Single returns with iteration in a range

[u220e]

Hi. I'm trying to generate a list of pairs of primes (x,y) within a range of values such that the digit length of their products is between 19 and 35. I've written a few different code variations that (unfortunately) either (1) generate ALL the integer pairs (that equal 19, 20, 21, etc.) or (2) never seem to halt. 

I really want the iteration to be as follows: find the first pair that equals 19, then locate the first pair that equals 20, and so on so until I have one list of 17 pairs of primes---one pair for each digit length. Here's what I have so far:

x=var('x')

y=var('y')

for x in sxrange (10**9,10**(36)):

   for y in sxrange (961748941,982451653):

      if x.is_prime()==1 and y.is_prime()==1:

            if (floor(log((x*y),10)+1)<=35)==1:

               print(x,y); print(floor(log((x*y),10)+1); break

Then I tried defining y=982451653 so I could use only one iterable using the following code:

for x in sxrange (10**9,10**(36)):

   if x.is_prime()==1:

      if (floor(log((x*y),10)+1)>=19)==1:

         continue

      print(x,y); print(floor(log((x*y),10)+1); break

which returns only one value:

1000000007 982451653

18

Sorry for the n00b post. I've only been using Sage for three days. 

Thanks,

David

 

           

[u220e]

Anybody?

[Vincent Delecroix]

First of all if p and q are primes then p - q is even unless p=2 or q=2.

Next, there is no need to declare variable in Python.

Finally, there are optimized methods to access primes. Look
for prime_range, next_prime, Primes, etc

x = 3
while True:
y = (10**18 // x).next_prime()
ymax = (10**36 + x - 2) // x
while y <= ymax:
print("x = %d and y = %d" % (x, y))
y = y.next_prime()
x = x.next_prime()

[slelievre]

Not sure why one would want the "first pair" each time.

Below we define a function that produces an iterator

yielding random prime pairs one after the other,

with primes picked at random in a range ensuring

their product will have the correct number of digits.

```

def prime_pair_for_each_product_ndigits(nmin, nmax):

    for n in range(nmin, nmax + 1):

        lo = isqrt(10**(n-1))

        hi = isqrt(10**n)

        a = random_prime(hi, lbound=lo)

        b = random_prime(hi, lbound=lo)

        yield a, b

```

This might give something like the following.

```

sage: p_q_list = list(prime_pair_for_each_product_ndigits(19, 35))

sage: p_q_list

[(2257885207, 1029222697),

 (7906953709, 8831254513),

 (28123041337, 18086888887),

 (59156603659, 75212477107),

 (244478980829, 297135812329),

 (878180166047, 926189502323),

 (1390098443147, 1010518243127),

 (5150835567223, 3603512345189),

 (16533079879703, 15727405198679),

 (34437803922611, 57693414719911),

 (102979771890571, 141205565889301),

 (941693653240727, 468548529571597),

 (1375078260756671, 1726461802816903),

 (8524331332200121, 4310462307066121),

 (19014345158785303, 31601933129557883),

 (92121426759262499, 64338223205154251),

 (262242817443146321, 251117727289363427)]

```

We check the number of digits of each product.

```

sage: f = lambda n: f'{n:36d} has {n.ndigits():2d} digits'

sage: print('\n'.join(f(n) for n in (p*q for p, q in p_q_list)))

                 2323866702264943279 has 19 digits

                69828320626688338717 has 20 digits

               508658323826826921919 has 21 digits

              4449314698430409934513 has 22 digits

             72643460565990932840741 has 23 digits

            813361250941000432227181 has 24 digits

           1404719836542484333000669 has 25 digits

          18561099554526665790140147 has 26 digits

         260022446450216138134512337 has 27 digits

        1986834503750174243684807621 has 28 digits

       14541316964959210349671680871 has 29 digits

      441229176532847985852022831019 has 30 digits

     2374020093080293654628048809913 has 31 digits

    36743808900391354263355551200641 has 32 digits

   600890064210265812194221708193549 has 33 digits

  5926928916814700284047132294733249 has 34 digits

 65853820314282336219416564107002067 has 35 digits

```

[u220e]

Thank you.

[slelievre]

Le mardi 23 juin 2020 20:33:11 UTC+2, slelievre a écrit :

Not sure why one would want the "first pair" each time.

Below we define a function that produces an iterator

yielding random prime pairs one after the other,

with primes picked at random in a range ensuring

their product will have the correct number of digits.

```

def prime_pair_for_each_product_ndigits(nmin, nmax):

    for n in range(nmin, nmax + 1):

        lo = isqrt(10**(n-1))

        hi = isqrt(10**n)

        a = random_prime(hi, lbound=lo)

        b = random_prime(hi, lbound=lo)

        yield a, b

```

This might give a product with one digit less

in extremely rare cases. To avoid that, replace

        lo = isqrt(10**(n-1))

with

        lo = isqrt(10**(n-1)) + 1