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Block #317,126

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/17/2013, 11:29:22 AM Β· Difficulty 10.1548 Β· 6,479,220 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
afd9a305775f7308df8823cff08f82c303cc3df231a5489b3b46402b68ffbe07
View on Chainz β†—

Height

#317,126

Difficulty

10.154807

Transactions

1

Size

199 B

Version

2

Bits

0a27a16f

Nonce

224,796

Timestamp

12/17/2013, 11:29:22 AM

Confirmations

6,479,220

Merkle Root

056cefa9433a366f4c0b90af9b52a93b8d49e959aeed09bc21b51ff39a59ece2
Transactions (1)
Coinbase056cefa9433a36…b51ff39a59ece2
1 in β†’ 1 out9.6800 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.197 Γ— 10⁹¹(92-digit number)
11979355067102732871…91743879580581619200
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
1.197 Γ— 10⁹¹(92-digit number)
11979355067102732871…91743879580581619199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.395 Γ— 10⁹¹(92-digit number)
23958710134205465742…83487759161163238399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.791 Γ— 10⁹¹(92-digit number)
47917420268410931485…66975518322326476799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.583 Γ— 10⁹¹(92-digit number)
95834840536821862971…33951036644652953599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.916 Γ— 10⁹²(93-digit number)
19166968107364372594…67902073289305907199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.833 Γ— 10⁹²(93-digit number)
38333936214728745188…35804146578611814399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.666 Γ— 10⁹²(93-digit number)
76667872429457490376…71608293157223628799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.533 Γ— 10⁹³(94-digit number)
15333574485891498075…43216586314447257599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.066 Γ— 10⁹³(94-digit number)
30667148971782996150…86433172628894515199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.133 Γ— 10⁹³(94-digit number)
61334297943565992301…72866345257789030399
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 317126

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 afd9a305775f7308df8823cff08f82c303cc3df231a5489b3b46402b68ffbe07

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 #317,126 on Chainz β†—
Circulating Supply:57,614,761 XPMΒ·at block #6,796,345 Β· updates every 60s
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