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Block #247,470

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/6/2013, 7:17:21 PM Β· Difficulty 9.9648 Β· 6,553,652 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6714fffc8277ebbd43d509eb99e76ec7693a3125c235cf35cf00cd5a4663e87d
View on Chainz β†—

Height

#247,470

Difficulty

9.964837

Transactions

1

Size

228 B

Version

2

Bits

09f6ff97

Nonce

1,363

Timestamp

11/6/2013, 7:17:21 PM

Confirmations

6,553,652

Merkle Root

a6e29fb81e2d97e83bab77ae917641d69c249133248494edcbb70f56d5327b53
Transactions (1)
Coinbasea6e29fb81e2d97…b70f56d5327b53
1 in β†’ 2 out10.0600 XPM137 B
ARmAMwyu…P7Kn74ZTAbiw8n3q…ZnZfgvQW
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.

8.642 Γ— 10⁹⁢(97-digit number)
86420067225011484828…96534482852532352000
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
8.642 Γ— 10⁹⁢(97-digit number)
86420067225011484828…96534482852532351999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.728 Γ— 10⁹⁷(98-digit number)
17284013445002296965…93068965705064703999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.456 Γ— 10⁹⁷(98-digit number)
34568026890004593931…86137931410129407999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.913 Γ— 10⁹⁷(98-digit number)
69136053780009187863…72275862820258815999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.382 Γ— 10⁹⁸(99-digit number)
13827210756001837572…44551725640517631999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.765 Γ— 10⁹⁸(99-digit number)
27654421512003675145…89103451281035263999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.530 Γ— 10⁹⁸(99-digit number)
55308843024007350290…78206902562070527999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.106 Γ— 10⁹⁹(100-digit number)
11061768604801470058…56413805124141055999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.212 Γ— 10⁹⁹(100-digit number)
22123537209602940116…12827610248282111999
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 247470

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 6714fffc8277ebbd43d509eb99e76ec7693a3125c235cf35cf00cd5a4663e87d

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 #247,470 on Chainz β†—
Circulating Supply:57,653,042 XPMΒ·at block #6,801,121 Β· updates every 60s
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