follow by inspection.

For even

n

>

2

, the case follows immediately from the case for

n

-

1

since

n

is not prime.

So let

n

=

2

⁢

m

+

1

with

m

>

0

and consider

(

1

+

1

)

2

⁢

m

+

1

and its binomial expansion (

http://planetmath.org/BinomialTheorem

). Since

(

2

⁢

m

+

1

m

)

=

(

2

⁢

m

+

1

m

+

1

)

and each term occurs exactly once, it follows that

(

2

⁢

m

+

1

m

)

≤

4

m

. Each prime

p

with

m

+

1

<

p

≤

2

⁢

m

+

1

divides

(

2

⁢

m

+

1

m

)

, implying that their

product

also divides

(

2

⁢

m

+

1

m

)

. Hence

ϑ

⁢

(

2

⁢

m

+

1

)

-

ϑ

⁢

(

m

+

1

)

≤

log

⁡

(

2

⁢

m

+

1

m

)

≤

m

⁢

log

⁡

4

.

By the

induction hypothesis

,

ϑ

⁢

(

m

+

1

)

≤

(

m

+

1

)

⁢

log

⁡

4

and so

ϑ

⁢

(

2

⁢

m

+

1

)

≤

(

2

⁢

m

+

1

)

⁢

log

⁡

4

.
∎

References

1

G.H. Hardy, E.M. Wright,

An

Introduction

to the Theory of Numbers

, Oxford University Press, 1938.

Title

upper bound

on

ϑ

⁢

(

n

)

Canonical

name

UpperBoundOnvarthetan

Date of creation

2013-03-22 16:09:47

Last modified on

2013-03-22 16:09:47

Owner

mps (409)

Last modified by

mps (409)

Numerical id

5

Author

mps (409)

Entry type

Theorem

Classification

msc 11A41

Generated on Fri Feb 9 15:18:59 2018 by

LaTeXML
values of the prime counting function and estimates for selected inputs

values of the prime counting function and estimates for selected inputs

In illustrating the degree of error of various estimates of the

prime counting function

given in connection to the

prime number theorem

, it is customary to select powers of 10 as the inputs. These are given in the table below, mixed in with primes beginning and ending

prime gaps

, the fourth primes of selected

prime quadruplets

and selected record lows of the

Mertens function

. The values of the

logarithmic integral

and the division of

n

by its

natural logarithm

have been rounded off to the nearest

integer

.

n

π

⁢

(

n

)

∫

2

n

d

⁢

t

log

⁡

t

n

log

⁡

n

2

1

1

3

3

2

2

3

5

3

4

3

7

4

5

4

10

4

6

4

11

5

7

5

23

9

11

7

29

10

13

9

89

24

28

20

97

25

29

21

100

25

30

22

110

29

32

23

113

30

33

24

127

31

36

26

523

99

105

84

541

100

108

86

829

145

153

123

887

154

161

131

907

155

164

133

1000

168

178

145

1105

185

193

158

1129

189

196

161

1151

190

199

163

1327

217

224

185

1361

218

229

189

1489

237

246

204

1879

289

299

249

9551

1183

1197

1042

9587

1184

1201

1046

10000

1229

1246

1086

15683

1831

1847

1623

15727

1832

1852

1628

19609

2225

2249

1984

19661

2226

2254

1989

23833

2652

2672

2365

31397

3385

3412

3032

31469

3386

3419

3038

99139

9520

9555

8618

100000

9592

9630

8686

1000000

78498

78628

72382

10000000

664579

664918

620421

100000000

5761455

5762209

5428681

1000000000

50847534

50849235

48254942

10000000000

455052511

455055615

434294482

The smaller values (up to

n

=

2000

) have been verified by hand. Above that, I have trusted Mathematica 4.2 completely.

Title

values of the prime counting function and estimates for selected inputs

Canonical name

ValuesOfThePrimeCountingFunctionAndEstimatesForSelectedInputs

Date of creation

2013-03-22 16:38:53

Last modified on

2013-03-22 16:38:53

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Example

Classification

msc 11A41

Generated on Fri Feb 9 15:19:01 2018 by

LaTeXML
Wagstaff prime

Wagstaff prime

A

Wagstaff prime

p

is a

prime number

of the form

2

2

⁢

n

+

1

+

1

3

. The first few are 3, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883, etc., given in A000979 of Sloane’s OEIS. The exponent of 2 in the formula given above must be an

odd number

for the result to be an

integer

in the first place, and that exponent must not be

composite

.

Currently, the largest known Wagstaff prime, corresponding to an exponent of 42737, is approximately

4.383322622

×

10

12864

. As there is no known special

primality test

for Wagstaff primes, François Morain had to use

elliptic curve primality proving

(ECPP) over several months to prove the

primality

of this Wagstaff prime, finishing in August 2007. (Morain names these primes after Samuel Wagstaff, Jr.) A000978 lists nine exponents which give

probable primes

.

References

1

François Morain, “Distributed primality proving and the primality of

(

2

3539

+

1

)

3

”

Lecture Notes in Comput. Sci.

473

(1991): 110 - 123

Title

Wagstaff prime

Canonical name

WagstaffPrime

Date of creation

2013-03-22 17:42:33

Last modified on

2013-03-22 17:42:33

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 11A41

Generated on Fri Feb 9 15:19:04 2018 by

LaTeXML
Wall-Sun-Sun prime

Wall-Sun-Sun prime

A

Wall-Sun-Sun prime

is a

prime number

p

>

5

such that

p

2

|

F

p

-

(

p

5

)

, with

F

n

being the

n

th

Fibonacci number

and

(

p

5

)

being a

Legendre symbol

. The prime

p

always divides

F

p

-

(

p

5

)

, but no case is known for the square of a prime

p

2

also dividing that.

The search for these primes started in the 1990s as Donald Dines Wall, Zhi-Hong Sun and

Zhi-Wei Sun

searched for

counterexamples

to Fermat’s last

theorem

. But

Andrew Wiles

’s proof does not rule out the

existence

of these primes: if Fermat’s last theorem was false and there existed a prime exponent

p

such that

x

p

+

y

p

=

z

p

, the square of such a prime would also divide

F

p

-

(

p

5

)

, but with Fermat’s last theorem being true, the existence of a Wall-Sun-Sun prime would not present a

contradiction

.

As of 2005, the

lower bound

was

3.2

×

10

12

, given by McIntosh.

References

1

Richard Crandall &

Carl Pomerance

,

Prime Numbers: A Computational Perspective

, 2nd Edition. New York: Springer (2005): 32

Title

Wall-Sun-Sun prime

Canonical

name

WallSunSunPrime

Date of creation

2013-03-22 18:04:18

Last modified on

2013-03-22 18:04:18

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 11A41

Synonym

Fibonacci Wieferich prime

Generated on Fri Feb 9 15:19:06 2018 by

LaTeXML
weak prime

weak prime

If for the given

n

th prime

p

n

the

inequality

p

n

<

1

3

⁢

∑

i

=

n

-

1

n

+

1

p

i

is true, then

p

n

is said to be a

weak prime

. That is, the

arithmetic mean

of the given prime, the prime immediately below and the one immediately above, is more than the middle prime. The first few are 3, 7, 13, 19, 23, 31, 43, 47, 61, 73, 83, 89, listed in A051635 of Sloane’s OEIS.

Title

weak prime

Canonical

name

WeakPrime

Date of creation

2013-03-22 16:36:56

Last modified on

2013-03-22 16:36:56

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 11A41

Related topic

BalancedPrime

Related topic

StrongPrime

Generated on Fri Feb 9 15:19:07 2018 by

LaTeXML
Wilson prime

Wilson prime

If for a given prime

p

it is true that

(

p

-

1

)

!

≡

-

1

mod

p

2

, then

p

is called a

Wilson prime

. Like all other primes, Wilson primes satisfy the

primality

condition of Wilson’s theorem, but they also divide the

Wilson quotient

. Only three are known as of 2007, namely: 5, 13, 563 (A007540 in Sloane’s OEIS, which normally requires at least four terms before accepting

sequences

into the table). It is not known if there are infinitely many Wilson primes exist; the fourth Wilson prime would have to be greater than

10

9

.

Title

Wilson prime

Canonical name

WilsonPrime

Date of creation

2013-03-22 16:40:39

Last modified on

2013-03-22 16:40:39

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 11A41

Generated on Fri Feb 9 15:19:09 2018 by

LaTeXML
Wilson’s primeth recurrence

Wilson’s primeth recurrence

Define

p

x

to be the

x

-th

prime number

(for example,

p

15

=

47

). Then define the recurrence

a

0

=

1

and

a

n

=

p

a

n

-

1

for

n

>

0

. This is

Wilson’s

primeth recurrence

which results in the

sequence

1, 2, 3, 5, 11, 31, 127, 709, 5381, 52711, 648391, 9737333, 174440041, … (A7097 in Sloane’s OEIS). Given the

prime counting function

π

⁢

(

x

)

, the recurrence should check out thus:

π

⁢

(

a

n

)

=

a

n

-

1

.

It suffices to mention Euclid’s proof that there are infinitely many primes to show that this recurrence is also infinite. However, the terms of this recurrence quickly become large enough to show the limitations of today’s computational devices. Robert G. Wilson provided Sloane with just 15 terms. The last of those was shown to be erroneous by Paul Zimmerman, who was able to extend the known sequence by just two more terms. In 2007, David Baugh discovered two more terms.

References

1

N. J. A. Sloane, “My Favorite

Integer Sequences

”

Sequences and their Applications (Proceedings of SETA ’98)

, Springer-Verlag, London, 1999, pp. 103-130.

Title

Wilson’s primeth recurrence

Canonical

name

WilsonsPrimethRecurrence

Date of creation

2013-03-22 16:11:51

Last modified on

2013-03-22 16:11:51

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

6

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 11A41

Synonym

Wilson’s prime-th recurrence

Synonym

primeth recurrence

Synonym

prime-th recurrence

Synonym

primeth sequence

Synonym

prime-th sequence

Generated on Fri Feb 9 15:19:11 2018 by

LaTeXML