diff --git a/cal/lucas.cal b/cal/lucas.cal index b04a690..ddcd5df 100644 --- a/cal/lucas.cal +++ b/cal/lucas.cal @@ -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% - * 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% + * 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 0.0526% + * 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;