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Block #241,648

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/3/2013, 7:58:35 AM Β· Difficulty 9.9583 Β· 6,554,398 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
649782dc1b5882e93af10d9927d3df2ea4ecd26cc2148eeba1c2ef3f60363fed
View on Chainz β†—

Height

#241,648

Difficulty

9.958289

Transactions

1

Size

200 B

Version

2

Bits

09f55270

Nonce

119,249

Timestamp

11/3/2013, 7:58:35 AM

Confirmations

6,554,398

Merkle Root

993aa9fceafc61700f2c9a930f2efeb7a1fba798bd73235e07976e3c53bf13db
Transactions (1)
Coinbase993aa9fceafc61…976e3c53bf13db
1 in β†’ 1 out10.0700 XPM109 B
AbmMPQjW…C8vMVwEK
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.

1.427 Γ— 10⁹⁸(99-digit number)
14273224700450859824…07314533256200601600
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
1.427 Γ— 10⁹⁸(99-digit number)
14273224700450859824…07314533256200601601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.854 Γ— 10⁹⁸(99-digit number)
28546449400901719648…14629066512401203201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.709 Γ— 10⁹⁸(99-digit number)
57092898801803439296…29258133024802406401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.141 Γ— 10⁹⁹(100-digit number)
11418579760360687859…58516266049604812801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.283 Γ— 10⁹⁹(100-digit number)
22837159520721375718…17032532099209625601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.567 Γ— 10⁹⁹(100-digit number)
45674319041442751437…34065064198419251201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.134 Γ— 10⁹⁹(100-digit number)
91348638082885502875…68130128396838502401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.826 Γ— 10¹⁰⁰(101-digit number)
18269727616577100575…36260256793677004801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.653 Γ— 10¹⁰⁰(101-digit number)
36539455233154201150…72520513587354009601
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 241648

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 649782dc1b5882e93af10d9927d3df2ea4ecd26cc2148eeba1c2ef3f60363fed

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 #241,648 on Chainz β†—
Circulating Supply:57,612,461 XPMΒ·at block #6,796,045 Β· updates every 60s
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