In this Kata, you will be given a number and your task will be to return the nearest prime number. 

```Haskell
solve(4) = 3. The nearest primes are 3 and 5. If difference is equal, pick the lower one. 
solve(125) = 127
```

We'll be testing for numbers up to `1E10`. `500` tests.

More examples in test cases. 

Good luck!

If you like Prime Katas, you will enjoy this Kata: [Simple Prime Streaming](https://www.codewars.com/kata/5a908da30025e995880000e3)

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'from itertools import count\nfrom bisect import bisect_left as bisect\n\nn = 100005                                    # Sieve up to (10**10)**.5 + 5\nsieve, primes = [0]*((n>>1)+1), [2]           # optimized sieve (store only odd numbers\nfor i in range(3, n+1, 2):\n    if not sieve[i>>1]:\n        primes.append(i)\n        for j in range(i**2>>1, (n+1)>>1, i): sieve[j] = 1\n    \ndef solve(n):\n    if n%2 and n>>1 < len(sieve) and not sieve[n>>1]: return n                    # easy check: prime if sieve element is set to False\n    \n    idx = bisect(primes,n)                                                        # Insertion point of n in the prime list\n    return bigSearch(n, idx) if idx == len(primes) \\\n           else min( primes[max(0,idx-1):idx+2], key=lambda x: (abs(x-n), x))     # fast look up in the list of primes (check element before, under and after the insertion point)\n\ndef isPrime(n, iSq): return all(n%x for x in primes[:iSq])\n\ndef bigSearch(n, idx):\n    iSq = bisect(primes,n**.5,0,idx)                                              # insertion point of n**.5 in the prime list (for complex primality check)\n    isPair = not n%2\n    for x in count(0):\n        for c in [-1,1]:\n            p = n+c*(2*x + isPair)\n            if isPrime(p, iSq): return p\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'solve'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5592