XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #3,080,874

Block #3,080,874

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/6/2019, 10:09:26 AM Β· Difficulty 11.0205 Β· 3,761,599 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
afd7676307a1fafdea82d7172ab6fe34ef7157da11831f432d1c450454592f38
View on Chainz β†—

Difficulty

11.020485

Transactions

1

Size

200 B

Version

2

Bits

0b053e79

Nonce

1,632,356,173

Timestamp

3/6/2019, 10:09:26 AM

Confirmations

3,761,599

Merkle Root

5b9207a5cfc3bbbc0db87cb08551d0057247fe6bd20ccc4233c947e607f31aa8
Transactions (1)
Coinbase5b9207a5cfc3bb…c947e607f31aa8
1 in β†’ 1 out8.2200 XPM110 B
AUhjokok…k5m93PZR
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.

4.366 Γ— 10⁹⁴(95-digit number)
43664209358533867434…38306892437089304960
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
4.366 Γ— 10⁹⁴(95-digit number)
43664209358533867434…38306892437089304961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.732 Γ— 10⁹⁴(95-digit number)
87328418717067734868…76613784874178609921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.746 Γ— 10⁹⁡(96-digit number)
17465683743413546973…53227569748357219841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.493 Γ— 10⁹⁡(96-digit number)
34931367486827093947…06455139496714439681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.986 Γ— 10⁹⁡(96-digit number)
69862734973654187894…12910278993428879361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.397 Γ— 10⁹⁢(97-digit number)
13972546994730837578…25820557986857758721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.794 Γ— 10⁹⁢(97-digit number)
27945093989461675157…51641115973715517441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.589 Γ— 10⁹⁢(97-digit number)
55890187978923350315…03282231947431034881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.117 Γ— 10⁹⁷(98-digit number)
11178037595784670063…06564463894862069761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.235 Γ— 10⁹⁷(98-digit number)
22356075191569340126…13128927789724139521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.471 Γ— 10⁹⁷(98-digit number)
44712150383138680252…26257855579448279041
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 3080874

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 afd7676307a1fafdea82d7172ab6fe34ef7157da11831f432d1c450454592f38

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 #3,080,874 on Chainz β†—
Circulating Supply:57,984,202 XPMΒ·at block #6,842,472 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