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Block #159,540

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/11/2013, 4:56:56 AM Β· Difficulty 9.8651 Β· 6,656,421 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9b69ae715bff6cd13940fd7fa7bd3861d805d868c193be6aa78476550e7aa154
View on Chainz β†—

Height

#159,540

Difficulty

9.865136

Transactions

2

Size

356 B

Version

2

Bits

09dd798b

Nonce

124,532

Timestamp

9/11/2013, 4:56:56 AM

Confirmations

6,656,421

Merkle Root

63ffcb6c03dddcf49f5cf5eaeb29e0dc6dafa14afc4fcd09d3131492346be985
Transactions (2)
Coinbase046cdcfc1137dd…2603133a09f3bd
1 in β†’ 1 out10.2700 XPM109 B
ASiN1vnG…nPBYx4TC
ef804a8d1730f5…9a67f08563b495
1 in β†’ 1 out10.2600 XPM157 B
AMm2NR1w…19uBFzE6
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.

1.955 Γ— 10⁹⁡(96-digit number)
19553579738483531841…42547519583128620800
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
1.955 Γ— 10⁹⁡(96-digit number)
19553579738483531841…42547519583128620801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.910 Γ— 10⁹⁡(96-digit number)
39107159476967063683…85095039166257241601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.821 Γ— 10⁹⁡(96-digit number)
78214318953934127367…70190078332514483201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.564 Γ— 10⁹⁢(97-digit number)
15642863790786825473…40380156665028966401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.128 Γ— 10⁹⁢(97-digit number)
31285727581573650946…80760313330057932801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.257 Γ— 10⁹⁢(97-digit number)
62571455163147301893…61520626660115865601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.251 Γ— 10⁹⁷(98-digit number)
12514291032629460378…23041253320231731201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.502 Γ— 10⁹⁷(98-digit number)
25028582065258920757…46082506640463462401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.005 Γ— 10⁹⁷(98-digit number)
50057164130517841515…92165013280926924801
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 159540

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 9b69ae715bff6cd13940fd7fa7bd3861d805d868c193be6aa78476550e7aa154

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 #159,540 on Chainz β†—
Circulating Supply:57,771,803 XPMΒ·at block #6,815,960 Β· updates every 60s
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