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Home/Chain Registry/Block #1,344,019

Block #1,344,019

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/27/2015, 8:31:08 AM Β· Difficulty 10.8152 Β· 5,482,695 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1cd215aa633ac7646b55b512571e93790ff357df27238ddc6b9a7efbdd5cc99e
View on Chainz β†—

Difficulty

10.815230

Transactions

1

Size

200 B

Version

2

Bits

0ad0b2ee

Nonce

1,607,333,509

Timestamp

11/27/2015, 8:31:08 AM

Confirmations

5,482,695

Merkle Root

444d2f489e6115062c1f3b6787ff4f58a865539a4f8c3d6783541dec59c0dfc4
Transactions (1)
Coinbase444d2f489e6115…541dec59c0dfc4
1 in β†’ 1 out8.5400 XPM110 B
AW9NR1ua…UbCa9tRc
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.

8.096 Γ— 10⁹⁴(95-digit number)
80965759260133179845…31876905539450392800
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
8.096 Γ— 10⁹⁴(95-digit number)
80965759260133179845…31876905539450392801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.619 Γ— 10⁹⁡(96-digit number)
16193151852026635969…63753811078900785601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.238 Γ— 10⁹⁡(96-digit number)
32386303704053271938…27507622157801571201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.477 Γ— 10⁹⁡(96-digit number)
64772607408106543876…55015244315603142401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.295 Γ— 10⁹⁢(97-digit number)
12954521481621308775…10030488631206284801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.590 Γ— 10⁹⁢(97-digit number)
25909042963242617550…20060977262412569601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.181 Γ— 10⁹⁢(97-digit number)
51818085926485235100…40121954524825139201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.036 Γ— 10⁹⁷(98-digit number)
10363617185297047020…80243909049650278401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.072 Γ— 10⁹⁷(98-digit number)
20727234370594094040…60487818099300556801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.145 Γ— 10⁹⁷(98-digit number)
41454468741188188080…20975636198601113601
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 1344019

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 1cd215aa633ac7646b55b512571e93790ff357df27238ddc6b9a7efbdd5cc99e

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 #1,344,019 on Chainz β†—
Circulating Supply:57,857,865 XPMΒ·at block #6,826,713 Β· updates every 60s
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