How many Christians ?

[Huon]

Here is a simple table, which has been computed with three hypotheses :

1- The sect began around 40 CE.
2 - The initial number of members was 40 or 100 persons.
3 - The increase rate was 40 % or 50 % every ten years.

Of course, each of these hypotheses can be disputed. We have no data, except what can be grasped in the gospels, and these data are certainly not reliable.

Date * 1.5 * 1.4 * 1.5
40 40 100 100
50 60 140 150
60 90 196 225
70 135 274 338
80 203 384 506
90 304 538 759
100 456 753 1139
110 683 1054 1709
120 1025 1476 2563
130 1538 2066 3844
140 2307 2893 5767
150 3460 4050 8650
160 5190 5669 12975
170 7785 7937 19462

This list shows that the number of Christians was very small during the first century, and began to be somewhat important around 150 CE.

Another remark : these Christians lived in the most important towns of the Roman Empire, Rome, Alexandria, Antioch, Ephesus, and perhaps Carthage. Their number in each of these towns could be 100 to 300 during the first century.

The famous letter of Pliny the Younger to Trajan, concerning some Christians of Bithynia-Pontus around 110 CE, could be appreciated more quietly. We are told that one of Pliny's main concerns was the vast number of Christians involved. Hem, hem.

[Peter Kirby]

It may be instructive to look at new religious movements closer in time to our own.

Mormonism for example started less than two hundred years ago and reports some 16,000,000 members.

https://en.wikipedia.org/wiki/Soka_Gakkai

The movement was founded by educators Makiguchi and Toda in 1930, but not formally inaugurated until 1937. After a temporary disbandment during World War II when much of the leadership was imprisoned on charges of lèse-majesté, the membership base was expanded through controversial and aggressive recruitment methods to a claimed figure of 750,000 households by 1958, compared to 3,000 before the end of the war. Further expansion of the movement was led by its third president Daisaku Ikeda. According to its own account, it has 12 million members in 192 countries and territories around the world. While Ikeda has been successful in moving the group towards mainstream acceptance in some areas, it is still widely viewed with suspicion in Japan.

These figures are not actually all that suspicious, but we could conservatively take the second one at 1/3 of the stated value, i.e. 250,000 in 1958 and the third one at 1/4 of the stated value (actually just a conversion of 'members' into households, assuming some single person households), i.e., 3,000,000 around 1988, which was about when their membership basically hit a plateau in growth. Finally to make it more comparable to your own model, we will add a starting point with just 100 members (or 25 households) at the beginning year.

ca. 1930 : roughly 25 households
ca. 1938 : roughly 3,000 households
ca. 1958 : roughly 250,000 households
ca. 1988 : roughly 3,000,000 households

With this kind of data we can derive what kind of constant growth rate would be required in each period to reach the next number of households.

ca. 1930-1938 : roughly 82% growth rate per year
ca. 1938-1958 : roughly 25% growth rate per year
ca. 1958-1988 : roughly 8.6% growth rate per year

This illustration may have exceptionally high growth, but the principle that you will measure higher 'growth rates' (i.e. greater year-over-year percentage increases in membership) at the beginning of a new religious movement seems like the kind of thing that you'll find to be the rule, not the exception. Especially after the 'survivor' filter is applied (we're looking at the successful ones).

We can see this in other areas much more clearly, especially if we simply view religion as a consumer preference. Sometimes a new religious movement may replace an existing religious preference rapidly, for any number of reasons. You could compare this, for example, to the meteoric rise in the use of Google as a search engine or Apple iPhone as a mobile phone in recent times. In each case they swept through filling some kind of need of a market segment (Apple) or indeed nearly just all the market, in the English language anyway (Google). After doing so their use started to behave more like a steady growth function, after making the initial rapid gains in use that came from unveiling the new market choice and claiming a large swath of market share.

It would be obtuse to complain about breakdowns in an argument from analogy, which this is not (nobody's making claims about what has to be the case for the unknown here--it's still unknown exactly how early Christianity grew). It's an illustration of what should have been evident from the start, that a simple exponential growth function is inadequate for the purposes of modeling the change in membership in a new religious movement over time.

[Huon]

From newadvent encyclopedy :

(Reigned about A.D. 64 or 67 to 76 or 79).
All the ancient records of the Roman bishops which have been handed down to us by St. Irenaeus, Julius Africanus, St. Hippolytus, Eusebius, also the Liberian catalogue of 354, place the name of Linus directly after that of the Prince of the Apostles, St. Peter. These records are traced back to a list of the Roman bishops which existed in the time of Pope Eleutherus (about 174-189), when Irenaeus wrote his book "Adversus haereses". As opposed to this testimony, we cannot accept as more reliable Tertullian's assertion, which unquestionably places St. Clement (De praescriptione, xxii) after the Apostle Peter, as was also done later by other Latin scholars (Jerome, Illustrious Men 15). The Roman list in Irenaeus has undoubtedly greater claims to historical authority. This author claims that Pope Linus is the Linus mentioned by St. Paul in his 2 Timothy 4:21. The passage by Irenaeus (Against Heresies III.3.3) reads:
After the Holy Apostles (Peter and Paul) had founded and set the Church in order (in Rome) they gave over the exercise of the episcopal office to Linus. The same Linus is mentioned by St. Paul in his Epistle to Timothy. His successor was Anacletus.
We cannot be positive whether this identification of the pope as being the Linus mentioned in 2 Timothy 4:21 goes back to an ancient and reliable source, or originated later on account of the similarity of the name.

Linus's term of office, according to the papal lists handed down to us, lasted only twelve years. The Liberian Catalogue shows that it lasted twelve years, four months, and twelve days. The dates given in this catalogue, A.D. 56 until A.D. 67, are incorrect. Perhaps it was on account of these dates that the writers of the fourth century gave their opinion that Linus had held the position of head of the Roman community during the life of the Apostle; e.g., Rufinus in the preface to his translation of the pseudo-Clementine "Recognitiones". But this hypothesis has no historical foundation. It cannot be doubted that according to the accounts of Irenaeus concerning the Roman Church in the second century, Linus was chosen to be head of the community of Christians in Rome, after the death of the Apostle. For this reason his pontificate dates from the year of the death of the Apostles Peter and Paul, which, however, is not known for certain.

2 Timothy belongs to the Pauline corpus as a pastorale letter, dated between 100 and 150 CE. Certainly written by Paul (but which Paul ?).

The christian community of Rome could not record precisely the date of the death of their first bishop Peter (64 or 67) and the exact dates of his successor. Irenaeus wrote one century later.

The successor of Linus is called Anencletus, Anacletus or Cletus, and could have reigned between 76 and 88. He is said to have died a martyr during the reign of Domitian (81-96).

But this Cletus is not mentioned by Eusebius...

[Peter Kirby]

Uh, where are you going with this?

[Huon]

I am looking for the early history of the christians. I think that they were in a significant number in the great towns of the roman empire around 100 CE. There are IMO at least two possible researchs, the description of the persecutions, and secondly, the lists of the early bishops of Rome, Alexandria, Antioch.

The persecutions have been usually described as :

1 - Persecution of Nero (54-68)
2 - Persecution of Domitian (81-96)
3 - Persecution of Trajan (98-117)
4 - Persecution of Marcus Aurelius (161-180)
5 - Persecution of Severus (200-11)
6 - Persecution of Maximinus Thrax (235-238)
7 - Persecution of Decius (249-251)
8 - Persecution of Valerian (257-261)
9 - Persecution of Aurelian (270-275)
10 - Persecution of Diocletian (284-305)

My previous post concerned the list of the bishops of Rome. This list is very imprecise until Clement of Rome, around 100 CE.

[lsayre]

How and why did a church which was being persecuted in Rome decide to headquarter itself in Rome?

[MrMacSon]

How and why did a church which was being persecuted in Rome decide to headquarter itself in Rome?

Perhaps it didn't. Much of the early action seems to have been in Asia Minor & Bithynia-Pontus.

and the Roman Empire became centred in the east after Diocletian made Nicomedia the eastern capital city of the Roman Empire in 286 AD.

Then Constantine I transferred the imperial capital from Rome (its historic base) to Byzantium in 330 AD and designated his new capital Nova Roma or "New Rome" - he had renamed Byantium as Constantinople in 324 AD and undertaken a major building program.

• "he was well aware that Rome was an unsatisfactory capital. Rome was too far from the frontiers, and hence from the armies and the imperial courts, and it offered an undesirable playground for disaffected politicians. Yet it had been the capital of the state for over a thousand years, and it might have seemed unthinkable to suggest that the capital be moved to a different location. Nevertheless, Constantine identified the site of Byzantium as the right place: a place where an emperor could sit, readily defended, with easy access to the Danube or the Euphrates frontiers, his court supplied from the rich gardens and sophisticated workshops of Roman Asia, his treasuries filled by the wealthiest provinces of the Empire.
  
  "Constantinople was built over 6 years, and consecrated on 11 May 330 ... The new programme of building was carried out in great haste: columns, marbles, doors, and tiles were taken wholesale from the temples of the empire and moved to the new city. In similar fashion, many of the greatest works of Greek and Roman art were soon to be seen in its squares and streets. The emperor stimulated private building by promising householders gifts of land from the imperial estates in Asiana and Pontica and on 18 May 332 he announced that, as in Rome, free distributions of food would be made to the citizens. At the time, the amount is said to have been 80,000 rations a day, doled out from 117 distribution points around the city.
  
  "Constantine laid out a new square at the centre of old Byzantium, naming it the Augustaeum. The new senate-house (or Curia) was housed in a basilica on the east side."
  
  https://en.wikipedia.org/wiki/Constanti ... 2.80.93337

While the Roman Emperor Constantine the Great reigned (306–337 CE), Christianity began to transition to the dominant religion of the Roman Empire. Historians remain uncertain about Constantine's reasons for favoring Christianity, and theologians and historians have argued about which form of Early Christianity he subscribed to. There is no consensus among scholars as to whether he adopted his mother Helena's Christianity in his youth, or (as claimed by Eusebius of Caesarea) encouraged her to convert to the faith himself. Some scholars question whether he should be considered a Christian at all: "Constantine saw himself as an 'emperor of the Christian people'. If this made him a Christian is the subject of ... debate.",[1][2] and he did not receive baptism until shortly before his death.[3]

Constantine's decision to cease the persecution of Christians in the Roman Empire was a turning point for Early Christianity, sometimes referred to as the Triumph of the Church, the Peace of the Church or the Constantinian shift. In 313, Constantine and Licinius issued the Edict of Milan decriminalizing Christian worship. The emperor became a great patron of the Church and set a precedent for the position of the Christian emperor within the Church and the notion of orthodoxy, Christendom, ecumenical councils and the state church of the Roman Empire declared by edict in 380.

Constantine_the_Great_and_Christianity

'Conversion'

... he was over 42 when he finally declared himself a Christian.[9][10] Writing to Christians, Constantine made clear that he believed that he owed his successes the protection of that High God alone.[11]

Battle of Milvian Bridge
Eusebius of Caesarea and other Christian sources record that Constantine experienced a dramatic event in 312 at the Battle of the Milvian Bridge, after which Constantine claimed the emperorship in the West. According to these sources, Constantine looked up to the sun before the battle and saw a cross of light above it, and with it the Greek words "Ἐν Τούτῳ Νίκα" (~ "in this sign, conquer!"), often rendered in a Latin version, "in hoc signo vinces"(– "in this sign, you will conquer"). Constantine commanded his troops to adorn their shields with a Christian symbol (the Chi-Rho), and thereafter they were victorious.[2][12]

Following the battle, the new emperor ignored the altars to the gods prepared on the Capitoline and did not carry out the customary sacrifices to celebrate a general's victorious entry into Rome, instead heading directly to the imperial palace.[11] Most influential people in the empire, however, especially high military officials, had not been converted to Christianity and still participated in the traditional religions of Rome; Constantine's rule exhibited at least a willingness to appease these factions. The Roman coins minted up to eight years after the battle still bore the images of Roman gods.[2] The monuments he first commissioned, such as the Arch of Constantine, contained no reference to Christianity.[11][13]

Edict of Milan
In 313 Constantine and Licinius announced "that it was proper that the Christians and all others should have liberty to follow that mode of religion which to each of them appeared best",[14] thereby granting tolerance to all religions, including Christianity. The Edict of Milan went a step further than the earlier Edict of Toleration by Galerius in 311, returning confiscated Church property. This edict made the empire officially neutral with regard to religious worship; it neither made the traditional religions illegal nor made Christianity the state religion, as occurred later with the Edict of Thessalonica of 380. The Edict of Milan did, however, raise the stock of Christianity within the empire and it reaffirmed the importance of religious worship to the welfare of the state.[15]

2, 10, 11 Peter Brown (2003) The Rise of Christendom 2nd edition (Oxford, Blackwell Publishing) p. 60-1.

9 Brown, Peter (2012). The Rise of Western Christendom: Triumph and Diversity, A.D. 200-1000, 10th Anniversary Revised Edition: Triumph and Diversity, A.D. 200-1000. Making of Empire 3 (3 ed.). John Wiley & Sons. ISBN 9781118338841.

12 Eusebius, Life of Constantine.

13 J.R. Curran, Pagan City and Christian Capital. Rome in the Fourth Century (Oxford, 2000) pp. 70–90.

14 Lactantius, De Mortibus Persecutorum ("On the Deaths of the Persecutors") ch. 48.

15 Constantine and Licinius, "The 'Edict of Milan'," in 'Documents of the Christian Church', trans. and ed. Henry Bettenson (London: Oxford University Press, 1963), 22.

[MrMacSon]

The famous letter of Pliny the Younger to Trajan, concerning some Christians of Bithynia-Pontus around 110 CE, could be appreciated more quietly. We are told that one of Pliny's main concerns was the vast number of Christians involved. Hem, hem.

These 'Christians' could have been followers of a Christ (or Chrestus) other than Jesus

[Huon]

These 'Christians' could have been followers of a Christ (or Chrestus) other than Jesus

This could be another topic.

[lsayre]

Perhaps it didn't. Much of the early action seems to have been in Asia Minor & Bithynia-Pontus.

Thanks for all of this! But wasn't the Bishop of Rome considered throughout history (Catholic at least) to be the Pope?