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Block #2,798,648

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/18/2018, 12:09:05 AM Β· Difficulty 11.6787 Β· 4,042,690 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
413d1985c5c41dcd682817ad5cf85524704d6852e7440243ef42c5f243babb8c
View on Chainz β†—

Difficulty

11.678700

Transactions

1

Size

200 B

Version

2

Bits

0badbf42

Nonce

443,192,604

Timestamp

8/18/2018, 12:09:05 AM

Confirmations

4,042,690

Merkle Root

60b2233772ce6b0d0c629cba860b4a8b633d8b0b954267000952ed380f3ab230
Transactions (1)
Coinbase60b2233772ce6b…52ed380f3ab230
1 in β†’ 1 out7.3200 XPM110 B
ALG1HFLP…ymMBqFUC
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.

3.095 Γ— 10⁹⁴(95-digit number)
30951108164615451182…66781967381822262080
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
3.095 Γ— 10⁹⁴(95-digit number)
30951108164615451182…66781967381822262081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.190 Γ— 10⁹⁴(95-digit number)
61902216329230902365…33563934763644524161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.238 Γ— 10⁹⁡(96-digit number)
12380443265846180473…67127869527289048321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.476 Γ— 10⁹⁡(96-digit number)
24760886531692360946…34255739054578096641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.952 Γ— 10⁹⁡(96-digit number)
49521773063384721892…68511478109156193281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.904 Γ— 10⁹⁡(96-digit number)
99043546126769443784…37022956218312386561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.980 Γ— 10⁹⁢(97-digit number)
19808709225353888756…74045912436624773121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.961 Γ— 10⁹⁢(97-digit number)
39617418450707777513…48091824873249546241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.923 Γ— 10⁹⁢(97-digit number)
79234836901415555027…96183649746499092481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.584 Γ— 10⁹⁷(98-digit number)
15846967380283111005…92367299492998184961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.169 Γ— 10⁹⁷(98-digit number)
31693934760566222010…84734598985996369921
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 2798648

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 413d1985c5c41dcd682817ad5cf85524704d6852e7440243ef42c5f243babb8c

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 #2,798,648 on Chainz β†—
Circulating Supply:57,975,069 XPMΒ·at block #6,841,337 Β· updates every 60s
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