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Home/Chain Registry/Block #2,749,367

Block #2,749,367

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/15/2018, 2:13:43 AM Β· Difficulty 11.6472 Β· 4,093,738 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eed7c18dd7c18978be64f0716b8d89752f3c317b1e40cac9fbd5e708123923fc
View on Chainz β†—

Difficulty

11.647203

Transactions

1

Size

200 B

Version

2

Bits

0ba5af1a

Nonce

525,468,730

Timestamp

7/15/2018, 2:13:43 AM

Confirmations

4,093,738

Merkle Root

3de049fee62b14e4e4326372c87c3c355b9a15f76a7a97ddda950a3483809807
Transactions (1)
Coinbase3de049fee62b14…950a3483809807
1 in β†’ 1 out7.3600 XPM110 B
AZtxQr2F…7grUWrUz
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.

7.926 Γ— 10⁹³(94-digit number)
79265984495672689576…22863949685247942940
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
7.926 Γ— 10⁹³(94-digit number)
79265984495672689576…22863949685247942941
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.585 Γ— 10⁹⁴(95-digit number)
15853196899134537915…45727899370495885881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.170 Γ— 10⁹⁴(95-digit number)
31706393798269075830…91455798740991771761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.341 Γ— 10⁹⁴(95-digit number)
63412787596538151661…82911597481983543521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.268 Γ— 10⁹⁡(96-digit number)
12682557519307630332…65823194963967087041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.536 Γ— 10⁹⁡(96-digit number)
25365115038615260664…31646389927934174081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.073 Γ— 10⁹⁡(96-digit number)
50730230077230521328…63292779855868348161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.014 Γ— 10⁹⁢(97-digit number)
10146046015446104265…26585559711736696321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.029 Γ— 10⁹⁢(97-digit number)
20292092030892208531…53171119423473392641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.058 Γ— 10⁹⁢(97-digit number)
40584184061784417063…06342238846946785281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.116 Γ— 10⁹⁢(97-digit number)
81168368123568834126…12684477693893570561
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2749367

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 eed7c18dd7c18978be64f0716b8d89752f3c317b1e40cac9fbd5e708123923fc

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 #2,749,367 on Chainz β†—
Circulating Supply:57,989,204 XPMΒ·at block #6,843,104 Β· updates every 60s
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