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Block #794,541

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/2/2014, 11:35:27 PM Β· Difficulty 10.9750 Β· 6,030,429 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fd029ffd9ee81fb67bca463271782f3bb975bd3a0831a1519d2e209a13e8cb3b
View on Chainz β†—

Height

#794,541

Difficulty

10.974969

Transactions

1

Size

199 B

Version

2

Bits

0af99798

Nonce

1,992,287,162

Timestamp

11/2/2014, 11:35:27 PM

Confirmations

6,030,429

Merkle Root

225970babc18728e19296a4a4db25edf57d5e0b261ea04d02927bb4d9f1ac967
Transactions (1)
Coinbase225970babc1872…27bb4d9f1ac967
1 in β†’ 1 out8.2900 XPM110 B
AQVD9VfC…5QDekNhL
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.

4.462 Γ— 10⁹²(93-digit number)
44625098699614770066…07409657621190787880
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
4.462 Γ— 10⁹²(93-digit number)
44625098699614770066…07409657621190787881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.925 Γ— 10⁹²(93-digit number)
89250197399229540132…14819315242381575761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.785 Γ— 10⁹³(94-digit number)
17850039479845908026…29638630484763151521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.570 Γ— 10⁹³(94-digit number)
35700078959691816052…59277260969526303041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.140 Γ— 10⁹³(94-digit number)
71400157919383632105…18554521939052606081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.428 Γ— 10⁹⁴(95-digit number)
14280031583876726421…37109043878105212161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.856 Γ— 10⁹⁴(95-digit number)
28560063167753452842…74218087756210424321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.712 Γ— 10⁹⁴(95-digit number)
57120126335506905684…48436175512420848641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.142 Γ— 10⁹⁡(96-digit number)
11424025267101381136…96872351024841697281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.284 Γ— 10⁹⁡(96-digit number)
22848050534202762273…93744702049683394561
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 794541

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 fd029ffd9ee81fb67bca463271782f3bb975bd3a0831a1519d2e209a13e8cb3b

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 #794,541 on Chainz β†—
Circulating Supply:57,843,840 XPMΒ·at block #6,824,969 Β· updates every 60s
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