The branch had first reached the consulship in 441 BC under the presumed brother of Lucius, a Manius Papirius Crassus.
During their consulship the tribune of the plebs, Spurius Maelius, proposed a bill targeting two senators, Gaius Servilius Ahala and Lucius Minucius Esquilinus Augurinus.
The goal was to confiscate the property of Ahala, mark him as a caedes civis indemnati (loosely translated: unlawful murderer) and to condemn Minucius for false accusation.
The two consuls are traditionally identified as Gaius Papirius Crassus and Lucius Julius Iulus, the praenomens varies between sources.
The censors of 430 BC are named as Lucius Papirius and Publius Pinarius by both Cicero and Livy.