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Block #1,405,332

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/9/2016, 3:06:22 AM Β· Difficulty 10.8070 Β· 5,432,757 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6cb4393ed7c2ca7888ede868ab918f1259441079e7f22fed6aabff5871186798
View on Chainz β†—

Difficulty

10.806986

Transactions

1

Size

200 B

Version

2

Bits

0ace96a4

Nonce

230,591,920

Timestamp

1/9/2016, 3:06:22 AM

Confirmations

5,432,757

Merkle Root

2940d148eaaa7d1c62d3f9a336f53bf97fa301c59dfb4f09c276cc43eca51cc1
Transactions (1)
Coinbase2940d148eaaa7d…76cc43eca51cc1
1 in β†’ 1 out8.5500 XPM110 B
AWbaFYsD…G85T3K2p
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.

1.011 Γ— 10⁹⁡(96-digit number)
10119083196357677668…99846320424407320960
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
1.011 Γ— 10⁹⁡(96-digit number)
10119083196357677668…99846320424407320961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.023 Γ— 10⁹⁡(96-digit number)
20238166392715355337…99692640848814641921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.047 Γ— 10⁹⁡(96-digit number)
40476332785430710674…99385281697629283841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.095 Γ— 10⁹⁡(96-digit number)
80952665570861421348…98770563395258567681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.619 Γ— 10⁹⁢(97-digit number)
16190533114172284269…97541126790517135361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.238 Γ— 10⁹⁢(97-digit number)
32381066228344568539…95082253581034270721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.476 Γ— 10⁹⁢(97-digit number)
64762132456689137078…90164507162068541441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.295 Γ— 10⁹⁷(98-digit number)
12952426491337827415…80329014324137082881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.590 Γ— 10⁹⁷(98-digit number)
25904852982675654831…60658028648274165761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.180 Γ— 10⁹⁷(98-digit number)
51809705965351309663…21316057296548331521
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 1405332

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 6cb4393ed7c2ca7888ede868ab918f1259441079e7f22fed6aabff5871186798

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 #1,405,332 on Chainz β†—
Circulating Supply:57,949,062 XPMΒ·at block #6,838,088 Β· updates every 60s
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