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Block #262,125

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/16/2013, 12:43:55 PM Β· Difficulty 9.9696 Β· 6,564,204 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9d1f7f3cf258fcc9e3577be088d8a2f510b79df39d6066a6b15ec9f6e4e86464
View on Chainz β†—

Height

#262,125

Difficulty

9.969635

Transactions

1

Size

200 B

Version

2

Bits

09f83a02

Nonce

131,703

Timestamp

11/16/2013, 12:43:55 PM

Confirmations

6,564,204

Merkle Root

408a99174f48b30cf49fa6b16a2731eb7d4af17771cfb3df73615d0a48b4d095
Transactions (1)
Coinbase408a99174f48b3…615d0a48b4d095
1 in β†’ 1 out10.0500 XPM109 B
AZarUTeY…Xeczt6nx
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.

3.193 Γ— 10⁹⁢(97-digit number)
31938142511805349494…06147732671728486400
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
3.193 Γ— 10⁹⁢(97-digit number)
31938142511805349494…06147732671728486401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.387 Γ— 10⁹⁢(97-digit number)
63876285023610698989…12295465343456972801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.277 Γ— 10⁹⁷(98-digit number)
12775257004722139797…24590930686913945601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.555 Γ— 10⁹⁷(98-digit number)
25550514009444279595…49181861373827891201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.110 Γ— 10⁹⁷(98-digit number)
51101028018888559191…98363722747655782401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.022 Γ— 10⁹⁸(99-digit number)
10220205603777711838…96727445495311564801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.044 Γ— 10⁹⁸(99-digit number)
20440411207555423676…93454890990623129601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.088 Γ— 10⁹⁸(99-digit number)
40880822415110847353…86909781981246259201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.176 Γ— 10⁹⁸(99-digit number)
81761644830221694706…73819563962492518401
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 262125

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 9d1f7f3cf258fcc9e3577be088d8a2f510b79df39d6066a6b15ec9f6e4e86464

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 #262,125 on Chainz β†—
Circulating Supply:57,854,773 XPMΒ·at block #6,826,328 Β· updates every 60s
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