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prime number siteswaps

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bill coad

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Dec 13, 2008, 3:48:07 PM12/13/08
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The 'words that are valid siteswaps' topic made me think about numeric
subsets that are valid siteswaps. In siteswap theory, prime siteswaps
have their own definition regarding comosition of other patterns.
The question is, which prime numbers represent valid siteswap patterns and
what's the largest known one? What's the one that uses the most objects?
E.g. 94007 is a prime number and also a 4 ball pattern.

--
----== posted via www.jugglingdb.com ==----

ChaseMartin

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Dec 14, 2008, 3:14:22 AM12/14/08
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bill coad wrote:
>
> The 'words that are valid siteswaps' topic made me think about numeric
> subsets that are valid siteswaps. In siteswap theory, prime siteswaps
> have their own definition regarding comosition of other patterns.
> The question is, which prime numbers represent valid siteswap patterns and
> what's the largest known one? What's the one that uses the most objects?
> E.g. 94007 is a prime number and also a 4 ball pattern.
>

That would immediately rule out 3 and 9 ball patterns, since for the
siteswap to be valid, the sum of the digits must be a multiple of that
number, but if that is true then the number is not prime because it is
divisible by that number.

For example, siteswap 531 is not a prime number because it is divisible by
3 (5+3+1 = 9, which is a multiple of 3)

Also, for any bored math people out there, UCLA recently won $50,000 for
discovering a 12 million digit prime. The prime number was (2^43112609)-1.

http://www.mersenne.org/

PinkNigel

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Dec 14, 2008, 8:00:19 AM12/14/08
to
ChaseMartin wrote:

> That would immediately rule out 3 and 9 ball patterns, since for the
> siteswap to be valid, the sum of the digits must be a multiple of that
> number, but if that is true then the number is not prime because it is
> divisible by that number.
>
>

Well yea, except for 3, which is prime and a valid siteswap...

The low ones are easy, 2, 3, 5, 7, (hmm... does 11 count as a siteswap?
It's pushing it a bit as the one
ball pattern, but written as b it works. Still, writing it as b is kinda
cheating), 13, 17, 19, 31, 37, 53, 59,
71, 73, 79 and 97 all work before it gets tricky to spot them...

dmn001

unread,
Dec 14, 2008, 9:43:05 AM12/14/08
to

Here are a couple more:

2
3
5
7
11
13
17
19
31
37
53
59
71
73
79
97
1151
1201
1223
1249
1289
1429
1447
1483
1511
1559
1601
1609
1627
1663
1667
1753
1847
1861
1933
1951
1973
1999
2011
2099
2239
2293
2297
2347
2383
2411
2459
2473
2477
2617
2671
2693
2729
2819
2833
2837
2851
2963
3001
3023
3041
3049
3067
3089
3359
3373
3449
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3571
3607
3733
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9730691
9730711
9730727
9730961
9733751
9737081
9737711
9737797
9738017
9739061
9740069
9740161
9740177
9740771
9741707
9742661
9744979
9747701
9750077
9750617
9753979
9758857
9758999
9759289
9780227
9780317
9781127
9781201
9782011
9782779
9784007
9784777
9788089
9788201
9788377
9788809
9788827
9788897
9789011
9789727
9789781
9789797
9790091
9790127
9790201
9790901
9791959
9792611
9793601
9794857
9797089
9797377
9799681
9900091
9900179
9900181
9900467
9900827
9901117
9901277
9901709
9902017
9902861
9903077
9908081
9908207
9909001
9909017
9909161
9909499
9909701
9911339
9911701
9911717
9911861
9912491
9913139
9913931
9915119
9915209
9915281
9915911
9915979
9918017
9919061
9919489
9919939
9920161
9920177
9920861
9922229
9923129
9923471
9923831
9923899
9924407
9924979
9925271
9925969
9929929
9929999
9930061
9930419
9930491
9935027
9935711
9935797
9938389
9940067
9942029
9942461
9942731
9945071
9945161
9948899
9949099
9949909
9951407
9952037
9952897
9953869
9958279
9960029
9960281
9962027
9962779
9964007
9968197
9968201
9968809
9968971
9969367
9969709
9969797
9990017
9990499
9991489
9991939
9992231
9992497
9993397
9994099
9994837
9995827
9995971
9999299
9999337
9999481
9999929
9999931


Daniele Caselli

unread,
Dec 14, 2008, 10:33:28 AM12/14/08
to
On 14/12/2008 dmn001 wrote:
>
> Here are a couple more:
>
> [...]

> 99133
> 99223
> 99241
>
> 1111181
> 1111703
> 1111897
> [...]

Thank you!!

Just to know: why did you exclude the 6 digits prime
numbers? Is there no 6 digits prime number which is also
a valid siteswap? It seems odd...

Daniele

--

«È bello scrivere perché riunisce le due gioie:
parlare da solo e parlare a una folla.»
Cesare Pavese


PinkNigel

unread,
Dec 14, 2008, 11:19:40 AM12/14/08
to
PinkNigel wrote:
> does 11 count as a siteswap?

Ah, well according to the auto-link whatsit it does. So there you go then..

dmn001

unread,
Dec 14, 2008, 12:06:11 PM12/14/08
to
On Dec 14, 3:33 pm, Daniele Caselli <eleinadNOSPAMPLE...@email.it>
wrote:

Given what Pinknigel said, and the fact that if a number is divisible
by 6, it is also divisible by 3.

PinkNigel

unread,
Dec 14, 2008, 12:57:44 PM12/14/08
to
dmn001 wrote:

> Given what Pinknigel said, and the fact that if a number is divisible
> by 6, it is also divisible by 3.
>
>

(I wasn't the first to point out the divisibility test thing for 3 and 9)

Anyone got any idea what's going on with the posts in this thread? Is it
me or are some of them hiding?

dmn001

unread,
Dec 14, 2008, 2:21:26 PM12/14/08
to

oops i meant thanks to chasemartin! :) I posted in google groups, it
may take a while for the other usenet servers to update.

Erik Jernqvist

unread,
Dec 14, 2008, 3:01:55 PM12/14/08
to
bill coad wrote:
>
> The 'words that are valid siteswaps' topic made me think about numeric
> subsets that are valid siteswaps. In siteswap theory, prime siteswaps
> have their own definition regarding comosition of other patterns.
> The question is, which prime numbers represent valid siteswap patterns and
> what's the largest known one? What's the one that uses the most objects?
> E.g. 94007 is a prime number and also a 4 ball pattern.
>

Of the first 10,000 prime numbers, these are valid siteswaps:
(http://primes.utm.edu/lists/small/10000.txt)
(http://multivac.fatburen.org/juggling/checkss/)

11
11161
11251
11279
11369
1151
11701
11779
1201
12011
1223
12241
1249
12511
12791
1289
13
13001
13399
13691
14249
14519
14753
1511
1559
1601
1609
16111
16229
1627
16319
16369
1663
16661
1667
16729
17
17011
17291
1753
17791
17863
18191
18353
18691
18803
18899
19
19069
19163
19249
1951
19753
1999
2
2011
20161
20201
20369
20611
2099
22277
22367
2239
22727
22777
22817
22961
23131
23339
23357
23627
23677
23857
23929
2411
24239
24419
24469
2459
24919
25111
25229
25819
2671
27277
27281
27367
27817
27961
28181
2819
28307
28429
2851
28627
28631
28807
28901
28979
29167
29207
29789
3
3001
30011
30223
3023
30241
30313
3041
3049
3067
30773
3089
31
31231
31277
31727
31817
33347
33577
33581
3373
33923
33941
34283
34297
3449
3463
3467
34747
34913
34963
35291
35363
3539
3571
35863
36277
36781
37
3733
3823
38333
3863
3881
38833
3889
38923
39233
3931
39733
40123
4013
40529
4057
40849
40853
4093


41131
41177
41357
41389
41479

41627
41681
42397
42473
42491
42577
4273
42923
44089
44449
44453
44507
4457
44633
44647
44683
4493
44953


45191
45641
45673
45691
45853

46181
46307
4637
46451
46681
4673
46807
46889
46901
47441
47491
47527
47581
4813
4817
49057
49499
49633
49697
49999
5
50069
50753
5119
51239
51257
51419
52067
5209
5227
52517
52567
52733
52747
52783
5281
52963
53
53089


53147
53197
53453
53507
53633

5393
55163
5519
55249
55663
55799
5591
56167
56207
5623
56239
5641
5689
5717
57283
57413
58057
58147
58403
58453
59
6011
6091
61729
61751
61819
62011
62273
6271
62723
62773
62791
63029
63079
63353
63691
63803
63853
64019
6451
64613
64663
6491
66161
66701
66751
6679
67061
67273
67511
67723
67741
68141
68399
68501
68899
6899
69019
69163
69203
7
7001
70111
70201
70229
7027
70729
71


72227
72277
72367
72461
72727
72817
72911
73

73127
73181
7333
73681
73951
74167
74257
74419
74707
7481
7489
75161
75611
75869
77317
77731
77867
7823
78307
78401
7841
78479
7867


78839
78857
78889
78901
78929
78979
79

79757
8017
80273
80363
8053
80863
8093
81281
81727
81817
8233
8237
8273
83077
83383
83423
83833
84017
84067
84247
84463
84913
85061
85223
85313
85363
86461
8677
88397
88423
88883
88897
8893
89017
89413
89567
89783
89797
89963
90001
90173
90191
90353
90529
90641
90803
91127
9151
91631
91807
91951
9199
92077
9209
9227
92333
92347
92383
9241
92581
9281
92941
9397
94007
94057
94903
94949
94999
9511
95191
9551
95803
9601
96181
9623
96401
96451
96479
9649
96857
9689
96979
97
97081
97397
97423
97441
97577
97847
97883
97973
99089
99133

Daniele Caselli

unread,
Dec 14, 2008, 3:04:08 PM12/14/08
to
On 14/12/2008 dmn001 wrote:
>
> Given what Pinknigel said, and the fact that if a
> number is divisible by 6, it is also divisible by 3.

Ops, sorry for the stupid question :)

Anyway in your list there are some prime numbers that
are not valid siteswaps: the "arithmetic mean rule"
is a necessary condition, but not also a sufficient
condition. Hence for example, taking from your list:
1111703 is a prime number but, even if its sum is 14
and its period 7, it is not a valid siteswap!

Daniele

--

«Tristo è quel discepolo che non avanza il suo
maestro.»
Leonardo da Vinci, Codice Forster III.


dmn001

unread,
Dec 14, 2008, 3:27:53 PM12/14/08
to
On Dec 14, 8:04 pm, Daniele Caselli <eleinadNOSPAMPLE...@email.it>
wrote:

Thanks for pointing that out! I will write a better algorithm to check
it.

Daniele Caselli

unread,
Dec 14, 2008, 3:33:41 PM12/14/08
to
On 14/12/2008 dmn001 wrote:

> On Dec 14, 5:57 pm, PinkNigel wrote:
>
>> Anyone got any idea what's going on with the posts in
>> this thread? Is it me or are some of them hiding?
>
> I posted in google groups, it may take a while for
> the other usenet servers to update.

My news server has been having some problem these days,
but I don't think this is correlated with the improper
functioning of news.gradwell.net, because Google Groups
instead has all the posts of this thread, as its usual...

http://groups.google.com/group/rec.juggling/browse_thread/thread/adc9f25b2e9d76bd

Dan

dmn001

unread,
Dec 14, 2008, 4:12:38 PM12/14/08
to
this list should be ok now, i checked a few with another siteswap
validator. all the prime siteswaps up to 10 million. there are 4522 of
them.

2
3
5
7
11
13
17
19
31
37
53
59
71
73
79
97
1151
1201
1223
1249
1289

1511
1559
1601
1609
1627
1663
1667
1753

1951
1999
2011
2099
2239
2411
2459
2671
2819
2851


3001
3023
3041
3049
3067
3089
3373
3449
3463
3467

3539
3571


3733
3823
3863
3881
3889
3931
4013
4057

4093
4273
4457
4493
4637
4673
4813
4817


5119
5209
5227
5281
5393
5519
5591
5623
5641
5689
5717

6011
6091


6271
6451
6491
6679
6899
7001
7027

7333
7481
7489
7823
7841
7867
8017
8053
8093
8233
8237
8273
8677
8893


9151
9199
9209
9227
9241
9281
9397

9511
9551
9601
9623
9649
9689

11161
11251
11279
11369
11701
11779
12011
12241
12511
12791
13001
13399
13691
14249
14519
14753
16111
16229
16319
16369
16661
16729
17011
17291


17791
17863
18191
18353
18691

18803
18899
19069
19163
19249
19753
20161
20201
20369
20611
22277
22367
22727
22777
22817
22961
23131
23339
23357
23627
23677
23857
23929
24239
24419
24469
24919
25111
25229
25819
27277
27281
27367
27817
27961
28181
28307
28429
28627
28631


28807
28901
28979
29167
29207
29789

30011
30223
30241
30313
30773
31231
31277
31727
31817
33347
33577
33581
33923
33941
34283
34297
34747
34913
34963
35291
35363
35863
36277
36781
38333
38833
38923
39233
39733
40123
40529
40849
40853


41131
41177
41357
41389
41479

41627
41681
42397
42473
42491
42577
42923
44089


44449
44453
44507
44633
44647
44683

44953


45191
45641
45673
45691
45853

46181
46307
46451
46681
46807
46889
46901
47441
47491
47527


47581
49057
49499
49633
49697

49999
50069
50753
51239
51257
51419
52067
52517
52567
52733
52747
52783
52963
53089


53147
53197
53453
53507
53633

55163
55249
55663
55799
56167
56207
56239
57283
57413
58057
58147
58403
58453
61729
61751
61819
62011
62273
62723
62773
62791
63029
63079
63353
63691
63803
63853
64019
64613
64663
66161
66701
66751
67061
67273
67511
67723
67741
68141
68399
68501
68899
69019
69163
69203
70111
70201
70229
70729
72227
72277
72367
72461
72727
72817
72911
73127
73181


73681
73951
74167
74257
74419
74707

75161
75611
75869
77317
77731
77867
78307
78401
78479


78839
78857
78889
78901
78929
78979

79757
80273
80363
80863
81281
81727
81817
83077
83383
83423
83833
84017
84067
84247


84463
84913
85061
85223
85313
85363
86461

88397
88423
88883
88897


89017
89413
89567
89783
89797
89963
90001
90173
90191
90353
90529

90641
90803
91127
91631
91807


91951
92077
92333
92347
92383

92581
92941
94007
94057
94903
94949
94999
95191
95803
96181
96401
96451
96479
96857
96979


97081
97397
97423
97441
97577
97847
97883
97973
99089
99133

1111181
1111897
1112011
1112081
1113701
1118197
1118827
1120271
1120811
1120901
1123151
1123601
1127111
1127197
1127881
1129951
1130011
1130081
1130711
1134667
1137781
1138681
1149661
1150777
1150867
1152667
1152757
1157077
1158607
1181197
1181881
1181897
1182781
1183771
1184077
1184867
1188197
1188307
1188377
1190201
1190897
1192357
1192951
1194157
1194857


1197181
1197197
1197307
1197827
1197881
1197901
1197971
1199357

1201111
1201201
1201307
1202027
1202081
1202261
1203161
1209367
1209781
1222241
1222597
1222993
1224203
1224577
1224973
1226111
1226377
1229581
1229597
1229941
1229993
1231313
1231511
1231597
1234747
1236727
1236797
1238383
1238597
1241893
1244003
1244863
1248193
1248571
1248893
1249363
1249741
1251577


1252963
1256707
1256777
1256867
1258183
1258847

1258903
1258973
1259047
1271111
1271197
1271201
1271827
1271971
1272367
1272961
1273001
1273771
1278181
1278197
1278811
1278881
1279027
1279081
1279727
1279961
1292293
1292383
1292597
1293373
1293841
1294273
1294973
1296181
1299223
1299941
1300111
1300127
1300181
1300307
1303151
1304857
1307197
1313141
1314113
1314883
1316881
1316971
1319293
1330223
1330313
1337293
1337383
1337527
1347893
1350203
1350847
1350883
1352557
1356857
1357183
1357507
1357883
1359647
1370111
1370197
1370377
1372627
1372951
1373851
1374157
1374677
1377127
1377377
1377811
1377881
1379251
1379681
1382527
1382597
1384507
1384813
1384847
1386181
1386271
1386377
1386811
1386881
1386901
1389347
1389383
1389511
1400081
1400261
1407011
1407727
1408697
1411313
1413793
1416011
1416097
1418581
1420511
1424557
1426627
1426951
1427347
1427383


1444753
1447561
1450747
1450963
1451557

1456057
1456667
1457083
1457783
1458253
1470727
1470797
1471681
1471697
1474757
1477027
1477081
1477097
1477711
1477961
1478251
1478357
1478611
1478627
1481527
1481993
1483561
1483793
1484047
1486081
1486097
1486367
1486711
1486781
1488241
1488581
1490347
1490527
1490941
1493623
1493641
1493693
1494253
1494557
1494613
1496251
1497313
1497347
1497511
1500071
1500701
1507771
1508671
1508851
1511303
1512023
1512041
1516771
1518571
1518893
1519363
1519561
1520501
1522693
1527893
1537561
1538353
1551853
1558673
1570771
1572751
1577071
1577701
1578851
1579051
1579751
1581193
1582363
1584703
1586161
1586771
1588141
1588193
1588303
1588841
1589363
1589561
1590373
1590893
1592623
1592693
1596851
1597823
1601857
1607867
1609667
1609757
1612747


1616077
1618973
1619713
1619747
1620973

1622557
1622953
1627147
1627883
1629253
1629557
1629647
1631557
1631647
1631683
1636667
1636757
1637963
1638683
1640773
1677167
1677707
1679057
1681903
1681973
1682047
1682567
1682713
1688147
1688903
1689263
1689713
1690847
1690883
1692253
1692683
1696157
1697903
1811377
1811827
1813001
1814167
1814777
1818307
1819261
1819711
1819781
1820111
1820201
1823671
1824607
1824677
1824857
1827127
1827181
1827197
1827271
1827307
1827901
1830011
1831681
1833751
1834667
1834757
1837027
1837097
1837727
1837961
1840771
1842661


1847071
1847701
1847861
1848151
1849051
1849751

1851677
1852057
1857707
1859057


1881127
1881181
1881197
1881307
1881811
1881881
1882081
1882367
1882781

1884007
1888307
1888897
1889011
1889081
1890827
1890901
1892357
1897127
1901201
1901377
1901897
1902097
1902367
1902961
1903861
1904167
1908197
1908971
1909027
1909081
1922383
1922923
1923841
1923893
1924147
1924903
1924973
1926377
1926811
1926901
1929527
1929581
1929923
1931383
1933363
1933741
1934263
1936027
1936097
1938383
1941193
1941571
1942363
1942723
1942793
1946701
1946771
1948571
1949023
1949741
1952047
1952567
1952747
1952963
1953163
1953863
1958183
1958813
1959047
1959263
1971127
1971181
1971377
1971901
1972097
1972781
1978111
1978181
1978201
1979261
1992241
1992527
1993193
1994203
1996901
1999223
1999511
1999993
2011111
2011127
2011201
2011811
2011897
2012011
2012027
2012711
2013001
2013071
2014867
2018111
2018827
2018897
2019011
2020181
2027111
2027897
2029697


2030081
2030711
2031251
2031611
2033051

2034757
2038951
2041601
2048671
2050007
2050777
2057777
2058157
2058607
2058677
2058857
2081377
2081897
2082097
2082727
2082961
2083001
2083771
2084777
2088881
2088901
2088971
2089727
2089781
2090111
2090197
2090827
2099611
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ordo.v

unread,
Dec 14, 2008, 5:07:07 PM12/14/08
to
bill coad wrote:
>
> The 'words that are valid siteswaps' topic made me think about numeric
> subsets that are valid siteswaps. In siteswap theory, prime siteswaps
> have their own definition regarding comosition of other patterns.
> The question is, which prime numbers represent valid siteswap patterns and
> what's the largest known one? What's the one that uses the most objects?
> E.g. 94007 is a prime number and also a 4 ball pattern.
>

Can we prove that there are infinitely many prime numbers that are vaild
siteswaps?

PinkNigel

unread,
Dec 14, 2008, 5:25:06 PM12/14/08
to
ordo.v wrote:
>
>
> Can we prove that there are infinitely many prime numbers that are vaild
> siteswaps?
>

I suspect that would look very much like the proof that there are
infinitely many primes.
However, given that the largest known primes run to many millions of
digits, who's going to be juggling
them? (It'd make a more interesting competition than 360s, that's for
sure...)

PinkNigel

unread,
Dec 15, 2008, 1:11:41 AM12/15/08
to
PinkNigel wrote:
>
> ordo.v wrote:
> >
> >
> > Can we prove that there are infinitely many prime numbers that are vaild
> > siteswaps?
> >
>
> I suspect that would look very much like the proof that there are
> infinitely many primes.
> However, given that the largest known primes run to many millions of
> digits, who's going to be juggling
> them? (It'd make a more interesting competition than 360s, that's for
> sure...)
>

And then another thought - If you accept that, say, 101 is valid as a 101
ball cascade, then the infinite
valid prime siteswap proof looks exactly like the infinite prime proof. So
the whole question needs
revising with an upper limit on the number of objects.

bill coad

unread,
Dec 15, 2008, 1:53:07 AM12/15/08
to

Since the alphabet is used for digits greater than nine, 101 wouldn't be
the standard representation for a 101 ball cascade.

Can we prove there are infinitely many prime numbers that AREN'T valid
siteswaps?

Guy G

unread,
Dec 15, 2008, 7:06:43 AM12/15/08
to
bill coad wrote:
>
> PinkNigel wrote:
> >
> > PinkNigel wrote:
> > >
> > > ordo.v wrote:
> > > >
> > > >
> > > > Can we prove that there are infinitely many prime numbers that are
vaild
> > > > siteswaps?
> > > >
> > >
> > > I suspect that would look very much like the proof that there are
> > > infinitely many primes.
> > > However, given that the largest known primes run to many millions of
> > > digits, who's going to be juggling
> > > them? (It'd make a more interesting competition than 360s, that's for
> > > sure...)
> > >
> >
> > And then another thought - If you accept that, say, 101 is valid as a 101
> > ball cascade, then the infinite
> > valid prime siteswap proof looks exactly like the infinite prime proof. So
> > the whole question needs
> > revising with an upper limit on the number of objects.
> >
>
> Since the alphabet is used for digits greater than nine, 101 wouldn't be
> the standard representation for a 101 ball cascade.

What would be the standard representation of a 101 ball cascade? Going
off ASCII 97 being 'a' (10), it could be ASCII 101+87 = ź. On the PC I'm
using, that's a bit like '1/4', but I'm not sure how universal extended
ASCII is. http://asciitable.com/ seems to suggest that there are
variations of the extended character set, and actually lists a different
character for ASCII 188.

Anyway, my point was that if you wanted to represent a 101 ball cascade,
you would in fact need to write it as "101" but state what your intentions
were. Of course it does feel like cheating, mostly because it makes the
problem too easy. Not that I'm going to solve the harder one, mind you.

Guy

bill coad

unread,
Dec 15, 2008, 12:24:10 PM12/15/08
to

Comvention has been to use letters when we run out of digits at 9.
Practical limits have most ignoring what happens when we run out of 26
letters in the alphabet (English). Ed Carstens' JuggloPro program
distinguishes between upper and lower case letters, giving 52 of them.
Add 10 numerical digits and still only get a limit of 62. Sciences have
often used the Greek alphabet and similiar solutions could resolve the 101
ball pattern problem.
Point is that the number of digits or characters in the pattern represent
the period of the pattern making 101 an invalid period 3 pattern. Within
practical limits there should always be a single character available to
represent a given throw height.
Finding prime numbered patterns inherently limits throw heights to 9,
since incorporating letters to denote higher throws in patterns results in
strings that aren't defined as prime or composite numbers.

Guy G

unread,
Dec 15, 2008, 12:39:53 PM12/15/08
to

Not a bad idea, although it has its limits. I'd probably go for writing
comma separated values for a high siteswap to properly separate the
numbers. Or maybe curly brackets

> Point is that the number of digits or characters in the pattern represent
> the period of the pattern making 101 an invalid period 3 pattern.

True, although this is a limitation of writing conventions w.r.t
siteswaps, rather than anything to do with the actual theory. I see no
reason why 101 cannot represent a 101 ball cascade, as long as it's made
clear that the convention is being broken.

> Within
> practical limits there should always be a single character available to
> represent a given throw height.

I seem to recall someone getting a 49-ish, 3, 1, 3, 1, etc. on video a
while back. It was done with a bounce ball. I forget how it was written
though.

> Finding prime numbered patterns inherently limits throw heights to 9

Now that's got me considering the distribution of number of patterns with
respect to number of balls. Or to phrase it differently "how many prime
number siteswaps can I do?"

Guy

AliTheJuggler

unread,
Dec 15, 2008, 2:55:33 PM12/15/08
to

http://uk.youtube.com/watch?v=AvmP97Pcflo&feature=PlayList&p=658CF563A3785B28&index=19

bill coad

unread,
Dec 15, 2008, 3:53:21 PM12/15/08
to

> > I seem to recall someone getting a 49-ish, 3, 1, 3, 1, etc. on video a
> > while back. It was done with a bounce ball. I forget how it was written
> > though.
> >
> > > Finding prime numbered patterns inherently limits throw heights to 9
> >
> > Now that's got me considering the distribution of number of patterns with
> > respect to number of balls. Or to phrase it differently "how many prime
> > number siteswaps can I do?"
> >
> > Guy
> >
>
>
http://uk.youtube.com/watch?v=AvmP97Pcflo&feature=PlayList&p=658CF563A3785B28&index=19
>

After about a half dozen cycles of the 31, he failed to make the next
catch before the ball hit the ground again. If repeated bounces are
allowed, a precise steel ball on a very smooth surface could possibly
yeild a million bounces.
That could easily be excluded be considering the bounce surface to be a
third hand in a passing pattern where each bounce would be a throw.
If you just want to get theoretical, you could take the largest prime
number followed by a long string of zero's and say that's a 1 ball
pattern. That's essentially a vacuous solution.

Scott Seltzer

unread,
Dec 15, 2008, 4:57:45 PM12/15/08
to
AliTheJuggler wrote:

>
> Guy G wrote:
> >
> > I seem to recall someone getting a 49-ish, 3, 1, 3, 1, etc. on video a
> > while back. It was done with a bounce ball. I forget how it was written
> > though.
> >
> >
>
>
http://uk.youtube.com/watch?v=AvmP97Pcflo&feature=PlayList&p=658CF563A3785B28&index=19
>


I could define my life as being in a permanent siteswap pattern consisting
of dropswaps, mostly 0s, lots of 2s, and the occasional throws. Simply
average out all those numbers (those dropswaps are huge), and you'll know
the number of objects I'm manipulating.

-Scott

Miika

unread,
Dec 17, 2008, 5:57:21 AM12/17/08
to

If the twin prime conjecture is true, it would follow that there are
infinately many primes whose digits don't sum to a multiple of the number
of those digits. The primes are a hard bunch of numbers to say anything
about, as even this "easier" question seems hard to answer.

As for the large cascade, I think it should depend on what base the
primes are written in. For example, in binary 11 is the only siteswap that
is also a prime.

Why are some messages in this thread still hiding at IJDb?


-Miika

--

(btw, tämä on sadasseitsemäskymmenesviides viestini tässä uutisryhmässä.)

Daniele Caselli

unread,
Dec 17, 2008, 2:21:44 PM12/17/08
to
On 17/12/2008 Miika wrote:
>
> Why are some messages in this thread still hiding at
> IJDb?

Console yourself thinking that they were only hided:
sometimes news.gradwell.net *loses* some posts,
as Colin already know...

Dan

--

«Quelli di Tian'anmen erano veramente dei ragazzi
poveretti, sedotti da mitologie occidentali, un poco come
quelli che esultarono quando cadde il muro; ma insomma,
erano dei ragazzi che volevano la Coca-Cola.»
Edoardo Sanguineti, intervistato da La7 provoca


ordo.v

unread,
Dec 17, 2008, 9:20:15 PM12/17/08
to
PinkNigel wrote:
>
> PinkNigel wrote:
> >
> > ordo.v wrote:
> > >
> > >
> > > Can we prove that there are infinitely many prime numbers that are vaild
> > > siteswaps?
> > >
> >
> > I suspect that would look very much like the proof that there are
> > infinitely many primes.
> > However, given that the largest known primes run to many millions of
> > digits, who's going to be juggling
> > them? (It'd make a more interesting competition than 360s, that's for
> > sure...)
> >
>
> And then another thought - If you accept that, say, 101 is valid as a 101
> ball cascade,

That way ever number is a valid siteswap.

ordo.v

unread,
Dec 18, 2008, 6:12:30 AM12/18/08
to

Nice observation.

If we assume that the repunit prime conjecture [1] is true then there are
infinitely many primes that are siteswaps. Simply pick the primes from the
sequence 1, 11, 111, 1111, ......

[1] http://primes.utm.edu/glossary/page.php?sort=Repunit

sje...@gmail.com

unread,
Dec 18, 2008, 8:17:48 AM12/18/08
to
It does no one any good to "ask" why something seems interesting, it
is more a complaint than a real inquiry. But the lists, which had to
be corrected, are to me so useless as to be offensive. A person did
not compile it, and there is nothing for a person to do with it, so
why load the archives with all that text about nothing?

There have been siteswap generators for a long time. And many people
really do, apparently, go through those previous lists to try out some
of the possibilities. And there really are people who have in that
way, or some other, learned to do bizarre collections of tosses,
including bouncing with multiplex for an extreme example, and
'db97531' which cannot be exceeded, imo, either for results or actual
possibility. Fine, for them, if they like, and can do, that sort of
thing. Meanwhile, there is a man, whose video was posted here at the
same time, who makes a nice enough career juggling balls and baseball
bats in the same patterns used by jugglers shown on ancient Greek
pottery and by the infamous Chris Bliss with different music. And the
music was more interesting to some people posting here than the
patterns.

What interests me more is what makes a pattern "interesting" enough
for someone to try to do it. One person's post in this topic shows a
short list, culled from the thousands, as if those would be good
ones. Ok, now, Why? Or, since to me those are dogs for being all
ones and a single too-high toss, why not? How could anyone ever make
any use of such lists, as Matt Hall, for instance, reduced to a crude
webpage many years ago? You can get short and color-coded categorized
lists from the Raspini Project, but who has done them all and so needs
more than that? The generator for Juggling Lab's animator makes lists
by criteria, which this latest list does not include, such as number
of balls, longest period, highest toss value, etc. Again, so what?
What makes any of those the one you would choose to slave away at, and
maybe eventually include in another of the thousands of videos that
few people would ever see anyway -- and then only want the name of the
song?

Quantity, there has been too much of for too long already, already.
Quality?

-

Peter Bone

unread,
Dec 18, 2008, 8:49:02 AM12/18/08
to
bill coad wrote:
>
> The 'words that are valid siteswaps' topic made me think about numeric
> subsets that are valid siteswaps. In siteswap theory, prime siteswaps
> have their own definition regarding comosition of other patterns.
> The question is, which prime numbers represent valid siteswap patterns and
> what's the largest known one? What's the one that uses the most objects?
> E.g. 94007 is a prime number and also a 4 ball pattern.
>

The biggest 8 digit prime ss is
99994277
Other interesting ones are
11111119
99991999

Guy G

unread,
Dec 18, 2008, 8:53:14 AM12/18/08
to

A fantastic closing line. Very funny indeed.

Guy

bill coad

unread,
Dec 18, 2008, 9:43:05 AM12/18/08
to
111 isn't prime, 3*37.

>
> [1] http://primes.utm.edu/glossary/page.php?sort=Repunit
>
The conjecture is that there are infinitely many repunit primes but this
link says there are only 5 known repunit primes, all of which are valid
siteswaps.

bill coad

unread,
Dec 18, 2008, 9:52:01 AM12/18/08
to

Color coded cards were from the Gandini Project. The ones I made long ago
weren't colored, and yes - most of my bouncing patterns are multiplex.

Peter Bone

unread,
Dec 18, 2008, 10:32:57 AM12/18/08
to

The first 10 digit prime ss is
1111112291
The first 10 digit prime ss for more than 2 balls is
1111153999
I may actually try this with every other 1 behind the back.

Erik Jernqvist

unread,
Dec 18, 2008, 11:04:04 AM12/18/08
to
Miika wrote:

> As for the large cascade, I think it should depend on what base the
> primes are written in. For example, in binary 11 is the only siteswap that
> is also a prime.

Every Mersenne prime in binary is also a siteswap (in any base you want
since it's just ones). However, the number of Mersenne primes are unknown.

Miika

unread,
Dec 18, 2008, 6:49:03 PM12/18/08
to
Erik Jernqvist wrote:
>
> Miika wrote:
>
> > As for the large cascade, I think it should depend on what base the
> > primes are written in. For example, in binary 11 is the only siteswap that
> > is also a prime.
>
> Every Mersenne prime in binary is also a siteswap (in any base you want
> since it's just ones). However, the number of Mersenne primes are unknown.
>

Thanks for catching that. I was thinking too fast.


bill coad wrote:
>
> Can we prove there are infinitely many prime numbers that AREN'T valid
> siteswaps?
>

So I was doing the dishes and I thought of an idea for a proof of how
siteswaps can't form arithmetic progression like primes can. This ended up
being too complicated for the task at hand because I stumbled onto a
simpler idea:

As previously stated in this thread, if the length of a siteswap is
divisible by three (and since the digits must sum to a multiple of the
length), then this number is divisible by three and is not a prime. This
means that for any number with 3k digits (the numbers between the
10^(3k-1) and 10^(3k) ) there can't be any primes that are siteswaps. On
the other hand, there is always a prime number between n and 2n, so there
are other types of primes in the range given above (see
http://mathworld.wolfram.com/BertrandsPostulate.html ). Consequently there
are infinately many primes that are not siteswaps.


Hopefully not thinking too fast,


-Miika

--

(btw, tämä on sadasseitsemäskymmenesyhdeksäs viestini tässä
uutisryhmässä.)

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