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Block #314,937

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/16/2013, 6:09:07 AM Β· Difficulty 10.0787 Β· 6,523,204 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c2267bcff92e88cd141276e4b34fc28dc38efe5d96b128be8a38810dfe8f68c1
View on Chainz β†—

Height

#314,937

Difficulty

10.078733

Transactions

1

Size

212 B

Version

2

Bits

0a1427da

Nonce

245,573

Timestamp

12/16/2013, 6:09:07 AM

Confirmations

6,523,204

Merkle Root

4a61826000d7bbb038d792442ac8eb304569178ad92457fa83a8474ef476ca83
Transactions (1)
Coinbase4a61826000d7bb…a8474ef476ca83
1 in β†’ 1 out9.8300 XPM118 B
AZxPvBWY…e18sa12g
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.

6.555 Γ— 10¹⁰⁴(105-digit number)
65550720162318807927…24055969668122166000
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
6.555 Γ— 10¹⁰⁴(105-digit number)
65550720162318807927…24055969668122165999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.311 Γ— 10¹⁰⁡(106-digit number)
13110144032463761585…48111939336244331999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.622 Γ— 10¹⁰⁡(106-digit number)
26220288064927523171…96223878672488663999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.244 Γ— 10¹⁰⁡(106-digit number)
52440576129855046342…92447757344977327999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.048 Γ— 10¹⁰⁢(107-digit number)
10488115225971009268…84895514689954655999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.097 Γ— 10¹⁰⁢(107-digit number)
20976230451942018536…69791029379909311999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.195 Γ— 10¹⁰⁢(107-digit number)
41952460903884037073…39582058759818623999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.390 Γ— 10¹⁰⁢(107-digit number)
83904921807768074147…79164117519637247999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.678 Γ— 10¹⁰⁷(108-digit number)
16780984361553614829…58328235039274495999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.356 Γ— 10¹⁰⁷(108-digit number)
33561968723107229659…16656470078548991999
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 314937

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 c2267bcff92e88cd141276e4b34fc28dc38efe5d96b128be8a38810dfe8f68c1

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 #314,937 on Chainz β†—
Circulating Supply:57,949,397 XPMΒ·at block #6,838,140 Β· updates every 60s
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