Contradiction with Matthew 28:8
While John 20:3 depicts Peter and the other disciple running to the tomb, Matthew 28:8 describes the women leaving the tomb quickly with fear and great joy to bring the disciples word, suggesting varying details about who first went to tell the news or went to the tomb.
Matthew 28:8: And they departed quickly from the sepulchre with fear and great joy; and did run to bring his disciples word.
Contradiction with Mark 16:8
In Mark 16:8, the women flee from the tomb and say nothing to anyone because they were afraid, which differs from the account in John 20:3 where the disciples run towards the tomb.
Mark 16:8: And they went out quickly, and fled from the sepulchre; for they trembled and were amazed: neither said they any thing to any [man]; for they were afraid.
Contradiction with Luke 24:12
Luke 24:12 mentions only Peter running to the tomb and does not mention "the other disciple" as in John 20:3, presenting a discrepancy in the accounts of who went to the tomb.
Luke 24:12: Then arose Peter, and ran unto the sepulchre; and stooping down, he beheld the linen clothes laid by themselves, and departed, wondering in himself at that which was come to pass.