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Block #2,756,539

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/19/2018, 9:20:19 PM Β· Difficulty 11.6657 Β· 4,076,474 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7341213480808579bd8679bc3297f17d175f31dd9060ebd6dbd0b2cfe3cd1e66
View on Chainz β†—

Difficulty

11.665653

Transactions

1

Size

201 B

Version

2

Bits

0baa683f

Nonce

99,066,352

Timestamp

7/19/2018, 9:20:19 PM

Confirmations

4,076,474

Merkle Root

4ccc9370c9f10cfda79d64d09484c4a618b67f8727fb4e2c9d0041e067330fad
Transactions (1)
Coinbase4ccc9370c9f10c…0041e067330fad
1 in β†’ 1 out7.3400 XPM110 B
AVFiHEWS…drL3LiWH
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.

6.634 Γ— 10⁹⁢(97-digit number)
66343962438863383058…51142196827624620800
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
6.634 Γ— 10⁹⁢(97-digit number)
66343962438863383058…51142196827624620801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.326 Γ— 10⁹⁷(98-digit number)
13268792487772676611…02284393655249241601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.653 Γ— 10⁹⁷(98-digit number)
26537584975545353223…04568787310498483201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.307 Γ— 10⁹⁷(98-digit number)
53075169951090706447…09137574620996966401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.061 Γ— 10⁹⁸(99-digit number)
10615033990218141289…18275149241993932801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.123 Γ— 10⁹⁸(99-digit number)
21230067980436282578…36550298483987865601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.246 Γ— 10⁹⁸(99-digit number)
42460135960872565157…73100596967975731201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.492 Γ— 10⁹⁸(99-digit number)
84920271921745130315…46201193935951462401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.698 Γ— 10⁹⁹(100-digit number)
16984054384349026063…92402387871902924801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.396 Γ— 10⁹⁹(100-digit number)
33968108768698052126…84804775743805849601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.793 Γ— 10⁹⁹(100-digit number)
67936217537396104252…69609551487611699201
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 2756539

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 7341213480808579bd8679bc3297f17d175f31dd9060ebd6dbd0b2cfe3cd1e66

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 #2,756,539 on Chainz β†—
Circulating Supply:57,908,279 XPMΒ·at block #6,833,012 Β· updates every 60s
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