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Block #262,379

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/16/2013, 7:51:40 PM Β· Difficulty 9.9686 Β· 6,532,515 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
872ef34e75ab709c3cd46386cd0c2e28885d1db7f22334e60c19cbd072366ce9
View on Chainz β†—

Height

#262,379

Difficulty

9.968578

Transactions

1

Size

199 B

Version

2

Bits

09f7f4bb

Nonce

78,035

Timestamp

11/16/2013, 7:51:40 PM

Confirmations

6,532,515

Merkle Root

dc069283b6acf9ae32bbc040a8b3eea1ed57bae74b13493c1d190e44b8edfc3a
Transactions (1)
Coinbasedc069283b6acf9…190e44b8edfc3a
1 in β†’ 1 out10.0500 XPM109 B
Ad2vHAuH…8hRNjB6r
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.

3.818 Γ— 10⁹⁡(96-digit number)
38186348506787379077…82194958440885248000
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
3.818 Γ— 10⁹⁡(96-digit number)
38186348506787379077…82194958440885248001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.637 Γ— 10⁹⁡(96-digit number)
76372697013574758155…64389916881770496001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.527 Γ— 10⁹⁢(97-digit number)
15274539402714951631…28779833763540992001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.054 Γ— 10⁹⁢(97-digit number)
30549078805429903262…57559667527081984001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.109 Γ— 10⁹⁢(97-digit number)
61098157610859806524…15119335054163968001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.221 Γ— 10⁹⁷(98-digit number)
12219631522171961304…30238670108327936001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.443 Γ— 10⁹⁷(98-digit number)
24439263044343922609…60477340216655872001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.887 Γ— 10⁹⁷(98-digit number)
48878526088687845219…20954680433311744001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.775 Γ— 10⁹⁷(98-digit number)
97757052177375690439…41909360866623488001
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 262379

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 872ef34e75ab709c3cd46386cd0c2e28885d1db7f22334e60c19cbd072366ce9

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 #262,379 on Chainz β†—
Circulating Supply:57,603,188 XPMΒ·at block #6,794,893 Β· updates every 60s
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