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Block #294,096

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/4/2013, 4:42:08 PM Β· Difficulty 9.9909 Β· 6,532,000 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4ad2f6ecc44c63e96f8b86675f37214f61f40598ba4765f9796517b2d0fa14e5
View on Chainz β†—

Height

#294,096

Difficulty

9.990882

Transactions

1

Size

207 B

Version

2

Bits

09fdaa74

Nonce

22,082

Timestamp

12/4/2013, 4:42:08 PM

Confirmations

6,532,000

Merkle Root

27bc0b611ed59103ffb7d7c68d5a5ca86bf1a82b84132b3d0ad8614e7eeed8e9
Transactions (1)
Coinbase27bc0b611ed591…d8614e7eeed8e9
1 in β†’ 1 out10.0000 XPM116 B
AcLBm5Z9…S683d7c3
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.

4.436 Γ— 10⁹⁷(98-digit number)
44362274228510356960…88885163714830453700
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
4.436 Γ— 10⁹⁷(98-digit number)
44362274228510356960…88885163714830453699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.872 Γ— 10⁹⁷(98-digit number)
88724548457020713920…77770327429660907399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.774 Γ— 10⁹⁸(99-digit number)
17744909691404142784…55540654859321814799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.548 Γ— 10⁹⁸(99-digit number)
35489819382808285568…11081309718643629599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.097 Γ— 10⁹⁸(99-digit number)
70979638765616571136…22162619437287259199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.419 Γ— 10⁹⁹(100-digit number)
14195927753123314227…44325238874574518399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.839 Γ— 10⁹⁹(100-digit number)
28391855506246628454…88650477749149036799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.678 Γ— 10⁹⁹(100-digit number)
56783711012493256909…77300955498298073599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.135 Γ— 10¹⁰⁰(101-digit number)
11356742202498651381…54601910996596147199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.271 Γ— 10¹⁰⁰(101-digit number)
22713484404997302763…09203821993192294399
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 294096

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 4ad2f6ecc44c63e96f8b86675f37214f61f40598ba4765f9796517b2d0fa14e5

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 #294,096 on Chainz β†—
Circulating Supply:57,852,890 XPMΒ·at block #6,826,095 Β· updates every 60s
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