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Block #135,561

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/26/2013, 5:02:49 PM Β· Difficulty 9.8111 Β· 6,676,143 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
82d855a84e9a966d21feba04f9d6a9175c7bd5b7193ef963d2d6e29d9cb969b0
View on Chainz β†—

Height

#135,561

Difficulty

9.811121

Transactions

2

Size

4.21 KB

Version

2

Bits

09cfa5a6

Nonce

25,045

Timestamp

8/26/2013, 5:02:49 PM

Confirmations

6,676,143

Merkle Root

b7e64c8253a99a8a6452d5aa9386708f441e84db13e3d3aa0db1465737fb1d92
Transactions (2)
Coinbase47045d527a950b…c68ea13defb59c
1 in β†’ 1 out10.4200 XPM109 B
AFxtmUWz…sND4q5cA
ae1d2b7b9d5a1d…41bd1cad7d5238
33 in β†’ 2 out400.0107 XPM4.02 KB
AbMEW2LJ…Ntb1rfN5AM6vjhTo…f7Nt8tSJ
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.

3.304 Γ— 10⁸⁸(89-digit number)
33047604683679339709…22424126340565779000
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
3.304 Γ— 10⁸⁸(89-digit number)
33047604683679339709…22424126340565779001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.609 Γ— 10⁸⁸(89-digit number)
66095209367358679418…44848252681131558001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.321 Γ— 10⁸⁹(90-digit number)
13219041873471735883…89696505362263116001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.643 Γ— 10⁸⁹(90-digit number)
26438083746943471767…79393010724526232001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.287 Γ— 10⁸⁹(90-digit number)
52876167493886943534…58786021449052464001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.057 Γ— 10⁹⁰(91-digit number)
10575233498777388706…17572042898104928001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.115 Γ— 10⁹⁰(91-digit number)
21150466997554777413…35144085796209856001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.230 Γ— 10⁹⁰(91-digit number)
42300933995109554827…70288171592419712001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.460 Γ— 10⁹⁰(91-digit number)
84601867990219109655…40576343184839424001
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 135561

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 82d855a84e9a966d21feba04f9d6a9175c7bd5b7193ef963d2d6e29d9cb969b0

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 #135,561 on Chainz β†—
Circulating Supply:57,737,743 XPMΒ·at block #6,811,703 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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