Merge branch 'develop'

jet08013 · Jun 29, 2018 · ce36858 · ce36858
2 parents 84d0ed4 + 4d455cd
commit ce36858
Showing 1 changed file with 53 additions and 32 deletions.
diff --git a/ctnt2018/ECM.py b/ctnt2018/ECM.py
@@ -11,43 +11,64 @@ def ecm(N,arange=100,krange=10000):
     for a in range(-arange,arange):
         x,y=0,1
         for B in Primes10000:
-            k=B**(int(log(10000)/log(B)))
-            sx,sy,t=x,y,k
-            first=True
-            while t>0:
-                if t%2==1:
-                    if first:
-                        xm,ym=sx,sy
-                        first=False
-                    else:
-                        d,u,v=gmpy2.gcdext(sx-xm,N)
-                        if d>1:
-                            if d==N:
-                                break
-                            else:
-                                return d
-                        L=(u*(sy-ym)) % N
-                        x_sum=(L*L-xm-sx) % N
-                        ym=(L*(xm-x_sum)-ym) % N
-                        xm=x_sum
-                d,u,v=gmpy2.gcdext(2*sy,N)
-                if d>1:
-                    if d==N:
+            k=10000
+            while k>0:
+                k=k//B
+                sx,sy,t=x,y,B
+                first=True
+                while True:
+                    if t%2==1:
+                        if first:
+                            xm,ym=sx,sy
+                            first=False
+                        else:
+                            d,u,v=gmpy2.gcdext(sx-xm,N)
+                            if d>1:
+                                if d==N:
+                                    break
+                                else:
+                                    return d
+                            L=(u*(sy-ym)) % N
+                            x_sum=(L*L-xm-sx) % N
+                            ym=(L*(xm-x_sum)-ym) % N
+                            xm=x_sum
+                    t=t//2
+                    if t==0:
                         break
-                    else:
-                        return d
-                L=(u*(3*sx*sx+a)) % N
-                x2=(L*L-2*sx) % N
-                sy=(L*(sx-x2)-sy) %N
-                sx=x2
-                t=t//2
-            x,y=xm,ym
+                    d,u,v=gmpy2.gcdext(2*sy,N)
+                    if d>1:
+                        if d==N:
+                            break
+                        else:
+                            return d
+                    L=(u*(3*sx*sx+a)) % N
+                    x2=(L*L-2*sx) % N
+                    sy=(L*(sx-x2)-sy) %N
+                    sx=x2
+                x,y=xm,ym
     print('Failed')
 
 
+# First factored in 1980 by Brent and Pollard using rho method
+# Factorization of the Eighth Fermat Number
+# Richard Brent, John Pollard
+# Mathematics of Computation, Volume 36, Number 154, April 1981
+#V=1238926361552897
+#N=2**(256)+1
+#print('Factor of F8', ecm(N,arange=100,krange=10000),flush=True)
 
-N=2**(128)+1
-print('answer is', ecm(N,arange=100,krange=10000),flush=True)
+# These smaller factors were found in 1988 by Brent
+
+N=2**(2**11)+1
+d1=ecm(N,arange=100,krange=10000)
+print(d1)
+d2=ecm(N//d1)
+print(d2)
+M=N//(d1*d2)
+d3=ecm(M)
+print(d3)
+d4=ecm(M//d3)
+print('Factors of F11',d1,d2,d3,d4,flush=True)