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Block #374,481

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/25/2014, 1:32:43 AM Β· Difficulty 10.4228 Β· 6,450,263 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
824ffb7fd0be096d55efeb9db6698011aa3f62e8fa46cad34149582de6c7a042
View on Chainz β†—

Height

#374,481

Difficulty

10.422798

Transactions

1

Size

202 B

Version

2

Bits

0a6c3c7f

Nonce

13,659

Timestamp

1/25/2014, 1:32:43 AM

Confirmations

6,450,263

Merkle Root

b434e89163fab41b0aadc7a36282077e258395da864c42e9298022f7d70bc395
Transactions (1)
Coinbaseb434e89163fab4…8022f7d70bc395
1 in β†’ 1 out9.1900 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.

4.778 Γ— 10⁹⁸(99-digit number)
47780232399656846770…24217597043677975200
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
4.778 Γ— 10⁹⁸(99-digit number)
47780232399656846770…24217597043677975199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.556 Γ— 10⁹⁸(99-digit number)
95560464799313693540…48435194087355950399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.911 Γ— 10⁹⁹(100-digit number)
19112092959862738708…96870388174711900799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.822 Γ— 10⁹⁹(100-digit number)
38224185919725477416…93740776349423801599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.644 Γ— 10⁹⁹(100-digit number)
76448371839450954832…87481552698847603199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.528 Γ— 10¹⁰⁰(101-digit number)
15289674367890190966…74963105397695206399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.057 Γ— 10¹⁰⁰(101-digit number)
30579348735780381933…49926210795390412799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.115 Γ— 10¹⁰⁰(101-digit number)
61158697471560763866…99852421590780825599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.223 Γ— 10¹⁰¹(102-digit number)
12231739494312152773…99704843181561651199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.446 Γ— 10¹⁰¹(102-digit number)
24463478988624305546…99409686363123302399
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 374481

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 824ffb7fd0be096d55efeb9db6698011aa3f62e8fa46cad34149582de6c7a042

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 #374,481 on Chainz β†—
Circulating Supply:57,842,022 XPMΒ·at block #6,824,743 Β· updates every 60s
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