107.sagews

p=1073137282146338814025297276012340514033392142286643\
182285946106897867885100815144444489959819534285998417\
753833519511397207193450879131705172428770801749585396\
377454681078165004036511715043877217438068707562700109\
319150934601131782394001492737704925458198054954529649\
68476117438596882036667823702963803652097
is_prime(p)

True

# What is the size of the group Z_p^\times?
d=p-1

# What is the prime factorization of d?
F=factor(d)
F

2^207 * 3^515

# What is the largest
F[-1][0]

3

"""    
We find all 32-bit primes with 3-smooth totient
(aka primes of the form 2^v*3^v+1)
(aka Pierpont primes)
and collect them in the set S
"""

# the set S collects all Pierpont primes in our given range.
# - initialize S
# - loop over all possible values for v
# - adjust u according to the range requirements
# - test 2^u*3^v+1 for primality
# - if yes, add to S; if no, ignore
S=[]
for v in srange(0,floor(log(2^(1024) - 1,3))):
    u=ceil(log((2^(1023) - 1)/3^v,2))
    p=2^u*3^v+1
    if is_prime(p):
        S=S+[p,u,v]
S

[107313728214633881402529727601234051403339214228664318228594610689786788510081514444448995981953428599841775383351951139720719345087913170517242877080174958539637745468107816500403651171504387721743806870756270010931915093460113178239400149273770492545819805495452964968476117438596882036667823702963803652097, 207, 515]

# compute the number of decimal digits
floor(log(S[0],10))+1

309