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Block #51,792

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/16/2013, 7:26:23 AM Β· Difficulty 8.9035 Β· 6,772,952 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2993fdc610843e66b27a1c8053fcb5e758d9ab6c9df30caa8b9b669793c64c89
View on Chainz β†—

Height

#51,792

Difficulty

8.903461

Transactions

1

Size

200 B

Version

2

Bits

08e74930

Nonce

359

Timestamp

7/16/2013, 7:26:23 AM

Confirmations

6,772,952

Merkle Root

294357f946ac0486f1f49640c78cac52864efbf7fdd96fc045c99e5b064b1f3e
Transactions (1)
Coinbase294357f946ac04…c99e5b064b1f3e
1 in β†’ 1 out12.6000 XPM109 B
ATd6Gy38…xU5yvzGp
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.

7.715 Γ— 10⁹⁷(98-digit number)
77154262204352863621…85474182193274470560
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
7.715 Γ— 10⁹⁷(98-digit number)
77154262204352863621…85474182193274470561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.543 Γ— 10⁹⁸(99-digit number)
15430852440870572724…70948364386548941121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.086 Γ— 10⁹⁸(99-digit number)
30861704881741145448…41896728773097882241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.172 Γ— 10⁹⁸(99-digit number)
61723409763482290897…83793457546195764481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.234 Γ— 10⁹⁹(100-digit number)
12344681952696458179…67586915092391528961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.468 Γ— 10⁹⁹(100-digit number)
24689363905392916358…35173830184783057921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.937 Γ— 10⁹⁹(100-digit number)
49378727810785832717…70347660369566115841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.875 Γ— 10⁹⁹(100-digit number)
98757455621571665435…40695320739132231681
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8
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 51792

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 2993fdc610843e66b27a1c8053fcb5e758d9ab6c9df30caa8b9b669793c64c89

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 #51,792 on Chainz β†—
Circulating Supply:57,842,022 XPMΒ·at block #6,824,743 Β· updates every 60s
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