Category: C Applications
Live Person-to-Person Tutoring
Blog Entry © Tuesday, October 29, 2024, by James Pate Williams, Jr. Second Order Quantum Mechanical Perturbation Calculation Part II
Blog Entry (c) Monday September 16, 2024, by James Pate Williams, Jr. Ramanujan Highly Composite Numbers
Ramanujan Highly Composite Numbers
## 2 3 5 7 11 13
1 2 1
2 4 2
3 6 1 1
4 12 2 1
5 24 3 1
6 36 2 2
7 48 4 1
8 60 2 1 1
9 120 3 1 1
10 180 2 2 1
11 240 4 1 1
12 360 3 2 1
13 720 4 2 1
14 840 3 1 1 1
15 1260 2 2 1 1
16 1680 4 1 1 1
17 2520 3 2 1 1
18 5040 4 2 1 1
19 7560 3 3 1 1
20 10080 5 2 1 1
21 15120 4 3 1 1
22 20160 6 2 1 1
23 25200 4 2 2 1
24 27720 3 2 1 1 1
25 45360 4 4 1 1
26 50400 5 2 2 1
27 55440 4 2 1 1 1
28 83160 3 3 1 1 1
29 110880 5 2 1 1 1
30 166320 4 3 1 1 1
31 221760 6 2 1 1 1
32 277200 4 2 2 1 1
33 332640 5 3 1 1 1
34 498960 4 4 1 1 1
35 554400 5 2 2 1 1
36 665280 6 3 1 1 1
37 720720 4 2 1 1 1 1
38 1081080 3 3 1 1 1 1
39 1441440 5 2 1 1 1 1
40 2162160 4 3 1 1 1 1
Runtime in seconds = 182.490
Type any character to exit application
Blog Entry (c) Tuesday September 3, 2024, by James Pate Williams, Jr.
Blog Entry (c) Saturday August 31, 2024, by James Pate Williams, Jr. An Elementary School Problem Found Online
Solve for a real root of the equation
f(x)=log6l(5+x)+log6l(x)=0
First we test our log6l(x) function
log6l(12) = 1.386853
log6l(36) = 2.000000
x = 0.1925824036
f = 0.0000000000
Blog Entry (c) Friday August 30, 2024, by James Pate Williams, Jr. Another Simple Math Problem
We use an evolutionary hill-climber and the solution of the quadratic equation to solve the easy problem below:
Solution of f(a,x)=sin(sqrt(ax-x^2))=0
Subject to the constraint x+y=100
Where x and y are the two roots of
g(a,x)=ax-x^2-n*n*pi*pi=0
and n=15
a = 100.347888933988
x = 32.947113268776
y = 67.400775665213
g = 0.000000000000
s = 100.347888933988
runtime in seconds = 43.730000
Blog Entry (c) Wednesday August 28, 2024, by James Pate Williams, Jr.
Blog Entry (c) Tuesday, August 27, 2024, Graphing New Goldwasser-Kilian Primality Test Results by James Pate Williams, Jr.
The x -axis is the number to be tested, the y-axis is prime number bound for factoring, and the z-axis is the runtime in seconds.
Blog Entry (c) Wednesday, August 21, 2024, by James Pate Williams, Jr. New and Improved Version of the Goldwasser-Kilian Primality Test
I corrected my powering modulo a prime routine. I added Pollard’s p – 1 factoring method and Shanks-Mestre elliptic curve point counting algorithm.
number to be tested or 0 to quit:
10000019
number of primes in factor base:
10000
Prime sieving time = 3.220000
N[0] = 10000019
a = 7838973
b = 2449531
m = 9995356
q = 356977
P = (9786147, 3226544)
P1 = (0, 1)
P2 = (5887862, 8051455)
N[1] = 356977
a = 45561
b = 178451
m = 357946
q = 178973
P = (80627, 163299)
P1 = (0, 1)
P2 = (52101, 282559)
N[2] = 178973
a = 135281
b = 76426
m = 178996
q = 73
P = (10238, 98035)
P1 = (0, 1)
P2 = (46702, 94326)
number is proven prime
runtime in seconds = 35.471000
number to be tested or 0 to quit:
10015969
number of primes in factor base:
10000
Prime sieving time = 3.424000
N[0] = 10015969
a = 6613193
b = 3951715
m = 10013908
q = 2503477
P = (998314, 8329764)
P1 = (0, 1)
P2 = (6944357, 1053776)
N[1] = 2503477
a = 1175442
b = 379813
m = 2505736
q = 293
P = (646462, 1631861)
P1 = (0, 1)
P2 = (1477980, 88719)
number is proven prime
runtime in seconds = 5.612000
number to be tested or 0 to quit:
99997981
number of primes in factor base:
10000
Prime sieving time = 4.152000
N[0] = 99997981
a = 34129462
b = 80482974
m = 100001414
q = 181
P = (19305995, 40493835)
P1 = (0, 1)
P2 = (33828245, 72969559)
number is proven prime
runtime in seconds = 11.500000
number to be tested or 0 to quit:
100001819
number of primes in factor base:
100000
Prime sieving time = 3.218000
N[0] = 100001819
a = 2694060
b = 17329746
m = 100008102
q = 5569
P = (124594, 14596756)
P1 = (0, 1)
P2 = (32514144, 56926555)
number is proven prime
runtime in seconds = 76.301000
number to be tested or 0 to quit:
100005317
number of primes in factor base:
100000
Prime sieving time = 3.269000
N[0] = 100005317
a = 45478318
b = 328034
m = 99988256
q = 3124633
P = (62548529, 30179124)
P1 = (0, 1)
P2 = (70379514, 76899689)
N[1] = 3124633
a = 2605576
b = 1809212
m = 3127654
q = 503
P = (1236288, 2081401)
P1 = (0, 1)
P2 = (2264479, 2583693)
number is proven prime
runtime in seconds = 459.979000
number to be tested or 0 to quit:
100000007
number of primes in factor base:
100000
Prime sieving time = 3.209000
N[0] = 100000007
a = 50593669
b = 72502607
m = 100005736
q = 2053
P = (72365335, 69885097)
P1 = (0, 1)
P2 = (55023241, 20078454)
number is proven prime
runtime in seconds = 163.705000
number to be tested or 0 to quit:
100014437
number of primes in factor base:
100000
Prime sieving time = 3.919000
N[0] = 100014437
a = 49955472
b = 45482796
m = 100024160
q = 263
P = (41650735, 8652103)
P1 = (0, 1)
P2 = (53790105, 37282431)
number is proven prime
runtime in seconds = 12.915000
