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Home/Chain Registry/Block #166,579

Block #166,579

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/16/2013, 12:22:18 AM Β· Difficulty 9.8684 Β· 6,658,173 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dc4f5b3087c98fbb504ac51e99a68c1df698453c55d806ee77b97a247f3e2b04
View on Chainz β†—

Height

#166,579

Difficulty

9.868399

Transactions

1

Size

198 B

Version

2

Bits

09de4f6a

Nonce

17,361

Timestamp

9/16/2013, 12:22:18 AM

Confirmations

6,658,173

Merkle Root

8fd5b4fe42fe813bdc8c735895625dc415650da005fad4a2eb63120134cd32b5
Transactions (1)
Coinbase8fd5b4fe42fe81…63120134cd32b5
1 in β†’ 1 out10.2500 XPM109 B
AMa6LrBT…pGxPwh7T
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.

1.298 Γ— 10⁹¹(92-digit number)
12987127257280830470…14155759132758916000
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
1.298 Γ— 10⁹¹(92-digit number)
12987127257280830470…14155759132758915999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.597 Γ— 10⁹¹(92-digit number)
25974254514561660941…28311518265517831999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.194 Γ— 10⁹¹(92-digit number)
51948509029123321882…56623036531035663999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.038 Γ— 10⁹²(93-digit number)
10389701805824664376…13246073062071327999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.077 Γ— 10⁹²(93-digit number)
20779403611649328753…26492146124142655999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.155 Γ— 10⁹²(93-digit number)
41558807223298657506…52984292248285311999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.311 Γ— 10⁹²(93-digit number)
83117614446597315012…05968584496570623999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.662 Γ— 10⁹³(94-digit number)
16623522889319463002…11937168993141247999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.324 Γ— 10⁹³(94-digit number)
33247045778638926005…23874337986282495999
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 166579

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 dc4f5b3087c98fbb504ac51e99a68c1df698453c55d806ee77b97a247f3e2b04

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 #166,579 on Chainz β†—
Circulating Supply:57,842,087 XPMΒ·at block #6,824,751 Β· updates every 60s
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