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Block #166,089

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/15/2013, 5:10:37 PM Β· Difficulty 9.8669 Β· 6,660,850 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4f1917d5a2508f1e832a57feb2b7d6d4d81501268c66f4a3d76015d0908c673b
View on Chainz β†—

Height

#166,089

Difficulty

9.866904

Transactions

1

Size

198 B

Version

2

Bits

09dded64

Nonce

525,077

Timestamp

9/15/2013, 5:10:37 PM

Confirmations

6,660,850

Merkle Root

7db77ddceff80523757c60c44ec6de47c14be8606214944710b162f4a46b1125
Transactions (1)
Coinbase7db77ddceff805…b162f4a46b1125
1 in β†’ 1 out10.2600 XPM109 B
Ad4r8ZFu…p3oa5EDi
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.

2.169 Γ— 10⁹¹(92-digit number)
21696591267893631228…76639476065495825960
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
2.169 Γ— 10⁹¹(92-digit number)
21696591267893631228…76639476065495825961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.339 Γ— 10⁹¹(92-digit number)
43393182535787262457…53278952130991651921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.678 Γ— 10⁹¹(92-digit number)
86786365071574524914…06557904261983303841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.735 Γ— 10⁹²(93-digit number)
17357273014314904982…13115808523966607681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.471 Γ— 10⁹²(93-digit number)
34714546028629809965…26231617047933215361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.942 Γ— 10⁹²(93-digit number)
69429092057259619931…52463234095866430721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.388 Γ— 10⁹³(94-digit number)
13885818411451923986…04926468191732861441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.777 Γ— 10⁹³(94-digit number)
27771636822903847972…09852936383465722881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.554 Γ— 10⁹³(94-digit number)
55543273645807695945…19705872766931445761
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 166089

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 4f1917d5a2508f1e832a57feb2b7d6d4d81501268c66f4a3d76015d0908c673b

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 #166,089 on Chainz β†—
Circulating Supply:57,859,686 XPMΒ·at block #6,826,938 Β· updates every 60s
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