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Block #262,068

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/16/2013, 11:31:17 AM Β· Difficulty 9.9698 Β· 6,534,321 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f5a7c8e73c863dfab31cdd5f2443ea0d5b1ba080d40925a00c7ad2d39e89bc32
View on Chainz β†—

Height

#262,068

Difficulty

9.969751

Transactions

2

Size

573 B

Version

2

Bits

09f8419a

Nonce

848,798

Timestamp

11/16/2013, 11:31:17 AM

Confirmations

6,534,321

Merkle Root

9e1a800fc328e80c153d4999bf7da135b34aa3148f9748ddf489b846f5353616
Transactions (2)
Coinbase303a16e79f74f7…6be0de5b09ec7f
1 in β†’ 1 out10.0600 XPM110 B
AeKNrjNj…1NEq95Ta
40804b1dba401c…8888d723b8565a
2 in β†’ 2 out4.3978 XPM374 B
AGrTcXdN…gonizjRNAbFyPB9s…9jTFY77c
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.

5.362 Γ— 10⁹²(93-digit number)
53624498483432886350…80442720039876697120
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
5.362 Γ— 10⁹²(93-digit number)
53624498483432886350…80442720039876697121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.072 Γ— 10⁹³(94-digit number)
10724899696686577270…60885440079753394241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.144 Γ— 10⁹³(94-digit number)
21449799393373154540…21770880159506788481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.289 Γ— 10⁹³(94-digit number)
42899598786746309080…43541760319013576961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.579 Γ— 10⁹³(94-digit number)
85799197573492618160…87083520638027153921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.715 Γ— 10⁹⁴(95-digit number)
17159839514698523632…74167041276054307841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.431 Γ— 10⁹⁴(95-digit number)
34319679029397047264…48334082552108615681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.863 Γ— 10⁹⁴(95-digit number)
68639358058794094528…96668165104217231361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.372 Γ— 10⁹⁡(96-digit number)
13727871611758818905…93336330208434462721
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 262068

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 f5a7c8e73c863dfab31cdd5f2443ea0d5b1ba080d40925a00c7ad2d39e89bc32

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 #262,068 on Chainz β†—
Circulating Supply:57,615,108 XPMΒ·at block #6,796,388 Β· updates every 60s
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