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Home/Chain Registry/Block #1,404,240

Block #1,404,240

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/8/2016, 9:38:23 AM Β· Difficulty 10.8053 Β· 5,420,693 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f11b94703deca039e69900ea85acd7ee16a6a55610eed0f8fa622b8a2a09e97b
View on Chainz β†—

Difficulty

10.805279

Transactions

1

Size

200 B

Version

2

Bits

0ace26be

Nonce

1,374,307,782

Timestamp

1/8/2016, 9:38:23 AM

Confirmations

5,420,693

Merkle Root

0154639e9ad03fcc808312896814da103654ac800773079370955a44335fac42
Transactions (1)
Coinbase0154639e9ad03f…955a44335fac42
1 in β†’ 1 out8.5500 XPM110 B
AV6AauEg…NpuknjZ6
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.

3.408 Γ— 10⁹³(94-digit number)
34089480067052557467…30875953731825972480
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
3.408 Γ— 10⁹³(94-digit number)
34089480067052557467…30875953731825972481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.817 Γ— 10⁹³(94-digit number)
68178960134105114935…61751907463651944961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.363 Γ— 10⁹⁴(95-digit number)
13635792026821022987…23503814927303889921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.727 Γ— 10⁹⁴(95-digit number)
27271584053642045974…47007629854607779841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.454 Γ— 10⁹⁴(95-digit number)
54543168107284091948…94015259709215559681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.090 Γ— 10⁹⁡(96-digit number)
10908633621456818389…88030519418431119361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.181 Γ— 10⁹⁡(96-digit number)
21817267242913636779…76061038836862238721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.363 Γ— 10⁹⁡(96-digit number)
43634534485827273558…52122077673724477441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.726 Γ— 10⁹⁡(96-digit number)
87269068971654547117…04244155347448954881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.745 Γ— 10⁹⁢(97-digit number)
17453813794330909423…08488310694897909761
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 1404240

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 f11b94703deca039e69900ea85acd7ee16a6a55610eed0f8fa622b8a2a09e97b

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 #1,404,240 on Chainz β†—
Circulating Supply:57,843,539 XPMΒ·at block #6,824,932 Β· updates every 60s
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