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Block #403,166

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/13/2014, 11:31:04 PM Β· Difficulty 10.4329 Β· 6,397,663 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c879ef9a76522329bf43dced53c6d7ac573301b6ee3962471fc0ee771ec051ec
View on Chainz β†—

Height

#403,166

Difficulty

10.432902

Transactions

1

Size

204 B

Version

2

Bits

0a6ed2a8

Nonce

24,725

Timestamp

2/13/2014, 11:31:04 PM

Confirmations

6,397,663

Merkle Root

9283257516749f6e3e4ad585b4df4fae5c3d00c892c88b11323f2b2b47ffebf7
Transactions (1)
Coinbase9283257516749f…3f2b2b47ffebf7
1 in β†’ 1 out9.1700 XPM116 B
AbwWkWZt…kawDhufa
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.

1.386 Γ— 10⁹¹(92-digit number)
13869153640946021919…03072922185420564360
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
1.386 Γ— 10⁹¹(92-digit number)
13869153640946021919…03072922185420564361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.773 Γ— 10⁹¹(92-digit number)
27738307281892043838…06145844370841128721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.547 Γ— 10⁹¹(92-digit number)
55476614563784087676…12291688741682257441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.109 Γ— 10⁹²(93-digit number)
11095322912756817535…24583377483364514881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.219 Γ— 10⁹²(93-digit number)
22190645825513635070…49166754966729029761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.438 Γ— 10⁹²(93-digit number)
44381291651027270140…98333509933458059521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.876 Γ— 10⁹²(93-digit number)
88762583302054540281…96667019866916119041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.775 Γ— 10⁹³(94-digit number)
17752516660410908056…93334039733832238081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.550 Γ— 10⁹³(94-digit number)
35505033320821816112…86668079467664476161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.101 Γ— 10⁹³(94-digit number)
71010066641643632225…73336158935328952321
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 403166

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 c879ef9a76522329bf43dced53c6d7ac573301b6ee3962471fc0ee771ec051ec

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 #403,166 on Chainz β†—
Circulating Supply:57,650,689 XPMΒ·at block #6,800,828 Β· updates every 60s
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