391

391
Wknight94 · CC BY-SA 3.0 · source
Name	391
Numeral	CCCXCI
Factorization	17 × 23
Divisors	1, 17, 23, 391

391

391 is an integer following 390 and preceding 392. As a composite number equal to the product of the primes 17 and 23, it appears in numeric sequences studied by mathematicians such as Pierre de Fermat, Leonhard Euler, Carl Friedrich Gauss, Évariste Galois, and Srinivasa Ramanujan. The number also marks the year 391 CE, notable in the late Roman Empire during the reign of Theodosius I and intersecting with events involving figures like Ambrose of Milan, Arcadius, Honorius, and institutions such as the Roman Empire (Western) and Roman Empire (Eastern).

Number

In arithmetic contexts, 391 = 17 × 23, connecting it to studies by Euclid and later factorization work by Adrien-Marie Legendre and Carl Pomerance. It is a semiprime, placing it in lists alongside numbers examined by G. H. Hardy, John Littlewood, and Paul Erdős. In modular arithmetic investigations influenced by Joseph-Louis Lagrange and Édouard Lucas, 391 offers examples for testing primality algorithms developed by Agrawal–Kayal–Saxena researchers and utilized by cryptographers like Whitfield Diffie and Ronald Rivest. Recreational mathematics communities referencing Martin Gardner and D. R. Kaprekar sometimes note 391 in puzzles and base-conversion problems.

Year 391

The year 391 CE falls within the late fourth century during the joint rule of emperors Theodosius I, Arcadius, and Honorius. Events of the year figure in accounts by chroniclers such as Socrates of Constantinople, Sozomen, and Zosimus. Diplomatic and legal measures from this period influenced relations among powers like the Visigoths, led by Alaric I, the Huns, and the Roman administrations in Ravenna and Constantinople. Ecclesiastical proceedings documented by Ambrose of Milan and correspondences involving John Chrysostom reflect tensions between imperial policy and episcopal authority.

Military and Political Events

Military and political developments in 391 CE intersect with campaigns and movements involving tribes and commanders documented by historians such as Ammianus Marcellinus (for earlier context) and later interpreters like Edward Gibbon. The dynamics between the Visigoths under Alaric I and Roman magistrates shaped frontier stability near provinces like Moesia and regions referenced in sources concerning Illyricum. The imperial court in Constantinople managed relationships with powerful generals and officials influenced by figures such as Rufinus (earlier in the decade) and successors whose careers are traced in the writings of Procopius (for later analysis). Diplomatic arrangements and edicts from Theodosius I and his administration affected provincial governors and urban elites in cities like Antioch, Alexandria, and Rome.

Religion and Christianity

Religious transformations in 391 CE were prominent: imperial legislation under Theodosius I curtailed pagan practices, actions recorded by ecclesiastical historians such as Theodoret of Cyrrhus and debated by opponents like Julian (emperor), whose earlier policies contrasted with Christianizing emperors. Bishop Ambrose of Milan played a central role in disputes over church property and imperial conduct, while theologians such as Athanasius of Alexandria, John Chrysostom, Gregory Nazianzen, and Jerome engaged in doctrinal controversies reflected in synodal activity tied to sees like Constantinople, Alexandria, and Antioch. Temple closures and the suppression of traditional rites involved locations such as the Serapeum of Alexandria and debates among pagans including intellectuals in places associated with Neoplatonism figures like Hypatia (later) and teachers in the schools of Athens and Alexandria. The legal and pastoral interactions between emperors and bishops shaped the trajectory of Christianity across imperial provinces.

Science, Culture, and Society

Cultural life in 391 CE continued the legacies of literary and scholarly traditions tied to authors and educators such as Quintus Smyrnaeus (earlier epic tradition), Paulus Orosius, and rhetoricians connected to schools in Athens and Alexandria. Artistic production in mosaics and church architecture anticipated developments later associated with builders and patrons in Ravenna and ecclesiastical patrons like Basil of Caesarea. Intellectual networks linking commentators on classical literature, manuscript preservation efforts tied to scriptoria in monastic centers influenced by Basil of Caesarea and Benedict of Nursia (later) contributed to transmission of texts by Homer, Virgil, and Plato. Social tensions involving urban populations, civic curiales, and aristocratic landholders are chronicled in sources studied by modern historians such as Peter Brown and Averil Cameron.

Notable Births and Deaths

Notable figures associated with this period include bishops and intellectuals whose lives span the late fourth and early fifth centuries: deaths and births recorded in ecclesiastical chronologies involve people like Paulus Orosius (active), provincial governors, and military leaders who intersect with the careers of Alaric I, Eugenius (usurper), and clerics such as Ambrose of Milan. Other contemporaries appearing in prosopographical collections compiled by modern scholars like The Prosopography of the Later Roman Empire include senators, generals, and churchmen whose exact birth or death years are debated among historians including M. L. W. Laistner and Michael Kulikowski.

Category:Integers Category:4th century