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Old 2022-07-16, 12:28   #1761
EdH
 
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Quote:
Originally Posted by garambois View Post
Page updated.
. . .
The removal of yoyo reservations has freed up sequences of matched parity.
. . .
My scripts were already disregarding the table reservations for yoyo and using the ali.txt.all page to confirm reservations, so I'm not sure this will change my lists in the other thread, but it will be more clear when doing manual verifications now.

Thank you for all the work. I'll update my scripts with the additions and see what things look like today.
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Old 2022-07-18, 15:20   #1762
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Quote:
Originally Posted by garambois View Post
I have serious problems with CADO-NFS when the "Info:Linear Algebra: lingen ETA: not available yet" part starts.
. . .
Quote:
Originally Posted by VBCurtis View Post
I have the same problem- even one other thread running makes lingen take hours rather than minutes.
. . .
Possibly Good news! The CADO-NFS Team has pointed me to the environment variable OMP_DYNAMIC. Try the following command in the CADO-NFS terminal prior to running the cado-nfs.py command:
Code:
export OMP_DYNAMIC=true
Let me know if this helps with the issue.

Thank you to the CADO-NFS team!
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Old 2022-07-18, 15:46   #1763
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Quote:
Originally Posted by sweety439 View Post
Also, you can add a new category “Lehmer five”, including bases 276, 552, 564, 660, 966
Quote:
Originally Posted by garambois View Post
We had already discussed this a long time ago.
This category may not be final, so we will not add it.
This was the original intent of the "Open" tab, so if we're not adding a category for currently open sequences, can we have that tab deleted? Even an alternative analysis of its meaning as "bases with open exponents" fails, as it includes double-square bases which are complete for our purposes.

---------

Unrelated, I have poached 38^19, 54^67, and 41^68 from yoyo and terminated them. More possibly to come.

Last fiddled with by Happy5214 on 2022-07-18 at 15:47 Reason: Terminated sequences
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Old 2022-07-18, 16:54   #1764
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Quote:
Originally Posted by EdH View Post
Try the following command in the CADO-NFS terminal prior to running the cado-nfs.py command:...
I will try this very quickly, thank you very much !
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Old 2022-07-18, 16:56   #1765
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Quote:
Originally Posted by Happy5214 View Post
Even an alternative analysis of its meaning as "bases with open exponents" fails, as it includes double-square bases which are complete for our purposes.
This will be fixed in the next update.
Thank you for reporting it.
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Old 2022-07-18, 18:02   #1766
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4-for-4 on poached yoyo sequences today:

Code:
57^62:i2117 merges with 77840:i1
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Old 2022-07-19, 09:10   #1767
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Another termination (67^74) and another merge (below) by me from poached yoyo sequences:

Code:
56^33:i3561 merges with 87612:i4
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Old 2022-07-20, 07:56   #1768
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Many thanks Happy, these mergers will appear on the page when it is next updated.
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Old 2022-07-20, 09:45   #1769
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Information on the summer works in progress


Last year, in post #1360, I presented lists of points to place on a graph. There was a list for each prime number less than 100. I placed these points on a graph and looked at the graph to see if a straight line, or a regular curve, was drawn. I didn't see anything.
I was not at all satisfied, because I would have liked to have a program that would analyze this numerical data to automatically find preferred lines or curves on which many of these points would be placed.
Hence my question in post #1756.
So naturally I tried to write a program to do this job and after several days I found a fairly simple idea that seems to work at least for polynomial forms.
Let's take the example of the set of points for the prime number 3 from post #1360.
Code:
[[2, 2], [2, 4], [2, 55], [2, 164], [2, 305], [2, 317], [3, 1], [3, 2], [3, 5], [3, 247], [5, 38], [6, 152], [7, 4], [7, 77], [10, 124], [11, 2], [11, 15], [12, 1], [12, 2], [13, 15], [14, 76], [14, 80], [15, 1], [19, 15], [20, 2], [20, 8], [21, 21], [21, 55], [22, 80], [23, 3], [26, 1], [29, 2], [29, 69], [30, 1], [30, 82], [30, 92], [31, 79], [33, 1], [35, 49], [37, 11], [38, 11], [38, 30], [40, 14], [41, 2], [42, 1], [43, 15], [44, 58], [45, 1], [45, 34], [46, 1], [47, 13], [50, 73], [52, 1], [52, 34], [53, 2], [53, 27], [53, 30], [54, 1], [54, 10], [55, 53], [58, 18], [59, 49], [66, 1], [72, 1], [74, 6], [74, 20], [75, 45], [79, 97], [98, 45]]
I briefly recall what this data means : the sequences 2^2, 2^4, 2^55, ... 3^1, 3^2, 3^5, ... 98^45 end with the prime number 3.
My program tests all polynomials a*x^2+b*x+c.
And the program searches in this list all points that lie exactly on the curves that have these polynomials as equations.
Here is the result below, when I ran the program to test all polynomials with all integer values for a, b and c such that |a|<=20, |b|<=40, |c|<=1000 :
Code:
a = -20 / 20
a = -19 / 20
a = -18 / 20
...
nothing
...
a = -4 / 20
count = 3 for f = -3*x^2 + 21*x + 134    [[2, 164], [6, 152], [11, 2]]
a = -3 / 20
count = 3 for f = -2*x^2 + 26*x + -42    [[2, 2], [5, 38], [11, 2]]
a = -2 / 20
count = 3 for f = -1*x^2 + 24*x + -42    [[2, 2], [7, 77], [21, 21]]
count = 3 for f = -1*x^2 + 29*x + -77    [[3, 1], [7, 77], [26, 1]]
count = 3 for f = -1*x^2 + 32*x + -232    [[13, 15], [19, 15], [20, 8]]
count = 3 for f = -1*x^2 + 36*x + -98    [[3, 1], [30, 82], [33, 1]]
count = 3 for f = -1*x^2 + 39*x + -323    [[12, 1], [13, 15], [21, 55]]
a = -1 / 20
count = 3 for f = 0*x^2 + -13*x + 262    [[14, 80], [19, 15], [20, 2]]
count = 3 for f = 0*x^2 + -4*x + 105    [[7, 77], [21, 21], [26, 1]]
count = 3 for f = 0*x^2 + -3*x + 154    [[10, 124], [35, 49], [47, 13]]
count = 3 for f = 0*x^2 + -3*x + 172    [[30, 82], [31, 79], [54, 10]]
count = 3 for f = 0*x^2 + -1*x + 43    [[5, 38], [41, 2], [42, 1]]
count = 13 for f = 0*x^2 + 0*x + 1    [[3, 1], [12, 1], [15, 1], [26, 1], [30, 1], [33, 1], [42, 1], [45, 1], [46, 1], [52, 1], [54, 1], [66, 1], [72, 1]]
count = 8 for f = 0*x^2 + 0*x + 2    [[2, 2], [3, 2], [11, 2], [12, 2], [20, 2], [29, 2], [41, 2], [53, 2]]
count = 4 for f = 0*x^2 + 0*x + 15    [[11, 15], [13, 15], [19, 15], [43, 15]]
count = 3 for f = 0*x^2 + 1*x + -26    [[37, 11], [40, 14], [53, 27]]
count = 3 for f = 0*x^2 + 1*x + 2    [[2, 4], [3, 5], [13, 15]]
count = 3 for f = 0*x^2 + 3*x + -8    [[3, 1], [21, 55], [30, 82]]
a = 0 / 20
count = 3 for f = 1*x^2 + -37*x + 301    [[11, 15], [12, 1], [29, 69]]
count = 3 for f = 1*x^2 + -31*x + 222    [[2, 164], [11, 2], [20, 2]]
count = 3 for f = 1*x^2 + -27*x + 181    [[12, 1], [15, 1], [21, 55]]
count = 3 for f = 1*x^2 + -22*x + 42    [[2, 2], [20, 2], [21, 21]]
a = 1 / 20
count = 3 for f = 2*x^2 + -9*x + 14    [[2, 4], [3, 5], [10, 124]]
a = 2 / 20
count = 3 for f = 3*x^2 + -12*x + 14    [[2, 2], [3, 5], [7, 77]]
a = 3 / 20
count = 3 for f = 4*x^2 + -21*x + 28    [[2, 2], [3, 1], [7, 77]]
a = 4 / 20
a = 5 / 20
count = 3 for f = 6*x^2 + -30*x + 38    [[2, 2], [3, 2], [5, 38]]
a = 6 / 20
a = 7 / 20
...
nothing
...
a = 19 / 20
a = 20 / 20
"count" is the number of points in the list that are on the curve for the polynomial and I only display the polynomials if count>=3.
Most of the time count=3. This is certainly due to chance.
Even if count=4, it must certainly be due to chance, but it is rarer.
On the other hand, if count>4, it is certainly something other than random.
But this is only the case for a=0 and b=0, i.e. for a polynomial which is a constant, here 1 (count=13) and 2 (count=8).
The count=4 occurs for the constant 15.
Of course, if I take the example of count=13, I see that I get a sequence of bases b, such that for b^1, the sequences end with the prime number 3 : 3, 12, 15, 26, 30...
If I take the example of count=8, I see that I get a sequence of bases b, such that for b^2, the sequences end with the prime number 3 : 2, 3, 11, 12 ,20...
I then enter these sequences of integers in the OEIS and... NOTHING ! Unknown sequences !

I also tested the program with polynomials of degree 3, d*x^3+a*x^2+b*x+c, here is the result for d, a, b and c such that |d|<=10, |a|<=10, |b|<=40, |c|<=500 :
Code:
d = -10 / 10    a = -10 / 10
d = -10 / 10    a = -9 / 10
...
nothing
...
d = -1 / 10    a = 8 / 10
d = -1 / 10    a = 9 / 10
count = 3 for f = -1*x^3 + 10*x^2 + -1*x + 134    [[2, 164], [10, 124], [11, 2]]
count = 3 for f = -1*x^3 + 10*x^2 + 23*x + -130    [[3, 2], [6, 152], [11, 2]]
d = -1 / 10    a = 10 / 10
d = 0 / 10    a = -10 / 10
d = 0 / 10    a = -9 / 10
d = 0 / 10    a = -8 / 10
d = 0 / 10    a = -7 / 10
d = 0 / 10    a = -6 / 10
d = 0 / 10    a = -5 / 10
d = 0 / 10    a = -4 / 10
count = 3 for f = 0*x^3 + -3*x^2 + 21*x + 134    [[2, 164], [6, 152], [11, 2]]
d = 0 / 10    a = -3 / 10
count = 3 for f = 0*x^3 + -2*x^2 + 26*x + -42    [[2, 2], [5, 38], [11, 2]]
d = 0 / 10    a = -2 / 10
count = 3 for f = 0*x^3 + -1*x^2 + 24*x + -42    [[2, 2], [7, 77], [21, 21]]
count = 3 for f = 0*x^3 + -1*x^2 + 29*x + -77    [[3, 1], [7, 77], [26, 1]]
count = 3 for f = 0*x^3 + -1*x^2 + 32*x + -232    [[13, 15], [19, 15], [20, 8]]
count = 3 for f = 0*x^3 + -1*x^2 + 36*x + -98    [[3, 1], [30, 82], [33, 1]]
count = 3 for f = 0*x^3 + -1*x^2 + 39*x + -323    [[12, 1], [13, 15], [21, 55]]
d = 0 / 10    a = -1 / 10
count = 3 for f = 0*x^3 + 0*x^2 + -13*x + 262    [[14, 80], [19, 15], [20, 2]]
count = 3 for f = 0*x^3 + 0*x^2 + -4*x + 105    [[7, 77], [21, 21], [26, 1]]
count = 3 for f = 0*x^3 + 0*x^2 + -3*x + 154    [[10, 124], [35, 49], [47, 13]]
count = 3 for f = 0*x^3 + 0*x^2 + -3*x + 172    [[30, 82], [31, 79], [54, 10]]
count = 3 for f = 0*x^3 + 0*x^2 + -1*x + 43    [[5, 38], [41, 2], [42, 1]]
count = 13 for f = 0*x^3 + 0*x^2 + 0*x + 1    [[3, 1], [12, 1], [15, 1], [26, 1], [30, 1], [33, 1], [42, 1], [45, 1], [46, 1], [52, 1], [54, 1], [66, 1], [72, 1]]
count = 8 for f = 0*x^3 + 0*x^2 + 0*x + 2    [[2, 2], [3, 2], [11, 2], [12, 2], [20, 2], [29, 2], [41, 2], [53, 2]]
count = 4 for f = 0*x^3 + 0*x^2 + 0*x + 15    [[11, 15], [13, 15], [19, 15], [43, 15]]
count = 3 for f = 0*x^3 + 0*x^2 + 1*x + -26    [[37, 11], [40, 14], [53, 27]]
count = 3 for f = 0*x^3 + 0*x^2 + 1*x + 2    [[2, 4], [3, 5], [13, 15]]
count = 3 for f = 0*x^3 + 0*x^2 + 3*x + -8    [[3, 1], [21, 55], [30, 82]]
d = 0 / 10    a = 0 / 10
count = 3 for f = 0*x^3 + 1*x^2 + -37*x + 301    [[11, 15], [12, 1], [29, 69]]
count = 3 for f = 0*x^3 + 1*x^2 + -31*x + 222    [[2, 164], [11, 2], [20, 2]]
count = 3 for f = 0*x^3 + 1*x^2 + -27*x + 181    [[12, 1], [15, 1], [21, 55]]
count = 3 for f = 0*x^3 + 1*x^2 + -22*x + 42    [[2, 2], [20, 2], [21, 21]]
d = 0 / 10    a = 1 / 10
count = 3 for f = 0*x^3 + 2*x^2 + -9*x + 14    [[2, 4], [3, 5], [10, 124]]
d = 0 / 10    a = 2 / 10
count = 3 for f = 0*x^3 + 3*x^2 + -12*x + 14    [[2, 2], [3, 5], [7, 77]]
d = 0 / 10    a = 3 / 10
count = 3 for f = 0*x^3 + 4*x^2 + -21*x + 28    [[2, 2], [3, 1], [7, 77]]
d = 0 / 10    a = 4 / 10
d = 0 / 10    a = 5 / 10
count = 3 for f = 0*x^3 + 6*x^2 + -30*x + 38    [[2, 2], [3, 2], [5, 38]]
d = 0 / 10    a = 6 / 10
d = 0 / 10    a = 7 / 10
d = 0 / 10    a = 8 / 10
d = 0 / 10    a = 9 / 10
d = 0 / 10    a = 10 / 10
count = 3 for f = 1*x^3 + -10*x^2 + -9*x + 214    [[2, 164], [7, 4], [10, 124]]
d = 1 / 10    a = -10 / 10
count = 3 for f = 1*x^3 + -9*x^2 + -18*x + 228    [[2, 164], [5, 38], [7, 4]]
count = 3 for f = 1*x^3 + -9*x^2 + 29*x + -28    [[2, 2], [3, 5], [7, 77]]
d = 1 / 10    a = -9 / 10
count = 3 for f = 1*x^3 + -8*x^2 + 20*x + -14    [[2, 2], [3, 1], [7, 77]]
d = 1 / 10    a = -8 / 10
d = 1 / 10    a = -7 / 10
d = 1 / 10    a = -6 / 10
d = 1 / 10    a = -5 / 10
count = 3 for f = 1*x^3 + -4*x^2 + 1*x + 8    [[2, 2], [3, 2], [5, 38]]
d = 1 / 10    a = -4 / 10
d = 1 / 10    a = -3 / 10
d = 1 / 10    a = -2 / 10
d = 1 / 10    a = -1 / 10
d = 1 / 10    a = 0 / 10
count = 3 for f = 1*x^3 + 1*x^2 + -23*x + 38    [[2, 4], [3, 5], [6, 152]]
d = 1 / 10    a = 1 / 10
count = 3 for f = 1*x^3 + 2*x^2 + -31*x + 50    [[2, 4], [3, 2], [6, 152]]
d = 1 / 10    a = 2 / 10
d = 1 / 10    a = 3 / 10
d = 1 / 10    a = 4 / 10
d = 1 / 10    a = 5 / 10
d = 1 / 10    a = 6 / 10
d = 1 / 10    a = 7 / 10
d = 1 / 10    a = 8 / 10
d = 1 / 10    a = 9 / 10
d = 1 / 10    a = 10 / 10
count = 3 for f = 2*x^3 + -10*x^2 + 13*x + 2    [[2, 4], [3, 5], [6, 152]]
d = 2 / 10    a = -10 / 10
count = 3 for f = 2*x^3 + -9*x^2 + 5*x + 14    [[2, 4], [3, 2], [6, 152]]
d = 2 / 10    a = -9 / 10
d = 2 / 10    a = -8 / 10
...
nothing
...
d = 10 / 10    a = 9 / 10
d = 10 / 10    a = 10 / 10
Of course, for d=0, we find the results of before for the polynomials of the second degree.

I am doing some tests of this program to develop an intuition that will allow me to notice interesting things, if there are any !
I have also done some tests for other forms of equations than polynomials : b*a^x+c, but it didn't give anything interesting.
I don't know what other form of equation I should try ?
I'm open to suggestions !



Let me introduce another idea.


I have taken all the data from post #1360.
And I have presented them differently, here is how :
Code:
[(2, 2, 1), (3, 2, 2), (3, 2, 4), (3, 2, 55), (3, 2, 164), (3, 2, 305), (3, 2, 317), (3, 3, 1), (3, 3, 2), (3, 3, 5), (3, 3, 247), (3, 5, 38), (3, 6, 152), (3, 7, 4), (3, 7, 77), (3, 10, 124), (3, 11, 2), (3, 11, 15), (3, 12, 1), (3, 12, 2), (3, 13, 15), (3, 14, 76), (3, 14, 80), (3, 15, 1), (3, 19, 15), (3, 20, 2), (3, 20, 8), (3, 21, 21), (3, 21, 55), (3, 22, 80), (3, 23, 3), (3, 26, 1), (3, 29, 2), (3, 29, 69), (3, 30, 1), (3, 30, 82), (3, 30, 92), (3, 31, 79), (3, 33, 1), (3, 35, 49), (3, 37, 11), (3, 38, 11), (3, 38, 30), (3, 40, 14), (3, 41, 2), (3, 42, 1), (3, 43, 15), (3, 44, 58), (3, 45, 1), (3, 45, 34), (3, 46, 1), (3, 47, 13), (3, 50, 73), (3, 52, 1), (3, 52, 34), (3, 53, 2), (3, 53, 27), (3, 53, 30), (3, 54, 1), (3, 54, 10), (3, 55, 53), (3, 58, 18), (3, 59, 49), (3, 66, 1), (3, 72, 1), (3, 74, 6), (3, 74, 20), (3, 75, 45), (3, 79, 97), (3, 98, 45), (5, 5, 1), (7, 2, 3), (7, 2, 10), (7, 2, 12), (7, 2, 141), (7, 2, 278), (7, 2, 387), (7, 2, 421), (7, 3, 6), (7, 3, 8), (7, 3, 118), (7, 3, 198), (7, 3, 305), (7, 7, 1), (7, 7, 2), (7, 7, 8), (7, 7, 127), (7, 10, 1), (7, 11, 5), (7, 12, 21), (7, 13, 2), (7, 13, 87), (7, 14, 1), (7, 14, 19), (7, 14, 21), (7, 15, 10), (7, 17, 24), (7, 17, 91), (7, 18, 13), (7, 18, 52), (7, 18, 70), (7, 19, 2), (7, 20, 1), (7, 21, 8), (7, 21, 17), (7, 22, 1), (7, 22, 19), (7, 23, 11), (7, 26, 3), (7, 26, 19), (7, 26, 50), (7, 26, 80), (7, 28, 9), (7, 28, 47), (7, 30, 52), (7, 30, 70), (7, 34, 1), (7, 34, 7), (7, 34, 9), (7, 35, 11), (7, 37, 2), (7, 38, 1), (7, 38, 13), (7, 40, 2), (7, 41, 49), (7, 42, 2), (7, 43, 20), (7, 45, 4), (7, 45, 55), (7, 46, 33), (7, 47, 8), (7, 47, 42), (7, 48, 61), (7, 50, 17), (7, 53, 8), (7, 56, 38), (7, 58, 5), (7, 58, 27), (7, 61, 2), (7, 62, 1), (7, 66, 5), (7, 68, 10), (7, 72, 25), (7, 74, 11), (7, 75, 1), (7, 75, 63), (7, 79, 7), (11, 2, 60), (11, 2, 316), (11, 2, 480), (11, 2, 499), (11, 3, 15), (11, 3, 189), (11, 3, 303), (11, 5, 15), (11, 7, 143), (11, 10, 20), (11, 11, 1), (11, 11, 137), (11, 13, 31), (11, 14, 14), (11, 14, 28), (11, 17, 2), (11, 18, 1), (11, 18, 55), (11, 18, 76), (11, 21, 1), (11, 21, 47), (11, 24, 2), (11, 26, 36), (11, 35, 83), (11, 37, 50), (11, 47, 47), (11, 51, 1), (11, 53, 15), (11, 53, 67), (11, 58, 2), (11, 58, 24), (11, 65, 2), (11, 65, 33), (11, 67, 3), (11, 72, 4), (11, 72, 58), (11, 72, 63), (11, 79, 3), (11, 98, 2), (13, 2, 358), (13, 3, 3), (13, 3, 31), (13, 3, 67), (13, 5, 9), (13, 11, 3), (13, 11, 27), (13, 13, 1), (13, 20, 72), (13, 23, 49), (13, 23, 77), (13, 24, 70), (13, 35, 1), (13, 38, 86), (13, 43, 3), (13, 43, 17), (13, 50, 62), (13, 56, 8), (13, 62, 2), (13, 75, 13), (13, 79, 23), (17, 3, 63), (17, 6, 2), (17, 7, 55), (17, 13, 21), (17, 15, 79), (17, 17, 1), (17, 19, 97), (17, 23, 2), (17, 24, 1), (17, 24, 4), (17, 38, 42), (17, 39, 1), (17, 45, 5), (17, 46, 10), (17, 51, 31), (17, 55, 1), (17, 58, 70), (17, 60, 28), (19, 2, 39), (19, 2, 76), (19, 2, 190), (19, 2, 219), (19, 2, 505), (19, 3, 275), (19, 5, 233), (19, 10, 2), (19, 10, 12), (19, 10, 44), (19, 12, 4), (19, 13, 3), (19, 13, 141), (19, 15, 21), (19, 19, 1), (19, 22, 32), (19, 40, 6), (19, 41, 7), (19, 42, 10), (19, 42, 22), (19, 45, 15), (19, 55, 29), (19, 60, 30), (19, 65, 1), (19, 72, 74), (19, 79, 13), (19, 98, 6), (23, 3, 12), (23, 3, 181), (23, 7, 3), (23, 7, 9), (23, 11, 127), (23, 17, 79), (23, 18, 6), (23, 18, 17), (23, 18, 64), (23, 21, 61), (23, 23, 1), (23, 40, 36), (23, 44, 68), (23, 47, 3), (23, 55, 15), (23, 57, 1), (23, 57, 17), (23, 65, 3), (23, 74, 64), (23, 79, 49), (29, 5, 41), (29, 14, 92), (29, 18, 50), (29, 18, 116), (29, 22, 8), (29, 26, 68), (29, 29, 1), (29, 46, 36), (29, 47, 39), (29, 48, 4), (29, 61, 5), (29, 63, 67), (29, 72, 43), (31, 2, 5), (31, 2, 101), (31, 2, 146), (31, 3, 169), (31, 5, 3), (31, 5, 161), (31, 6, 17), (31, 11, 38), (31, 11, 93), (31, 11, 107), (31, 12, 14), (31, 19, 35), (31, 19, 37), (31, 31, 1), (31, 31, 2), (31, 31, 11), (31, 40, 30), (31, 44, 30), (31, 56, 52), (31, 58, 1), (31, 61, 55), (31, 67, 2), (31, 68, 1), (31, 74, 21), (31, 98, 3), (37, 2, 68), (37, 2, 125), (37, 2, 243), (37, 3, 90), (37, 5, 4), (37, 7, 6), (37, 7, 79), (37, 10, 3), (37, 10, 5), (37, 10, 74), (37, 11, 40), (37, 12, 98), (37, 14, 2), (37, 14, 35), (37, 22, 7), (37, 22, 21), (37, 22, 23), (37, 22, 74), (37, 23, 10), (37, 24, 6), (37, 26, 31), (37, 28, 3), (37, 28, 11), (37, 29, 50), (37, 35, 2), (37, 37, 1), (37, 42, 16), (37, 44, 3), (37, 44, 19), (37, 45, 11), (37, 47, 16), (37, 51, 2), (37, 53, 87), (37, 55, 43), (37, 63, 3), (37, 74, 5), (37, 75, 8), (37, 79, 6), (41, 2, 6), (41, 2, 8), (41, 2, 23), (41, 2, 47), (41, 2, 112), (41, 2, 117), (41, 2, 281), (41, 2, 373), (41, 2, 405), (41, 2, 411), (41, 6, 5), (41, 6, 13), (41, 7, 11), (41, 11, 14), (41, 11, 57), (41, 12, 32), (41, 12, 56), (41, 12, 119), (41, 15, 2), (41, 15, 6), (41, 17, 65), (41, 18, 39), (41, 20, 3), (41, 24, 18), (41, 33, 2), (41, 35, 8), (41, 35, 34), (41, 37, 20), (41, 37, 73), (41, 38, 54), (41, 40, 11), (41, 40, 20), (41, 40, 21), (41, 40, 52), (41, 41, 1), (41, 42, 5), (41, 43, 25), (41, 43, 81), (41, 44, 49), (41, 45, 8), (41, 45, 22), (41, 45, 36), (41, 47, 2), (41, 48, 1), (41, 48, 3), (41, 50, 16), (41, 51, 18), (41, 52, 25), (41, 55, 21), (41, 56, 1), (41, 57, 2), (41, 59, 39), (41, 61, 9), (41, 62, 3), (41, 62, 13), (41, 62, 40), (41, 63, 1), (41, 65, 4), (41, 66, 25), (41, 75, 2), (41, 79, 2), (41, 79, 4), (41, 79, 17), (41, 98, 10), (41, 98, 41), (43, 2, 9), (43, 2, 62), (43, 2, 210), (43, 2, 271), (43, 2, 510), (43, 3, 4), (43, 3, 22), (43, 3, 80), (43, 3, 86), (43, 6, 26), (43, 6, 32), (43, 6, 77), (43, 7, 16), (43, 7, 28), (43, 7, 51), (43, 10, 42), (43, 11, 13), (43, 11, 28), (43, 11, 56), (43, 13, 4), (43, 13, 8), (43, 13, 40), (43, 13, 95), (43, 13, 98), (43, 14, 5), (43, 14, 23), (43, 14, 25), (43, 15, 14), (43, 17, 12), (43, 17, 16), (43, 17, 101), (43, 18, 34), (43, 19, 4), (43, 19, 55), (43, 20, 21), (43, 20, 70), (43, 21, 2), (43, 21, 6), (43, 21, 98), (43, 22, 2), (43, 23, 4), (43, 24, 10), (43, 24, 19), (43, 24, 31), (43, 24, 36), (43, 26, 6), (43, 26, 38), (43, 26, 78), (43, 26, 88), (43, 28, 13), (43, 28, 18), (43, 29, 3), (43, 29, 59), (43, 31, 14), (43, 31, 26), (43, 33, 3), (43, 33, 23), (43, 33, 45), (43, 34, 3), (43, 34, 28), (43, 34, 44), (43, 35, 4), (43, 37, 97), (43, 38, 38), (43, 39, 6), (43, 40, 1), (43, 40, 35), (43, 42, 13), (43, 43, 1), (43, 43, 2), (43, 43, 55), (43, 44, 1), (43, 45, 2), (43, 46, 3), (43, 46, 5), (43, 47, 17), (43, 48, 9), (43, 50, 1), (43, 51, 5), (43, 51, 13), (43, 51, 50), (43, 52, 9), (43, 53, 4), (43, 57, 26), (43, 59, 2), (43, 59, 6), (43, 59, 18), (43, 60, 1), (43, 60, 6), (43, 62, 8), (43, 62, 9), (43, 62, 50), (43, 63, 6), (43, 65, 12), (43, 65, 32), (43, 66, 21), (43, 66, 56), (43, 67, 10), (43, 67, 63), (43, 68, 14), (43, 68, 18), (43, 74, 1), (43, 75, 6), (43, 75, 11), (43, 75, 46), (43, 75, 73), (43, 79, 30), (43, 79, 31), (43, 79, 56), (43, 98, 5), (43, 98, 29), (47, 2, 453), (47, 3, 9), (47, 28, 34), (47, 30, 10), (47, 40, 22), (47, 47, 1), (47, 65, 47), (47, 98, 75), (53, 2, 20), (53, 2, 78), (53, 2, 214), (53, 2, 347), (53, 2, 450), (53, 48, 50), (53, 48, 70), (53, 53, 1), (53, 72, 18), (53, 75, 31), (59, 3, 94), (59, 6, 128), (59, 7, 14), (59, 7, 24), (59, 7, 64), (59, 10, 7), (59, 10, 23), (59, 11, 8), (59, 11, 58), (59, 11, 80), (59, 13, 6), (59, 13, 38), (59, 14, 9), (59, 14, 49), (59, 15, 36), (59, 17, 64), (59, 19, 6), (59, 19, 25), (59, 20, 59), (59, 20, 71), (59, 24, 9), (59, 24, 13), (59, 26, 59), (59, 26, 71), (59, 28, 7), (59, 28, 23), (59, 29, 4), (59, 29, 36), (59, 31, 8), (59, 31, 10), (59, 33, 4), (59, 33, 6), (59, 35, 6), (59, 38, 77), (59, 39, 2), (59, 39, 12), (59, 42, 3), (59, 44, 5), (59, 45, 6), (59, 45, 28), (59, 45, 30), (59, 51, 32), (59, 52, 3), (59, 52, 11), (59, 55, 4), (59, 57, 4), (59, 58, 17), (59, 59, 1), (59, 60, 3), (59, 60, 17), (59, 61, 12), (59, 65, 50), (59, 66, 17), (59, 74, 33), (59, 75, 18), (59, 75, 38), (61, 30, 90), (61, 39, 3), (61, 43, 23), (61, 45, 7), (61, 52, 6), (61, 52, 36), (61, 60, 9), (61, 61, 1), (61, 67, 61), (61, 75, 43), (67, 2, 147), (67, 14, 6), (67, 19, 53), (67, 45, 47), (67, 57, 13), (67, 67, 1), (71, 2, 43), (71, 2, 177), (71, 6, 14), (71, 12, 58), (71, 13, 53), (71, 13, 113), (71, 18, 77), (71, 21, 11), (71, 22, 36), (71, 26, 66), (71, 50, 2), (71, 61, 11), (71, 63, 33), (71, 66, 70), (73, 2, 67), (73, 3, 98), (73, 5, 10), (73, 6, 3), (73, 7, 133), (73, 10, 11), (73, 10, 13), (73, 12, 3), (73, 17, 48), (73, 20, 4), (73, 22, 94), (73, 23, 6), (73, 28, 5), (73, 31, 3), (73, 34, 2), (73, 34, 5), (73, 43, 14), (73, 46, 7), (73, 57, 47), (73, 60, 62), (73, 63, 14), (73, 65, 57), (73, 74, 74), (73, 98, 1), (79, 3, 113), (79, 6, 4), (79, 17, 39), (79, 34, 56), (79, 50, 6), (79, 79, 1), (83, 2, 376), (83, 5, 5), (83, 5, 36), (83, 5, 57), (83, 56, 44), (89, 2, 32), (89, 2, 82), (89, 3, 111), (89, 7, 101), (89, 37, 23), (89, 47, 31), (89, 57, 5), (89, 68, 12), (97, 2, 51), (97, 2, 73), (97, 7, 43), (97, 19, 38), (97, 38, 34), (97, 43, 57), (97, 68, 2), (97, 98, 80)]
How to read this data ?
Here is the meaning of each triplet (x,y,z) :
x prime number that ends the sequence aliquot y^z.
y is the base and z the exponent.
I placed all these points in a 3 dimensional marker using Sage software. This allowed me to visualize in 3 dimensions if all these points were placed completely randomly or in privileged areas of the space.
At the beginning when I had this idea, I naively thought that all these points would be placed on a nice folded surface of which we could then look for the equation!
Nothing at all special to visualize with this new idea, except something we all knew already : There are many more points in the two planes of space with equations x=41 and especially x=43.
This is because there are many more aliquot sequences that end with the prime numbers 41 and especially 43 !
You can visualize these data (I hope) thanks to the two attached files to be decompressed and placed in the same folder. Then open the file "n^i_plot3d.html".
I just point out that to have more visibility, I deleted all the points that have a z>130 or so.


I wanted to inform you of all these works, knowing that I do not present you all the works in progress here, many are similar to those of the past years.
Indeed, you have all worked very hard to increase the amount of data to be processed.
This way, you know what all your calculations can be used for !
You may have noticed that the examples presented above were obtained with last year's data.
In the second half of August, I will redo this work with all the data available after the big harvest and with all the primes up to 150.
We will then see if something interesting will come out of it !
Thank you all for your colossal work !


PS : Edwin, I don't forget your work on the occurrence of large primes >10^9.
Attached Files
File Type: zip n^i_plot3d_fichiers.zip (150.2 KB, 7 views)
File Type: zip n^i_plot3d.html.zip (8.0 KB, 8 views)

Last fiddled with by garambois on 2022-07-20 at 10:09 Reason: Pagination correction and added two 3D visualization files.
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Old 2022-07-22, 08:57   #1770
garambois
 
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"Garambois Jean-Luc"
Oct 2011
France

977 Posts
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Page updated.
Many thanks to all for your help.

Added base : 1184 (2-cycle).
Added the size of the cycles in the "Navigation" table, for more clarity (e.g. (220, 284) was replaced by C2=(220, 284)).
Addition of the mergers announced by Happy for bases 56 and 57.
Removal of "Doubles of squares" bases from the "Open" category if all their sequences are finished.

Updated bases : All the bases announced below.

Code:
20^104: Prime - GDB *
21^107: Prime - GDB *
21^115: Prime - GDB *
21^123: Prime - GDB *
22^106: Prime - GDB *
22^108: Prime - GDB *
24^102: Prime - GDB *
24^104: Prime - GDB *
24^106: Prime - GDB * 
24^114: Prime - GDB *
26^102: Prime - GDB *
29^103: Prime - GDB *
31^105: Prime - GDB *
31^109: Prime - GDB *
34^100: Prime - GDB *
42^92: Prime - GDB *
42^96: Prime - GDB *
44^92: Prime - GDB *
48^90: Prime - GDB *
48^98: Prime - GDB *
52^98: Prime - GDB *
55^91: Prime - GDB *
55^95: Prime - GDB *
57^93: Prime - GDB *
59^99: Prime - GDB *
60^90: Prime - GDB *
60^92: Prime - GDB *
61^91: Prime - GDB *
65^93: Prime - GDB *
69^85: Prime - GDB *
74^88: Prime - GDB *
77^75: Prime - GDB *
77^91: Prime - GDB *
82^82: Prime - GDB *
83^91: Prime - GDB *
85^77: Prime - GDB *
87^85: Prime - GDB *
88^68: Prime - GDB *
88^72: Prime - GDB *
88^76: Prime - GDB *
89^83: Prime - GDB *
93^77: Prime - GDB *
107^79: Prime - GDB *
113^73: Prime - GDB *
127^75: Prime - GDB *
127^77: Prime - GDB *
127^79: Prime - GDB *
127^83: Prime - GDB *
137^83: Prime - GDB *
157^79: Prime - GDB *
167^79: Prime - GDB *
179^69: Prime - GDB *
193^63: Prime - GDB *
197^71: Prime - GDB *
227^59: Prime - GDB *
229^67: Prime - GDB *
233^59: Prime - GDB *
233^65: Prime - EDH *
233^73: Prime - GDB *
241^65: Prime - GDB *
288^63: Prime - GDB *
338^62: Prime - GDB *
385^63: Prime - GDB *
1152^43: Prime - GDB *
1210^46: Prime - GDB *
1250^50: Prime - GDB *
14536^36: Prime - GDB *
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Old 2022-07-22, 10:24   #1771
gd_barnes
 
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May 2007
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261148 Posts
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Nice work on the update!

Just an FYI, base 1155 all exponents >= 50 of both parities were initialized by me a couple weeks ago.

Last fiddled with by gd_barnes on 2022-07-22 at 10:33 Reason: remove erroneous statement
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