### Problem 8
The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.

Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?

$73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450$



```python
x = 7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450 
x = str(x)

def prod(x):
    """Computes product of a string of integers"""
    y = 1
    for c in x:
        y *= int(c)
    return y

biggest = 0
for i in range(1000):
    # x is 1000-digits long
    product = prod(x[i:i+13])
    biggest = product if product > biggest else biggest
    
print(biggest)

```

    23514624000


### Problem 9
A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,

$$\begin{align}
a^2 + b^2 = c^2
\end{align}$$
For example, $32 + 42 = 9 + 16 = 25 = 52$.

There exists exactly one Pythagorean triplet for which $a + b + c = 1000$.

Find the product $abc$.


```python
import math
for a in range(1000):
    for b in range(1000):
        c = math.sqrt(a**2 + b**2)
        if a + b + c == 1000 and a < b < c:
            print(a,b,c)
            print(a*b*c)
```

    200 375 425.0
    31875000.0



```python

```

10fa6f1e7548ca449895c54866a91160a49b203f
ipynb
Jupyter Notebook
euler/euler.ipynb
cadecrandall/sandbox
10da307abc40fc04b766a6a9d15ea547f6b2eeb4
MIT
euler/euler.ipynb
cadecrandall/sandbox
10da307abc40fc04b766a6a9d15ea547f6b2eeb4
MIT
euler/euler.ipynb
cadecrandall/sandbox
10da307abc40fc04b766a6a9d15ea547f6b2eeb4
MIT
Qwen/Qwen-72B
1. YES
2. YES