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Block #179,042

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/24/2013, 7:23:42 PM Β· Difficulty 9.8639 Β· 6,615,410 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fda1d3684207ab58b5c92cdb3f8de9ca7ef6c901ff4b410eaf263e88dc3696ff
View on Chainz β†—

Height

#179,042

Difficulty

9.863887

Transactions

1

Size

200 B

Version

2

Bits

09dd27b3

Nonce

2,369

Timestamp

9/24/2013, 7:23:42 PM

Confirmations

6,615,410

Merkle Root

ea524568c8ec33f2aad5515f80d3de020d9d94a265ce0694f684d59b0177efd9
Transactions (1)
Coinbaseea524568c8ec33…84d59b0177efd9
1 in β†’ 1 out10.2600 XPM109 B
Af4wD75X…Lxgjq8Ud
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.

9.451 Γ— 10⁹⁡(96-digit number)
94517035233560576234…45339867195310188800
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
9.451 Γ— 10⁹⁡(96-digit number)
94517035233560576234…45339867195310188801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.890 Γ— 10⁹⁢(97-digit number)
18903407046712115246…90679734390620377601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.780 Γ— 10⁹⁢(97-digit number)
37806814093424230493…81359468781240755201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.561 Γ— 10⁹⁢(97-digit number)
75613628186848460987…62718937562481510401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.512 Γ— 10⁹⁷(98-digit number)
15122725637369692197…25437875124963020801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.024 Γ— 10⁹⁷(98-digit number)
30245451274739384395…50875750249926041601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.049 Γ— 10⁹⁷(98-digit number)
60490902549478768790…01751500499852083201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.209 Γ— 10⁹⁸(99-digit number)
12098180509895753758…03503000999704166401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.419 Γ— 10⁹⁸(99-digit number)
24196361019791507516…07006001999408332801
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 179042

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 fda1d3684207ab58b5c92cdb3f8de9ca7ef6c901ff4b410eaf263e88dc3696ff

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 #179,042 on Chainz β†—
Circulating Supply:57,599,656 XPMΒ·at block #6,794,451 Β· updates every 60s
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