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Block #154,670

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/7/2013, 8:02:45 PM Β· Difficulty 9.8645 Β· 6,671,022 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1c89721692bbf519b58070e5dcfca916c14077410fd384045d0268c11ba5982c
View on Chainz β†—

Height

#154,670

Difficulty

9.864525

Transactions

1

Size

196 B

Version

2

Bits

09dd5187

Nonce

9,747

Timestamp

9/7/2013, 8:02:45 PM

Confirmations

6,671,022

Merkle Root

cc89c5b5d47d0d0867390dea4a898ce8a5ee5ffdeca9dd07c8cfd4bf820ae3cd
Transactions (1)
Coinbasecc89c5b5d47d0d…cfd4bf820ae3cd
1 in β†’ 1 out10.2600 XPM109 B
ASiN1vnG…nPBYx4TC
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.

4.132 Γ— 10⁸⁷(88-digit number)
41325442393897586208…94877189836660768500
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
4.132 Γ— 10⁸⁷(88-digit number)
41325442393897586208…94877189836660768501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.265 Γ— 10⁸⁷(88-digit number)
82650884787795172417…89754379673321537001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.653 Γ— 10⁸⁸(89-digit number)
16530176957559034483…79508759346643074001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.306 Γ— 10⁸⁸(89-digit number)
33060353915118068967…59017518693286148001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.612 Γ— 10⁸⁸(89-digit number)
66120707830236137934…18035037386572296001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.322 Γ— 10⁸⁹(90-digit number)
13224141566047227586…36070074773144592001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.644 Γ— 10⁸⁹(90-digit number)
26448283132094455173…72140149546289184001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.289 Γ— 10⁸⁹(90-digit number)
52896566264188910347…44280299092578368001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.057 Γ— 10⁹⁰(91-digit number)
10579313252837782069…88560598185156736001
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 154670

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 1c89721692bbf519b58070e5dcfca916c14077410fd384045d0268c11ba5982c

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 #154,670 on Chainz β†—
Circulating Supply:57,849,647 XPMΒ·at block #6,825,691 Β· updates every 60s
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