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Home/Chain Registry/Block #1,411,814

Block #1,411,814

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/13/2016, 4:06:14 PM Β· Difficulty 10.8050 Β· 5,429,157 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
41e0cdecde80ef4823e05d664b84efef4cd2ffe98dd3fc3fdfefc001641029a3
View on Chainz β†—

Difficulty

10.804975

Transactions

1

Size

199 B

Version

2

Bits

0ace12df

Nonce

1,734,978,799

Timestamp

1/13/2016, 4:06:14 PM

Confirmations

5,429,157

Merkle Root

caa1e79a970e95f5fad30f230f37a6a4cf84ba00b748b4e56b1fecd69ed2ba92
Transactions (1)
Coinbasecaa1e79a970e95…1fecd69ed2ba92
1 in β†’ 1 out8.5500 XPM110 B
AdMaYJEY…TFuUUBtx
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.

1.966 Γ— 10⁹²(93-digit number)
19662706661623593979…52156510247000197120
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
1.966 Γ— 10⁹²(93-digit number)
19662706661623593979…52156510247000197121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.932 Γ— 10⁹²(93-digit number)
39325413323247187958…04313020494000394241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.865 Γ— 10⁹²(93-digit number)
78650826646494375916…08626040988000788481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.573 Γ— 10⁹³(94-digit number)
15730165329298875183…17252081976001576961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.146 Γ— 10⁹³(94-digit number)
31460330658597750366…34504163952003153921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.292 Γ— 10⁹³(94-digit number)
62920661317195500733…69008327904006307841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.258 Γ— 10⁹⁴(95-digit number)
12584132263439100146…38016655808012615681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.516 Γ— 10⁹⁴(95-digit number)
25168264526878200293…76033311616025231361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.033 Γ— 10⁹⁴(95-digit number)
50336529053756400586…52066623232050462721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.006 Γ— 10⁹⁡(96-digit number)
10067305810751280117…04133246464100925441
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 1411814

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 41e0cdecde80ef4823e05d664b84efef4cd2ffe98dd3fc3fdfefc001641029a3

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 #1,411,814 on Chainz β†—
Circulating Supply:57,972,126 XPMΒ·at block #6,840,970 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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