Bathing during the month of Māgha at the Māgha-melā still takes place. This is a very old melā (assembly), dating from time immemorial. It is said that ever since the Lord in the form of Mohinī took a bucket of nectar and kept it at Prayāga, holy men have gathered there every year and observed the Māgha-melā. Every twelfth year there is a Kumbha-melā, a great festival, and all the holy men from all over India assemble there. The brāhmaṇa wanted to take advantage of the Māgha-melā and bathe there.
Bathing at the confluence of the Ganges and Yamunā, near the fort at Allahabad (Prayāga), is mentioned in the revealed scriptures:

māghe māsi gamiṣyanti gaṅgā-yāmuna-saṅgamam
gavāṁ śata-sahasrasya samyag dattaṁ ca yat-phalam
prayāge māgha-māse vai try-ahaṁ snātasya tat-phalam
"If one goes to Prayāga and bathes at the confluence of the Ganges and Yamunā in the month of Māgha, he attains the result of giving hundreds and thousands of cows in charity. Simply by bathing for three days there, he attains the results of such a pious activity." Because of this, the Sanoḍiyā brāhmaṇa was very eager to go to Prayāga and bathe. Generally karmīs (fruitive laborers) take advantage of bathing there during the month of Māgha, thinking that they will be rewarded in the future. Those who are situated in devotional service do not very strictly follow this karma-kāṇḍīya process.
(Sri Caitanya Caritamrta------2:18:145-------purport).

The great saint Nārada is so liberated that he can go to the Vaikuṇṭha planets to see Nārāyaṇa and then immediately come to this planet in the material world and go to Prayāga to bathe in the confluence of three rivers. The word tri-veṇī refers to a confluence of three rivers. This confluence is still visited by many hundreds of thousands of people who go there to bathe, especially during the Māgha-melā, which occurs during the month of January. A liberated person who has no material body can go anywhere and everywhere; therefore a living entity is called sarva-ga, which indicates that he can go anywhere and everywhere. Presently scientists are trying to go to other planets, but due to their material bodies, they are not free to move at will. However, when one is situated in his original spiritual body, he can move anywhere and everywhere without difficulty. Within this material world there is a planet called Siddhaloka, whose inhabitants can go from one planet to another without the aid of a machine or space rocket. In the material world every planet has a specific advantage (vibhūti-bhinna). In the spiritual world, however, all the planets and their inhabitants are composed of spiritual energy. Because there are no material impediments, it is said that everything in the spiritual world is one.
(Sri Caitanya Caritamrta------2:24:230-------purport).

When Rūpa Gosvāmī met Lord Śrī Caitanya Mahāprabhu at Prayāga (Allahabad), he offered his respectful obeisances by submitting that Lord Caitanya was more magnanimous than any other avatāra of Kṛṣṇa because He was distributing love of Kṛṣṇa. His mission was to enhance love of Godhead. In the human form of life the highest achievement is to attain the platform of love of Godhead. Lord Caitanya did not invent a system of religion, as people sometimes assume. Religious systems are meant to show the existence of God, who is then generally approached as the cosmic order-supplier. But Lord Śrī Caitanya Mahāprabhu's transcendental mission is to distribute love of Godhead to everyone. Anyone who accepts God as the Supreme can take to the process of chanting Hare Kṛṣṇa and become a lover of God. Therefore Lord Caitanya is the most magnanimous. This munificent broadcasting of devotional service is possible only for Kṛṣṇa Himself. Therefore Lord Caitanya is Kṛṣṇa.
(Sri Caitanya Caritamrta------1:4:41-------purport).

When Lord Caitanya Mahāprabhu visited the village of Rāmakeli, He met Vallabha there. Later, Śrī Rūpa Gosvāmī, after meeting Śrī Caitanya Mahāprabhu, resigned from government service, and when he went to Vṛndāvana to meet Lord Caitanya, Vallabha accompanied him. The meeting of Rūpa Gosvāmī and Vallabha with Caitanya Mahāprabhu at Allahabad is described in the Madhya-līlā, Chapter Nineteen.
Actually, it is to be understood from the statement of Sanātana Gosvāmī that Śrī Rūpa Gosvāmī and Vallabha went to Vṛndāvana under the instructions of Śrī Caitanya Mahāprabhu. First they went to Mathurā, where they met a gentleman named Subuddhi Rāya, who maintained himself by selling dry fuel wood. He was very pleased to meet Śrī Rūpa Gosvāmī and Anupama, and he showed them the twelve forests of Vṛndāvana. Thus they lived in Vṛndāvana for one month and then again went to search for Sanātana Gosvāmī. Following the course of the Ganges, they reached Allahabad, or Prayāga-tīrtha, but because Sanātana Gosvāmī had come there by a different road, they did not meet him there, and when Sanātana Gosvāmī came to Mathurā he was informed of the visit of Rūpa Gosvāmī and Anupama by Subuddhi Rāya. When Rūpa Gosvāmī and Anupama met Caitanya Mahāprabhu at Benares, they heard about Sanātana Gosvāmī’s travels from Him, and thus they returned to Bengal, adjusted their affairs with the state and, on the order of Śrī Caitanya Mahāprabhu, went to see the Lord at Jagannātha Purī.
(Sri Caitanya Caritamrta------1:10:84-------purport).

Vallabha Bhaṭṭa is the head of the Vaiṣṇava sampradāya known as the Vallabhācārya-sampradāya in western India. There is a long story about Vallabha Ācārya narrated in the Caitanya-caritāmṛta, specifically in the Seventh Chapter of the Antya-līlā and the Nineteenth Chapter of the Madhya-līlā. Lord Caitanya Mahāprabhu visited the house of Vallabha Ācārya on the other side of Prayāga, in a place known as Āḍāila-grāma. Later, Vallabha Bhaṭṭa saw Caitanya Mahāprabhu at Jagannātha Purī to explain his commentary on Śrīmad-Bhāgavatam. He was very proud of his writings, but Śrī Caitanya Mahāprabhu corrected him, telling him that a Vaiṣṇava should be humble and follow in the footsteps of his predecessors. The Lord told him that his pride in being superior to Śrīdhara Svāmī was not at all befitting a Vaiṣṇava.
(Sri Caitanya Caritamrta------2:1:263-------purport).

Ganges and Yamunā mix at the confluence at Allahabad (Prayāga). The Yamunā flows from the western side and the Ganges from the eastern, and they merge. Since Caitanya Mahāprabhu bathed on the western side, He actually took His bath in the river Yamunā.
(Sri Caitanya Caritamrta------2:3:36-------purport).

Śrīla Bhaktisiddhānta Sarasvatī Ṭhākura states that while Śrī Caitanya Mahāprabhu passed through Bengal, He passed through Āṭisārā-grāma, Varāha-grāma and Chatrabhoga. He then reached the Orissa province, where He passed through Prayāga-ghāṭa; the Suvarṇarekhā River; Remuṇā; Yājapura, where He bathed at the Daśāśvamedha-ghāṭa, on the Vaitaraṇī River; Kaṭaka (Cuttak), where the Mahānadī River flows; Bhuvaneśvara, where there is a big lake known as Bindu-sarovara; Kamalapura; and Āṭhāranālā. In this way, passing through all these and other places, He reached Jagannātha Purī.
(Sri Caitanya Caritamrta------2:3:217-------purport).

The city of Prayāga is situated a few miles from the city of Allahabad. The name Prayāga is given due to successful sacrifices performed there. It is said, prakṛṣṭo yāgo yāga-phalaṁ yasmāt. If one performs sacrifices at Prayāga, he certainly gets immediate results without difficulty. Prayāga is also called Tīrtharāja, the king of all places of pilgrimage. This holy place is situated on the confluence of the rivers Ganges and Yamunā. Every year a fair takes place there known as Māgha-melā, and every twelve years a Kumbha-melā is also held. In any case, many people come to bathe there every year. During Māgha-melā, people from the local district generally come, and during Kumbha-melā people come from all over India to live there and bathe in the Ganges and Yamunā. Whoever goes there immediately feels the place's spiritual influence. A fort located there was constructed by the emperor Akbar about five hundred years ago, and near the fort is a place called Triveṇī. On the other side of Prayāga is an old place known as Pratiṣṭhāna-pura. It is also well known as Jhuṅsi. Many saintly people live there, and consequently it is very attractive from the spiritual point of view.
(Sri Caitanya Caritamrta------2:17:149-------purport).

When Śrī Caitanya Mahāprabhu took His bath at Akrūra-ghāṭa, He submerged Himself in the water for a long time. Balabhadra Bhaṭṭācārya decided to take Śrī Caitanya Mahāprabhu to Prayāga after visiting the holy place known as Soro-kṣetra. While stopping near a village on the way to Prayāga, Śrī Caitanya Mahāprabhu fainted in ecstatic love. Some Pāṭhāna soldiers who were passing through saw Śrī Caitanya Mahāprabhu and falsely concluded that the Lord's associates, Balabhadra Bhaṭṭācārya and others, had killed the Lord with a poison named dhuturā and were taking His wealth. Thus the soldiers arrested them. However, when Śrī Caitanya Mahāprabhu regained His senses, His associates were released. He talked with a person who was supposed to be a holy man in the party. From the Koran, Śrī Caitanya Mahāprabhu established devotional service to Kṛṣṇa. Thus the leader of the soldiers, named Vijulī Khān, surrendered to Śrī Caitanya Mahāprabhu, and he and his party became devotees of Lord Kṛṣṇa. The same village today is known as the village of Pāṭhāna Vaiṣṇavas. After bathing in the Ganges at Soro, Śrī Caitanya Mahāprabhu arrived at Prayāga, at the confluence of three rivers-the Ganges, Yamunā and Sarasvatī.
(Sri Caitanya Caritamrta------2:18--------summary).