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Block #314,887

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/16/2013, 5:22:09 AM Β· Difficulty 10.0782 Β· 6,485,533 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3929fd93ee52bf17cbc2e6366e7a7608ac9aebe2e271c37098abf57cf5b241f9
View on Chainz β†—

Height

#314,887

Difficulty

10.078243

Transactions

1

Size

207 B

Version

2

Bits

0a1407bd

Nonce

47,084

Timestamp

12/16/2013, 5:22:09 AM

Confirmations

6,485,533

Merkle Root

f56ab2da59e364534dfacc391127c52903bd5a1e8b49f0fe6827fb3bec95d666
Transactions (1)
Coinbasef56ab2da59e364…27fb3bec95d666
1 in β†’ 1 out9.8300 XPM116 B
AbwWkWZt…kawDhufa
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.

7.128 Γ— 10⁹⁷(98-digit number)
71282449004861695005…43052827545552994240
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
7.128 Γ— 10⁹⁷(98-digit number)
71282449004861695005…43052827545552994239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.425 Γ— 10⁹⁸(99-digit number)
14256489800972339001…86105655091105988479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.851 Γ— 10⁹⁸(99-digit number)
28512979601944678002…72211310182211976959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.702 Γ— 10⁹⁸(99-digit number)
57025959203889356004…44422620364423953919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.140 Γ— 10⁹⁹(100-digit number)
11405191840777871200…88845240728847907839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.281 Γ— 10⁹⁹(100-digit number)
22810383681555742401…77690481457695815679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.562 Γ— 10⁹⁹(100-digit number)
45620767363111484803…55380962915391631359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.124 Γ— 10⁹⁹(100-digit number)
91241534726222969607…10761925830783262719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.824 Γ— 10¹⁰⁰(101-digit number)
18248306945244593921…21523851661566525439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.649 Γ— 10¹⁰⁰(101-digit number)
36496613890489187843…43047703323133050879
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 314887

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 3929fd93ee52bf17cbc2e6366e7a7608ac9aebe2e271c37098abf57cf5b241f9

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 #314,887 on Chainz β†—
Circulating Supply:57,647,424 XPMΒ·at block #6,800,419 Β· updates every 60s
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