Scriptores Historiae Augustae,  Gordian  2, 3, 6, 17 (ca. 360 A.D.):

Gordian 2.3

Ipse consul ditissimus ac potentissimus, Romae Pompeianam domum possidens, in provinciis tantam terrarum habens quantum nemo privatus.

He himself [Gordian I] as consul was most rich and powerful; at Rome he owned the house of Pompeius, and in the provinces more land than any other subject. (D. Magie, trans.)

Gordian 3.7

Exstat silva eius memorabilis, quae picta est in domo rostrata Cn. Pompei, quae ipsius et patris eius et proavi fuit, quam Philippi temporibus vester fiscus invasit.

There also exists today a remarkable wild beast hunt of his pictured in Gnaeus Pompeius' "House of the Breaks;" this palace belonged to him [Gordian I], and to his father and his grandfather before him until your privy-purse took it over in the time of Philip. (D. Magie, trans.)

Gordian 6

Consul cum esset, aut in domo eius semper mansit aut, si in Pompeiana domo, ad illum vel mane vel sero processit.

When he [Gordian I] was consul, either he always remained at the old man's house, or, if he stayed at the House of Pompeius, he went either in the morning or evening to see him. (D. Magie, trans.)

Gordian 17

Si quidem argumento ad probandam generis qualitatem alii hoc esse desiderant, quod Africanus Gordianus senior appellatus est cogomine Scipionum, quod domum Pompeianam in urbe habuit, quod Antoninorum cognomine semper est nuncupatus, quod Antonium filium suum ipse significari voluit in senatu; quae singula videntur familias designare.

Others adduce the following facts as evidence to show the high quality of his family—that the elder Gordian was called Africanus, the honorary surname of the Scipios; that he possessed the House of Pompeius in the city; that he [Gordian II] was always given the surname of the Antonines; and that he himself expressed a desire in the senate that his son should be known as Antonius. Each of these, they believe, represents a family connection. (D. Magie, trans.)