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# redpawn2020 - primimity
The concept behind the three primes generations:
1. Randomly 1024-bit prime generated (p)
2. Random iterated value is generated (less than 256)
3. Find next prime function add 2 to n every time the n value is not a prime
4. After the iterated search ends , a find next prime function is called to produce (q)
5. The same process is conducted from prime 3 (r).
6. The summary: The difference between the three primes are not big.
Proposed method to start:
$$N=pqr$$ and the three primes are close to each other , lets find the cubic root of N and consider it as apprimated p.
7. After finding approximate p
I used this function to find the excat p,q,r ( I added a margin of 200000 to start the search)
```python
def attack(P):
P=P-200000;
print('P0',P)
while True:
if(n%P == 0):
print(P);
P+=1
```
The three primes are :
p=139926822890670655977195962770726941986198973494425759476822219188316377933161673759394901805855617939978281385708941597117531007973713846772205166659227214187622925135931456526921198848312215276630974951050306344412865900075089120689559331322162952820292429725303619113876104177529039691490258588465409208581
q=139926822890670655977195962770726941986198973494425759476822219188316377933161673759394901805855617939978281385708941597117531007973713846772205166659227214187622925135931456526921198848312215276630974951050306344412865900075089120689559331322162952820292429725303619113876104177529039691490258588465409397803
r=139926822890670655977195962770726941986198973494425759476822219188316377933161673759394901805855617939978281385708941597117531007973713846772205166659227214187622925135931456526921198848312215276630974951050306344412865900075089120689559331322162952820292429725303619113876104177529039691490258588465409494847
8. Given e, p,q,r , phi and d are calculated
```python
def check():
n=2739699434633097765008468371124644741923408864896396205946954196101304653772173210372608955799251139999322976228678445908704975780068946332615022064030241384638601426716056067126300711933438732265846838735860353259574129074615298010047322960704972157930663061480726566962254887144927753449042590678730779046154516549667611603792754880414526688217305247008627664864637891883902537649625488225238118503996674292057904635593729208703096877231276911845233833770015093213639131244386867600956112884383105437861665666273910566732634878464610789895607273567372933766243229798663389032807187003756226177111720510187664096691560511459141773632683383938152396711991246874813205614169161561906148974478519987935950318569760474249427787310865749167740917232799538099494710964837536211535351200520324575676987080484141561336505103872809932354748531675934527453231255132361489570816639925234935907741385330442961877410196615649696508210921
e=65537
c=2082926013138674164997791605512226759362824531322433048281306983526001801581956788909408046338065370689701410862433705395338736589120086871506362760060657440410056869674907314204346790554619655855805666327905912762300412323371126871463045993946331927129882715778396764969311565407104426500284824495461252591576672989633930916837016411523983491364869137945678029616541477271287052575817523864089061675401543733151180624855361245733039022140321494471318934716652758163593956711915212195328671373739342124211743835858897895276513396783328942978903764790088495033176253777832808572717335076829539988337505582696026111326821783912902713222712310343791755341823415393931813610365987465739339849380173805882522026704474308541271732478035913770922189429089852921985416202844838873352090355685075965831663443962706473737852392107876993485163981653038588544562512597409585410384189546449890975409183661424334789750460016306977673969147
p0=139926822890670655977195962770726941986198973494425759476822219188316377933161673759394901805855617939978281385708941597117531007973713846772205166659227214187622925135931456526921198848312215276630974951050306344412865900075089120689559331322162952820292429725303619113876104177529039691490258588465409208581
p1=139926822890670655977195962770726941986198973494425759476822219188316377933161673759394901805855617939978281385708941597117531007973713846772205166659227214187622925135931456526921198848312215276630974951050306344412865900075089120689559331322162952820292429725303619113876104177529039691490258588465409397803
p2=139926822890670655977195962770726941986198973494425759476822219188316377933161673759394901805855617939978281385708941597117531007973713846772205166659227214187622925135931456526921198848312215276630974951050306344412865900075089120689559331322162952820292429725303619113876104177529039691490258588465409494847
N=p0*p1*p2
phi= (p0-1)*(p1-1)*(p2-1)
if(N==n):
print("equal")
print(gmpy2.invert(e, phi))
d=gmpy2.invert(e, phi)
flag = gmpy2.powmod(c, d, N)
print(flag)
print(long_to_bytes(flag))
```
9. FLAGE IS : **flag{pr1m3_pr0x1m1ty_c4n_b3_v3ry_d4ng3r0u5}**
