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Block #184,630

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/28/2013, 7:13:11 PM Β· Difficulty 9.8601 Β· 6,630,428 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1e8afda04a5156ddd8127fcad5030da8a87feb71a29b9e9c90657035e2df0340
View on Chainz β†—

Height

#184,630

Difficulty

9.860113

Transactions

1

Size

206 B

Version

2

Bits

09dc305b

Nonce

100,663,462

Timestamp

9/28/2013, 7:13:11 PM

Confirmations

6,630,428

Merkle Root

97195d939a02dd95dd0cecb9f984422a55b4f6a5a03163db7a2a4c48b966628b
Transactions (1)
Coinbase97195d939a02dd…2a4c48b966628b
1 in β†’ 1 out10.2700 XPM116 B
AcLBm5Z9…S683d7c3
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.

5.585 Γ— 10⁹⁴(95-digit number)
55850859620197365745…64712670184332133120
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
5.585 Γ— 10⁹⁴(95-digit number)
55850859620197365745…64712670184332133119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.117 Γ— 10⁹⁡(96-digit number)
11170171924039473149…29425340368664266239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.234 Γ— 10⁹⁡(96-digit number)
22340343848078946298…58850680737328532479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.468 Γ— 10⁹⁡(96-digit number)
44680687696157892596…17701361474657064959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.936 Γ— 10⁹⁡(96-digit number)
89361375392315785192…35402722949314129919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.787 Γ— 10⁹⁢(97-digit number)
17872275078463157038…70805445898628259839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.574 Γ— 10⁹⁢(97-digit number)
35744550156926314077…41610891797256519679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.148 Γ— 10⁹⁢(97-digit number)
71489100313852628154…83221783594513039359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.429 Γ— 10⁹⁷(98-digit number)
14297820062770525630…66443567189026078719
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 184630

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 1e8afda04a5156ddd8127fcad5030da8a87feb71a29b9e9c90657035e2df0340

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 #184,630 on Chainz β†—
Circulating Supply:57,764,554 XPMΒ·at block #6,815,057 Β· updates every 60s
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