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Block #439,418

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/11/2014, 4:24:32 PM Β· Difficulty 10.3595 Β· 6,374,624 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
887d5b91c29d3dabd8261e24ce206d9a1bc89042f63555b9dbb94132a16db008
View on Chainz β†—

Height

#439,418

Difficulty

10.359537

Transactions

1

Size

199 B

Version

2

Bits

0a5c0a99

Nonce

77,779

Timestamp

3/11/2014, 4:24:32 PM

Confirmations

6,374,624

Merkle Root

0523757b792d8fb29441cc0f84040227f97bd8cd0774fb4306250a94d0cf5516
Transactions (1)
Coinbase0523757b792d8f…250a94d0cf5516
1 in β†’ 1 out9.3000 XPM109 B
ARYuCmXb…HnxRmwtf
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.

2.239 Γ— 10⁹⁡(96-digit number)
22392211486055972332…90086444779564528640
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
2.239 Γ— 10⁹⁡(96-digit number)
22392211486055972332…90086444779564528641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.478 Γ— 10⁹⁡(96-digit number)
44784422972111944665…80172889559129057281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.956 Γ— 10⁹⁡(96-digit number)
89568845944223889331…60345779118258114561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.791 Γ— 10⁹⁢(97-digit number)
17913769188844777866…20691558236516229121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.582 Γ— 10⁹⁢(97-digit number)
35827538377689555732…41383116473032458241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.165 Γ— 10⁹⁢(97-digit number)
71655076755379111465…82766232946064916481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.433 Γ— 10⁹⁷(98-digit number)
14331015351075822293…65532465892129832961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.866 Γ— 10⁹⁷(98-digit number)
28662030702151644586…31064931784259665921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.732 Γ— 10⁹⁷(98-digit number)
57324061404303289172…62129863568519331841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.146 Γ— 10⁹⁸(99-digit number)
11464812280860657834…24259727137038663681
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 439418

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 887d5b91c29d3dabd8261e24ce206d9a1bc89042f63555b9dbb94132a16db008

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 #439,418 on Chainz β†—
Circulating Supply:57,756,411 XPMΒ·at block #6,814,041 Β· updates every 60s
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