prime.py firstrun finds first 1,000,000th Prime 15485863 something to…

… work with.

Signed-off-by: Damian Williamson <[email protected]>

README.md

@@ -5,8 +5,14 @@
 A Prime is any number only divisible by 1 and itself searching first that a number is not even if it divides by 2, optimising using a "Vignette Sieve" that if not only up to n/2 needs to be tested as a divisor, then 3 if not only up to n/3 needs to be tested as divisor, n/5, n/7, n/11, n/13, n/17, n/19, n/23, n/29, n/31 & so on so that only divisibility by a prime needs to be checked for to prove not prime & since for example we have ruled out that the number is a factor of three or two so there is no natural number greater than n/3 that can be a divisor.
 
 ### Usage
+On first run use `prime.py firstrun` to build the data table. The data table *may be* provided. It can find up to 104729 the 10,000th Prime in 6 seconds and can be faster with `mpiexec`
 
-On first run use `prime.py firstrun` to build the data table. The data table *may be* provided.
+```log prime.py firstrun
+Initialise...
+Firstrun: Building _data
+Completed creating data to 10000 Primes
+Largest Prime in Index:104729
+```
 
 `prime.py [number to check]`
 
@@ -22,3 +28,4 @@ It should be possible to run with `mpiexec` [Build a Raspberry Pi cluster comput
 Professor. Damian A. James Williamson
 
 [1]: https://magpi.raspberrypi.com/articles/build-a-raspberry-pi-cluster-computer
+

notes

@@ -1,9 +1,14 @@
 setup
 
+input number
+input whether to fill missing primes
+
+first run no input fill data file up to some n
+
 file read
 file write
 is_prime
- from file
- add to file
+ from file check up to fraction
+ add to file fraction bigger than file check all not divisible by file up to fraction
 
-If prime output and add to file.
+If prime output

prime.py

@@ -5,7 +5,115 @@
 # Source Code produced by Willtech 2023
 # v0.1 hand coded by HRjJ
 
+#prime.py [number to check] []
+import time
+tt = time.time()
+
+print("Initialise...")
 ## setup dependencies
 import sys
+import re
+
+from mpmath import *
+mp.dps = 15000000000
+#@manual{mpmath,
+#  key     = {mpmath},
+#  author  = {The mpmath development team},
+#  title   = {mpmath: a {P}ython library for arbitrary-precision floating-point arithmetic (version 1.3.0)},
+#  note    = {{\tt http://mpmath.org/}},
+#  year    = {2023},
+#}
+
+#Imput handler
+try:
+ if sys.argv[1] is not None:
+  if sys.argv[1] == "firstrun":
+   x = -1
+  else:
+   try:
+    mp.dps = len(str(int(sys.argv[1])))
+    x = mpf(str(sys.argv[1]))
+   except:
+    exit ("Input error.")
+   if x < 1:
+    x = x * -1
+except:
+  mp.dps = 185
+  x = mpf('531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127')
+if x == 0:
+ exit('0 will not be prime');
+
+#Functions
+def fileread(primes):
+ primefile = open("_data", "r")
+ primes = primefile.read().split(",")
+ primefile.close
+ return primes
+
+def filesave(data):
+ content = str(data)
+ primefile = open("_data", "w")
+ primefile.write(content)
+ primefile.close
+
+def findprime(x, i):
+ j = mpf(x) / i
+ if str(j).split(".")[1] == "0":
+#  printoutput (x, i, j, 'Doh!') #
+  return (False)
+ else:
+#  printoutput (x, i, j, 'Ding!') #
+  return (True)
+
+def printoutput(x, i, j, f):
+ print ('Dividend:', x)
+ print ('Divisor:', i)
+ print ('Quotient:', j, 'from divisor:', i, f)
+ print ('---')
+
+def printfound(x):
+ print ('Found:', x)
+ print ('------')
+
+def createint(i):
+ return(int(i))
+
+#Development proof
+#primes = ""
+#primes = fileread(primes)
+
+#Runtime
+if x == -1: #firstrun
+ print ("Firstrun: Building _data")
+ arp = 1
+ primes = ""
+ primes = 1,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71
+ mp.dps = mpf(len(str(primes[len(primes)-1])))
+ while len(primes) <= 1000000:
+  arp = 1
+  x = mpf(str(primes[len(primes)-1]+2))
+  mp.dps = len(str(x))
+  if findprime(x, 2):
+   i = createint(primes[arp])
+   while i < x / i:
+    i = createint(primes[arp])
+    if findprime(mpf(x), i):
+     arp = arp + 1
+    else:
+     arp = 1
+     x = x + 2
+   printfound(x) #
+   primes = (*primes, int(x))
+  else:
+   print (primes)
+   print ('Looking for', x)
+   exit ('Math error creating _data.');
 
+ filesave(primes)
+ fileread(primes)
+ # print(primes) #
+ print ('Completed creating data to', len(primes)-1, 'Primes');
+ print ('Largest Prime in Index:' + str(int(''.join(filter(str.isdigit, str(primes[len(primes)-1]))))))
+ exit ("--- %s Seconds ---" % (time.time() - tt))
 
+#Main