XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #749,442

Block #749,442

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/2/2014, 6:05:13 AM Β· Difficulty 10.9764 Β· 6,077,359 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6f68af59816a2cbc2a4522ee34b4cc451070768d87a42d60ca96458f04ca6d7b
View on Chainz β†—

Height

#749,442

Difficulty

10.976358

Transactions

2

Size

400 B

Version

2

Bits

0af9f29c

Nonce

290,399,468

Timestamp

10/2/2014, 6:05:13 AM

Confirmations

6,077,359

Merkle Root

18ffd233f8800c032858f4aa7446748fdfd35599266ea7ffaba6ffeafc23480a
Transactions (2)
Coinbase7e57a8eba9f3b8…0b079474fb98a6
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
6602dcda595926…92b5dd8501257d
1 in β†’ 2 out8.2700 XPM193 B
AeKNrjNj…1NEq95TaAcpfxAE5…LCaYgJcv
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.

3.321 Γ— 10⁹⁷(98-digit number)
33214008908363068200…59367012163715379200
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
3.321 Γ— 10⁹⁷(98-digit number)
33214008908363068200…59367012163715379201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.642 Γ— 10⁹⁷(98-digit number)
66428017816726136400…18734024327430758401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.328 Γ— 10⁹⁸(99-digit number)
13285603563345227280…37468048654861516801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.657 Γ— 10⁹⁸(99-digit number)
26571207126690454560…74936097309723033601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.314 Γ— 10⁹⁸(99-digit number)
53142414253380909120…49872194619446067201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.062 Γ— 10⁹⁹(100-digit number)
10628482850676181824…99744389238892134401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.125 Γ— 10⁹⁹(100-digit number)
21256965701352363648…99488778477784268801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.251 Γ— 10⁹⁹(100-digit number)
42513931402704727296…98977556955568537601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.502 Γ— 10⁹⁹(100-digit number)
85027862805409454592…97955113911137075201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.700 Γ— 10¹⁰⁰(101-digit number)
17005572561081890918…95910227822274150401
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 749442

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 6f68af59816a2cbc2a4522ee34b4cc451070768d87a42d60ca96458f04ca6d7b

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 #749,442 on Chainz β†—
Circulating Supply:57,858,571 XPMΒ·at block #6,826,800 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy