Was the Apostle Paul a martyr?

A second-century tradition says that Peter and Paul were both martyred in Rome on the orders of Emperor Nero. However, Clement of Rome, writing at the end of the first century (1 Clement), ought to have known if this had been the case but seems to have believed that Paul went to the 'west' (Spain) and lived out his remaining years there. He also seems unaware that Peter either came to Rome or was executed there.