Tradition says that Linus became pope around 64 to 67 CE, but this should be treated with caution. Even the Catholic Encyclopedia concedes we know little about the early popes and nothing reliable about their chronology.
In fact, there probably was no first century bishop or pope named Linus. Francis Aloysius Sullivan (From Apostles to Bishops: The Development of the Episcopacy in the Early Church) says that the consensus of scholars is that the available evidence indicates that the church of Rome was led by a college of presbyters, rather than a single bishop, for at least several decades of the second century. This consensus is backed up by an analysis of early Christian writings.
Another answer from our community:
Linus became pope upon the death of St. Peter which happened between 64 and 67 AD.
Sylvester was elevated to the papacy in the year 314.
Pope St. Sylvester I
Pope St. Sylvester died on December 31, 335, at Rome, Italy.
Pope St. Sylvester I was pope in the year 325.
Pope Saint Sylvester is the patron saint of Feroleto Antico, Italy, and Poggio Catino, Italy.
Pope Sylvester served as Pope from January 314 to 335.
Pope St. Marcellinus (296-304) Pope St. Marcellus I (308-309) Pope St. Eusebius (April-August 309 or 310) Pope St. Miltiades (311-14) Pope St. Sylvester I (314-35) Pope St. Marcus (January-October 336) Pope St. Julius I (337-52) Pope Liberius (352-66) Pope St. Damasus I (366-83) Pope St. Siricius (384-99) Pope St. Anastasius I (399-401)
Pope Sylvester III died in 1062.
Pope Sylvester I died on 335-12-31.
Pope Sylvester II was born in 946.
Pope Sylvester III was born in 1000.
St. Patrick was never a pope. He was a bishop.
There are dozens of St. Sylvesters, and one of them was Pope (314-335). His feast day is December 31st.