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Block #174,561

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/21/2013, 6:10:15 PM Β· Difficulty 9.8613 Β· 6,641,873 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cfe43d9df9b686111fae75793109807e8d968c045819b53edc9cec084094f5de
View on Chainz β†—

Height

#174,561

Difficulty

9.861286

Transactions

1

Size

198 B

Version

2

Bits

09dc7d40

Nonce

13,492

Timestamp

9/21/2013, 6:10:15 PM

Confirmations

6,641,873

Merkle Root

8fa03ef369ca21c752f1d7c5d8a05dbe71ac66015c5a76a3b3cdcb7b955c2b3d
Transactions (1)
Coinbase8fa03ef369ca21…cdcb7b955c2b3d
1 in β†’ 1 out10.2700 XPM109 B
ASiN1vnG…nPBYx4TC
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.

1.882 Γ— 10⁹²(93-digit number)
18823245191271483526…80999217608443179000
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
1.882 Γ— 10⁹²(93-digit number)
18823245191271483526…80999217608443178999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.764 Γ— 10⁹²(93-digit number)
37646490382542967053…61998435216886357999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.529 Γ— 10⁹²(93-digit number)
75292980765085934107…23996870433772715999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.505 Γ— 10⁹³(94-digit number)
15058596153017186821…47993740867545431999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.011 Γ— 10⁹³(94-digit number)
30117192306034373642…95987481735090863999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.023 Γ— 10⁹³(94-digit number)
60234384612068747285…91974963470181727999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.204 Γ— 10⁹⁴(95-digit number)
12046876922413749457…83949926940363455999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.409 Γ— 10⁹⁴(95-digit number)
24093753844827498914…67899853880726911999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.818 Γ— 10⁹⁴(95-digit number)
48187507689654997828…35799707761453823999
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 174561

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 cfe43d9df9b686111fae75793109807e8d968c045819b53edc9cec084094f5de

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 #174,561 on Chainz β†—
Circulating Supply:57,775,599 XPMΒ·at block #6,816,433 Β· updates every 60s
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