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Home/Chain Registry/Block #344,742

Block #344,742

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/5/2014, 12:00:10 PM Β· Difficulty 10.2003 Β· 6,451,356 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
adb0193659e0a2bc1d836d3546ffcec75eff16d29fcae320b7c38c7b3ab20b72
View on Chainz β†—

Height

#344,742

Difficulty

10.200302

Transactions

1

Size

200 B

Version

2

Bits

0a334705

Nonce

26,794

Timestamp

1/5/2014, 12:00:10 PM

Confirmations

6,451,356

Merkle Root

96d00d73d8b36cbdeaa2ee4d4bfac2cc59fda613baa8e1c0517ce705218f7bcf
Transactions (1)
Coinbase96d00d73d8b36c…7ce705218f7bcf
1 in β†’ 1 out9.6000 XPM109 B
AeKNrjNj…1NEq95Ta
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.

6.694 Γ— 10⁹⁢(97-digit number)
66949538133189669527…00034066518492077760
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
6.694 Γ— 10⁹⁢(97-digit number)
66949538133189669527…00034066518492077761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.338 Γ— 10⁹⁷(98-digit number)
13389907626637933905…00068133036984155521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.677 Γ— 10⁹⁷(98-digit number)
26779815253275867810…00136266073968311041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.355 Γ— 10⁹⁷(98-digit number)
53559630506551735621…00272532147936622081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.071 Γ— 10⁹⁸(99-digit number)
10711926101310347124…00545064295873244161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.142 Γ— 10⁹⁸(99-digit number)
21423852202620694248…01090128591746488321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.284 Γ— 10⁹⁸(99-digit number)
42847704405241388497…02180257183492976641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.569 Γ— 10⁹⁸(99-digit number)
85695408810482776994…04360514366985953281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.713 Γ— 10⁹⁹(100-digit number)
17139081762096555398…08721028733971906561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.427 Γ— 10⁹⁹(100-digit number)
34278163524193110797…17442057467943813121
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 344742

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 adb0193659e0a2bc1d836d3546ffcec75eff16d29fcae320b7c38c7b3ab20b72

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 #344,742 on Chainz β†—
Circulating Supply:57,612,777 XPMΒ·at block #6,796,097 Β· updates every 60s
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