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Home/Chain Registry/Block #2,439,820

Block #2,439,820

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/25/2017, 3:48:34 AM Β· Difficulty 10.9238 Β· 4,399,011 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a1c58dbdf2b8bd6ab63c4305a99d5e03f0683609689d8e8a9d3bde0f06a831a5
View on Chainz β†—

Difficulty

10.923757

Transactions

1

Size

201 B

Version

2

Bits

0aec7b58

Nonce

1,143,405,590

Timestamp

12/25/2017, 3:48:34 AM

Confirmations

4,399,011

Merkle Root

687d8e76a80fcb1637f3d4b253ff96a8d926fec3257398a0847f7c1553771e62
Transactions (1)
Coinbase687d8e76a80fcb…7f7c1553771e62
1 in β†’ 1 out8.3700 XPM110 B
AZdsHTJH…NYwyX7ex
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.

2.391 Γ— 10⁹⁢(97-digit number)
23915324991185671002…67085309628185722880
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
2.391 Γ— 10⁹⁢(97-digit number)
23915324991185671002…67085309628185722881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.783 Γ— 10⁹⁢(97-digit number)
47830649982371342005…34170619256371445761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.566 Γ— 10⁹⁢(97-digit number)
95661299964742684010…68341238512742891521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.913 Γ— 10⁹⁷(98-digit number)
19132259992948536802…36682477025485783041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.826 Γ— 10⁹⁷(98-digit number)
38264519985897073604…73364954050971566081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.652 Γ— 10⁹⁷(98-digit number)
76529039971794147208…46729908101943132161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.530 Γ— 10⁹⁸(99-digit number)
15305807994358829441…93459816203886264321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.061 Γ— 10⁹⁸(99-digit number)
30611615988717658883…86919632407772528641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.122 Γ— 10⁹⁸(99-digit number)
61223231977435317766…73839264815545057281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.224 Γ— 10⁹⁹(100-digit number)
12244646395487063553…47678529631090114561
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 2439820

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 a1c58dbdf2b8bd6ab63c4305a99d5e03f0683609689d8e8a9d3bde0f06a831a5

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 #2,439,820 on Chainz β†—
Circulating Supply:57,954,908 XPMΒ·at block #6,838,830 Β· updates every 60s
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