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Block #244,223

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/4/2013, 5:50:23 PM Β· Difficulty 9.9627 Β· 6,568,250 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ea31a3c3193e9afb297bd2cd100dbb2a1f9cbb4d9aee4fe2d9d4baa85e66cae5
View on Chainz β†—

Height

#244,223

Difficulty

9.962705

Transactions

1

Size

204 B

Version

2

Bits

09f673d5

Nonce

16,779,033

Timestamp

11/4/2013, 5:50:23 PM

Confirmations

6,568,250

Merkle Root

0f8103b97b9dc46ddff4f85c2598496877a2c88b4f0e70e2a8e1c7cfa8c8f300
Transactions (1)
Coinbase0f8103b97b9dc4…e1c7cfa8c8f300
1 in β†’ 1 out10.0600 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.

6.254 Γ— 10⁹⁰(91-digit number)
62546284382765033610…94753345094719802620
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
6.254 Γ— 10⁹⁰(91-digit number)
62546284382765033610…94753345094719802619
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.250 Γ— 10⁹¹(92-digit number)
12509256876553006722…89506690189439605239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.501 Γ— 10⁹¹(92-digit number)
25018513753106013444…79013380378879210479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.003 Γ— 10⁹¹(92-digit number)
50037027506212026888…58026760757758420959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.000 Γ— 10⁹²(93-digit number)
10007405501242405377…16053521515516841919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.001 Γ— 10⁹²(93-digit number)
20014811002484810755…32107043031033683839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.002 Γ— 10⁹²(93-digit number)
40029622004969621510…64214086062067367679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.005 Γ— 10⁹²(93-digit number)
80059244009939243021…28428172124134735359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.601 Γ— 10⁹³(94-digit number)
16011848801987848604…56856344248269470719
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 244223

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 ea31a3c3193e9afb297bd2cd100dbb2a1f9cbb4d9aee4fe2d9d4baa85e66cae5

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 #244,223 on Chainz β†—
Circulating Supply:57,743,811 XPMΒ·at block #6,812,472 Β· updates every 60s
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