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Block #366,082

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/19/2014, 4:45:33 AM Β· Difficulty 10.4259 Β· 6,461,172 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e6e625fa7897fe47f6dd7d5a3021653a5df10811d227e4ca9d3c8257a0117e77
View on Chainz β†—

Height

#366,082

Difficulty

10.425895

Transactions

1

Size

199 B

Version

2

Bits

0a6d0778

Nonce

63,542

Timestamp

1/19/2014, 4:45:33 AM

Confirmations

6,461,172

Merkle Root

a56759c0cf2dabf9b46c1eae5466790d16d70d381657186e3ebeafa5942caaac
Transactions (1)
Coinbasea56759c0cf2dab…beafa5942caaac
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.

2.065 Γ— 10⁹³(94-digit number)
20653647957620119870…45081776813113239280
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
2.065 Γ— 10⁹³(94-digit number)
20653647957620119870…45081776813113239279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.130 Γ— 10⁹³(94-digit number)
41307295915240239740…90163553626226478559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.261 Γ— 10⁹³(94-digit number)
82614591830480479480…80327107252452957119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.652 Γ— 10⁹⁴(95-digit number)
16522918366096095896…60654214504905914239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.304 Γ— 10⁹⁴(95-digit number)
33045836732192191792…21308429009811828479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.609 Γ— 10⁹⁴(95-digit number)
66091673464384383584…42616858019623656959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.321 Γ— 10⁹⁡(96-digit number)
13218334692876876716…85233716039247313919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.643 Γ— 10⁹⁡(96-digit number)
26436669385753753433…70467432078494627839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.287 Γ— 10⁹⁡(96-digit number)
52873338771507506867…40934864156989255679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.057 Γ— 10⁹⁢(97-digit number)
10574667754301501373…81869728313978511359
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 366082

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 e6e625fa7897fe47f6dd7d5a3021653a5df10811d227e4ca9d3c8257a0117e77

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 #366,082 on Chainz β†—
Circulating Supply:57,862,135 XPMΒ·at block #6,827,253 Β· updates every 60s
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