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Block #408,041

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/17/2014, 9:25:25 AM Β· Difficulty 10.4305 Β· 6,402,158 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ddcceefcf0f016754c8dbde9431a5545fbce664b2b45bcebc3842a596367f393
View on Chainz β†—

Height

#408,041

Difficulty

10.430486

Transactions

2

Size

414 B

Version

2

Bits

0a6e345b

Nonce

1,729

Timestamp

2/17/2014, 9:25:25 AM

Confirmations

6,402,158

Merkle Root

234442c5c45e8691cf690792751d96efccbe346d05636cd1cc69dcc59d0442fa
Transactions (2)
Coinbasedf75fa964de522…203c0d1fce6174
1 in β†’ 2 out9.1900 XPM131 B
Ac2JYASP…tcBL5PEWAJno7LX2…vo4wdWtY
a5bbc0abd9b7c2…b0167c4de6ef1b
1 in β†’ 1 out1.1622 XPM192 B
AHv3G34T…nYg6e9rJ
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.

1.430 Γ— 10⁹⁸(99-digit number)
14307777483560596361…89306568758655066240
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
1.430 Γ— 10⁹⁸(99-digit number)
14307777483560596361…89306568758655066241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.861 Γ— 10⁹⁸(99-digit number)
28615554967121192722…78613137517310132481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.723 Γ— 10⁹⁸(99-digit number)
57231109934242385444…57226275034620264961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.144 Γ— 10⁹⁹(100-digit number)
11446221986848477088…14452550069240529921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.289 Γ— 10⁹⁹(100-digit number)
22892443973696954177…28905100138481059841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.578 Γ— 10⁹⁹(100-digit number)
45784887947393908355…57810200276962119681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.156 Γ— 10⁹⁹(100-digit number)
91569775894787816711…15620400553924239361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.831 Γ— 10¹⁰⁰(101-digit number)
18313955178957563342…31240801107848478721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.662 Γ— 10¹⁰⁰(101-digit number)
36627910357915126684…62481602215696957441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.325 Γ— 10¹⁰⁰(101-digit number)
73255820715830253369…24963204431393914881
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 408041

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 ddcceefcf0f016754c8dbde9431a5545fbce664b2b45bcebc3842a596367f393

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 #408,041 on Chainz β†—
Circulating Supply:57,725,664 XPMΒ·at block #6,810,198 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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