2019-04-10-142343.sagews

1+1

55^11

55^500

is_prime(1001)

a=randint(10^10,10^11)

a

is_prime(a)

def find_a_prime(lower,upper,trials):     #find a prime between upper and lower, using "trials" at the number of attempts    i=1    while i<=trials:        a=randint(lower,upper)             #a=random integer between the two bounds        if is_prime(a):                    # if a is prime, return it            return a        i=i+1                              #increase the counter and go back and do it again    return "Not found"

find_a_prime(10^108,10^109,60)

def show_powers(x,p):   # show powers of x in Z/p    i=0    list=[]    while i<p:          #        list.append ( [i, (x^i)%p] )   #add point (i,x^i) to list        i=i+1    graph=points(list)   # Plot all the points in "list" in a graph    show(graph)           # Display the graph    return

show_powers(2,1009)

def power(n,k,p): # Finds n^k mod p using the naive method    i=0    temp=1    while i<k:       temp=(temp*n)%p       i=i+1    return temp

def fpower(n,k,p):   # Finds n^k using Fast Powering    if k==0:       return 1    if k==1:       return n    if k%2==0:       temp=fpower(n,k/2,p)       temp=(temp^2)%p       return temp    temp=fpower(n,(k-1)/2,p)    temp=(n*temp*temp)%p    return temp

fpower(55,2000000017,101)