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Home/Chain Registry/Block #2,782,409

Block #2,782,409

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/6/2018, 11:01:45 PM Β· Difficulty 11.6563 Β· 4,059,781 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f86acbb618fd3759baf2eb0944dbef27c2c7d26cb49f131a4767d4f941d3a4d6
View on Chainz β†—

Difficulty

11.656274

Transactions

1

Size

200 B

Version

2

Bits

0ba80196

Nonce

1,252,169,152

Timestamp

8/6/2018, 11:01:45 PM

Confirmations

4,059,781

Merkle Root

2095fe97a7c574da661e444a8f511987563abd5b5541964f9f9244388f227cbc
Transactions (1)
Coinbase2095fe97a7c574…9244388f227cbc
1 in β†’ 1 out7.3500 XPM110 B
AYHgbbhL…nZYeKbmt
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.

5.150 Γ— 10⁹³(94-digit number)
51501021017220989503…96799627728555878600
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
5.150 Γ— 10⁹³(94-digit number)
51501021017220989503…96799627728555878601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.030 Γ— 10⁹⁴(95-digit number)
10300204203444197900…93599255457111757201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.060 Γ— 10⁹⁴(95-digit number)
20600408406888395801…87198510914223514401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.120 Γ— 10⁹⁴(95-digit number)
41200816813776791603…74397021828447028801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.240 Γ— 10⁹⁴(95-digit number)
82401633627553583206…48794043656894057601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.648 Γ— 10⁹⁡(96-digit number)
16480326725510716641…97588087313788115201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.296 Γ— 10⁹⁡(96-digit number)
32960653451021433282…95176174627576230401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.592 Γ— 10⁹⁡(96-digit number)
65921306902042866564…90352349255152460801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.318 Γ— 10⁹⁢(97-digit number)
13184261380408573312…80704698510304921601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.636 Γ— 10⁹⁢(97-digit number)
26368522760817146625…61409397020609843201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.273 Γ— 10⁹⁢(97-digit number)
52737045521634293251…22818794041219686401
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 2782409

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 f86acbb618fd3759baf2eb0944dbef27c2c7d26cb49f131a4767d4f941d3a4d6

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 #2,782,409 on Chainz β†—
Circulating Supply:57,981,913 XPMΒ·at block #6,842,189 Β· updates every 60s
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