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Home/Chain Registry/Block #1,411,642

Block #1,411,642

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/13/2016, 1:05:10 PM Β· Difficulty 10.8054 Β· 5,431,775 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
56d81b38ea6a4d9da666a1089bf7cb1baccbc7a4f210531d35801f78a39c16fd
View on Chainz β†—

Difficulty

10.805354

Transactions

1

Size

200 B

Version

2

Bits

0ace2bae

Nonce

663,306,672

Timestamp

1/13/2016, 1:05:10 PM

Confirmations

5,431,775

Merkle Root

ce6812d1dc30d1c030a9cdd8698d881e3346480e19d35a7d8188a4e807130907
Transactions (1)
Coinbasece6812d1dc30d1…88a4e807130907
1 in β†’ 1 out8.5500 XPM110 B
Ac71eYQ2…GL937JCo
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.

1.760 Γ— 10⁹⁡(96-digit number)
17602551773323824366…20684885618279797760
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
1.760 Γ— 10⁹⁡(96-digit number)
17602551773323824366…20684885618279797761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.520 Γ— 10⁹⁡(96-digit number)
35205103546647648733…41369771236559595521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.041 Γ— 10⁹⁡(96-digit number)
70410207093295297467…82739542473119191041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.408 Γ— 10⁹⁢(97-digit number)
14082041418659059493…65479084946238382081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.816 Γ— 10⁹⁢(97-digit number)
28164082837318118986…30958169892476764161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.632 Γ— 10⁹⁢(97-digit number)
56328165674636237973…61916339784953528321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.126 Γ— 10⁹⁷(98-digit number)
11265633134927247594…23832679569907056641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.253 Γ— 10⁹⁷(98-digit number)
22531266269854495189…47665359139814113281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.506 Γ— 10⁹⁷(98-digit number)
45062532539708990379…95330718279628226561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.012 Γ— 10⁹⁷(98-digit number)
90125065079417980758…90661436559256453121
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 1411642

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 56d81b38ea6a4d9da666a1089bf7cb1baccbc7a4f210531d35801f78a39c16fd

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 #1,411,642 on Chainz β†—
Circulating Supply:57,991,704 XPMΒ·at block #6,843,416 Β· updates every 60s
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