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Block #423,694

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/28/2014, 2:35:13 PM Β· Difficulty 10.3791 Β· 6,403,038 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a6fba6f6a9ad18381ebbd31ec7629a878e2ffb479528448c1ebb93b5b6c1749a
View on Chainz β†—

Height

#423,694

Difficulty

10.379149

Transactions

1

Size

221 B

Version

2

Bits

0a610fee

Nonce

589,347

Timestamp

2/28/2014, 2:35:13 PM

Confirmations

6,403,038

Merkle Root

827481946b0f4ac84608f64927a293c7f48db489567cfa28ebd22b4cdee36588
Transactions (1)
Coinbase827481946b0f4a…d22b4cdee36588
1 in β†’ 2 out9.2700 XPM131 B
AMVf7Jrg…xd5AVR7CAJno7LX2…vo4wdWtY
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.

5.092 Γ— 10⁹³(94-digit number)
50924572188164405303…79436951754949337440
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
5.092 Γ— 10⁹³(94-digit number)
50924572188164405303…79436951754949337441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.018 Γ— 10⁹⁴(95-digit number)
10184914437632881060…58873903509898674881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.036 Γ— 10⁹⁴(95-digit number)
20369828875265762121…17747807019797349761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.073 Γ— 10⁹⁴(95-digit number)
40739657750531524242…35495614039594699521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.147 Γ— 10⁹⁴(95-digit number)
81479315501063048485…70991228079189399041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.629 Γ— 10⁹⁡(96-digit number)
16295863100212609697…41982456158378798081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.259 Γ— 10⁹⁡(96-digit number)
32591726200425219394…83964912316757596161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.518 Γ— 10⁹⁡(96-digit number)
65183452400850438788…67929824633515192321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.303 Γ— 10⁹⁢(97-digit number)
13036690480170087757…35859649267030384641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.607 Γ— 10⁹⁢(97-digit number)
26073380960340175515…71719298534060769281
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 423694

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 a6fba6f6a9ad18381ebbd31ec7629a878e2ffb479528448c1ebb93b5b6c1749a

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 #423,694 on Chainz β†—
Circulating Supply:57,858,010 XPMΒ·at block #6,826,731 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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