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Block #159,292

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/11/2013, 12:24:39 AM Β· Difficulty 9.8658 Β· 6,665,226 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
afdea0a5c0b751e32f3c8b47e18ef7e1fece21cb500ede2ffe40f57d0382b619
View on Chainz β†—

Height

#159,292

Difficulty

9.865751

Transactions

1

Size

198 B

Version

2

Bits

09dda1db

Nonce

17,793

Timestamp

9/11/2013, 12:24:39 AM

Confirmations

6,665,226

Merkle Root

aa0c44dc7c29a79c6fe988c9f79f9c60d2622b36189b48ffabd801323a812b9c
Transactions (1)
Coinbaseaa0c44dc7c29a7…d801323a812b9c
1 in β†’ 1 out10.2600 XPM109 B
AW9b9DiP…b6CitLxC
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.

4.798 Γ— 10⁹²(93-digit number)
47988715022282562974…30556069847900928000
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
4.798 Γ— 10⁹²(93-digit number)
47988715022282562974…30556069847900928001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.597 Γ— 10⁹²(93-digit number)
95977430044565125948…61112139695801856001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.919 Γ— 10⁹³(94-digit number)
19195486008913025189…22224279391603712001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.839 Γ— 10⁹³(94-digit number)
38390972017826050379…44448558783207424001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.678 Γ— 10⁹³(94-digit number)
76781944035652100758…88897117566414848001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.535 Γ— 10⁹⁴(95-digit number)
15356388807130420151…77794235132829696001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.071 Γ— 10⁹⁴(95-digit number)
30712777614260840303…55588470265659392001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.142 Γ— 10⁹⁴(95-digit number)
61425555228521680606…11176940531318784001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.228 Γ— 10⁹⁡(96-digit number)
12285111045704336121…22353881062637568001
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 159292

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 afdea0a5c0b751e32f3c8b47e18ef7e1fece21cb500ede2ffe40f57d0382b619

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 #159,292 on Chainz β†—
Circulating Supply:57,840,206 XPMΒ·at block #6,824,517 Β· updates every 60s
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