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Home/Chain Registry/Block #3,485,181

Block #3,485,181

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/21/2019, 8:43:26 AM Β· Difficulty 10.9788 Β· 3,360,047 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
938d4bc91c65a88fefb6d3028609c27f365e320adb7eed5bd0fd4dc564012af2
View on Chainz β†—

Difficulty

10.978774

Transactions

1

Size

201 B

Version

2

Bits

0afa90f6

Nonce

307,878,926

Timestamp

12/21/2019, 8:43:26 AM

Confirmations

3,360,047

Merkle Root

3876b0056ef9b635adff6e5b2a19382713f4ccf607ac8bd3943c181e8c58f21a
Transactions (1)
Coinbase3876b0056ef9b6…3c181e8c58f21a
1 in β†’ 1 out8.2800 XPM110 B
ASiq2qtK…VMhmk7yL
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.299 Γ— 10⁹⁷(98-digit number)
42998549207149277512…58727167643494133760
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
4.299 Γ— 10⁹⁷(98-digit number)
42998549207149277512…58727167643494133761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.599 Γ— 10⁹⁷(98-digit number)
85997098414298555025…17454335286988267521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.719 Γ— 10⁹⁸(99-digit number)
17199419682859711005…34908670573976535041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.439 Γ— 10⁹⁸(99-digit number)
34398839365719422010…69817341147953070081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.879 Γ— 10⁹⁸(99-digit number)
68797678731438844020…39634682295906140161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.375 Γ— 10⁹⁹(100-digit number)
13759535746287768804…79269364591812280321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.751 Γ— 10⁹⁹(100-digit number)
27519071492575537608…58538729183624560641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.503 Γ— 10⁹⁹(100-digit number)
55038142985151075216…17077458367249121281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.100 Γ— 10¹⁰⁰(101-digit number)
11007628597030215043…34154916734498242561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.201 Γ— 10¹⁰⁰(101-digit number)
22015257194060430086…68309833468996485121
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 3485181

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 938d4bc91c65a88fefb6d3028609c27f365e320adb7eed5bd0fd4dc564012af2

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #3,485,181 on Chainz β†—
Circulating Supply:58,006,256 XPMΒ·at block #6,845,227 Β· updates every 60s
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