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Update v(1) stats with full 1000000 test sample

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Landon Curt Noll
2017-06-18 03:50:28 -07:00
parent 438554b0ed
commit 6bbb8c0e42
1 changed files with 47 additions and 45 deletions
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cal/lucas.cal
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@@ -805,62 +805,64 @@ rodseth_xhn(x, h, n)
*
* The above distribution was found to hold fairly well over many values of
* odd h that are also a multiple of 3 and for many values of n where h < 2^n.
* For example for in a sample size of 835823 numbers of the form h*2^n-1
* where odd h >= 12996351 is a multiple of 3, n >= 12996351, these are the
* smallest v(1) values that were found:
* For example for in a sample size of 1000000 numbers of the form h*2^n-1
* where h is an odd multiple of 3, 13002351 >= h >= 12996351,
* 4332116 >= n >= 12996351, these are the smallest v(1) values that were found:
*
* smallest percentage
* v(1) used
* -------------------
* 3 40.000%
* 5 25.683%
* 9 11.693%
* 11 10.452%
* 15 4.806%
* 17 2.348%
* 21 1.656%
* 29 1.281%
* 27 0.6881%
* 35 0.4536%
* 39 0.3121%
* 41 0.1760%
* 31 0.1414%
* 3 40.0000%
* 5 25.6833%
* 9 11.6924%
* 11 10.4528%
* 15 4.8048%
* 17 2.3458%
* 21 1.6568%
* 29 1.2814%
* 27 0.6906%
* 35 0.4529%
* 39 0.3140%
* 41 0.1737%
* 31 0.1413%
* 45 0.1173%
* 51 0.05576%
* 55 0.03300%
* 49 0.03185%
* 59 0.02090%
* 69 0.00980%
* 65 0.009367%
* 71 0.007205%
* 57 0.006341%
* 85 0.004611%
* 81 0.004179%
* 95 0.002882%
* 99 0.001873%
* 77 0.001153%
* 53 0.0007205%
* 67 0.0005764%
* 125 0.0005764%
* 105 0.0005764%
* 87 0.0004323%
* 111 0.0004323%
* 101 0.0002882%
* 83 0.0001441%
* 129 0.0001196%
* 51 0.0526%
* 55 0.0350%
* 49 0.0332%
* 59 0.0218%
* 69 0.0099%
* 65 0.0085%
* 71 0.0073%
* 57 0.0062%
* 85 0.0048%
* 81 0.0044%
* 95 0.0028%
* 99 0.0017%
* 77 0.0009%
* 53 0.0008%
* 67 0.0004%
* 105 0.0004%
* 111 0.0004%
* 125 0.0004%
* 87 0.0003%
* 101 0.0002%
* 83 0.0001%
* 109 0.0001%
* 121 0.0001%
* 129 0.0001%
*
* When h * 2^n-1 is prime and h is an odd multiple of 3, a smallest v(1) that
* is even is extremely rate. Of the list of 127287 known primes of the form
* h*2^n-1 when h was a multiple of 3, none has an smallest v(1) that was even.
*
* About 1 out of 835000 cases when h is a multiple of 3 use v(1) > 127 as the
* About 1 out of 1000000 cases when h is a multiple of 3 use v(1) > 127 as the
* smallest value of v(1).
*
* Given this information, when odd h is a multiple of 3 we try, in order,
* these sorted values of X:
*
* 3, 5, 9, 11, 15, 17, 21, 27, 29, 31, 35, 39, 41, 45, 49, 51, 53, 55,
* 57, 59, 65, 67, 69, 71, 77, 81, 83, 85, 87, 95, 99, 101, 105, 111, 125
* 3, 5, 9, 11, 15, 17, 21, 27, 29, 31, 35, 39, 41, 45, 49, 51, 53, 55, 57, 59,
* 65, 67, 69, 71, 77, 81, 83, 85, 87, 95, 99, 101, 105, 109, 111, 121, 125
*
* And stop on the first value of X where:
*
@@ -874,11 +876,11 @@ rodseth_xhn(x, h, n)
* If all x_tbl_len fail to satisfy Ref4 condition 1, then we begin a
* linear search at next_x until we find a proper X value.
*/
x_tbl_len = 35;
x_tbl_len = 38;
mat x_tbl[x_tbl_len];
x_tbl = {
3, 5, 9, 11, 15, 17, 21, 27, 29, 31, 35, 39, 41, 45, 49, 51, 53, 55,
57, 59, 65, 67, 69, 71, 77, 81, 83, 85, 87, 95, 99, 101, 105, 111, 125
3, 5, 9, 11, 15, 17, 21, 27, 29, 31, 35, 39, 41, 45, 49, 51, 53, 55, 57, 59,
65, 67, 69, 71, 77, 81, 83, 85, 87, 95, 99, 101, 105, 109, 111, 121, 125
};
next_x = 129;