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Block #2,642,493

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2018, 6:23:30 PM Β· Difficulty 11.6542 Β· 4,189,503 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6e674255d3758f2e36574bca7bd8dc0b417ccdbe3c20b6585ab6e444bd5775e6
View on Chainz β†—

Difficulty

11.654165

Transactions

1

Size

200 B

Version

2

Bits

0ba77759

Nonce

846,822,572

Timestamp

5/1/2018, 6:23:30 PM

Confirmations

4,189,503

Merkle Root

3ab1ceb1f67b80481e5d4c867c92f582b6465af3fbe3adfc5fafbc8e4202aa79
Transactions (1)
Coinbase3ab1ceb1f67b80…afbc8e4202aa79
1 in β†’ 1 out7.3500 XPM110 B
AJFnoZeM…8z19w9fa
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.

3.734 Γ— 10⁹⁴(95-digit number)
37343095697997171851…99823255913964844240
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
3.734 Γ— 10⁹⁴(95-digit number)
37343095697997171851…99823255913964844241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.468 Γ— 10⁹⁴(95-digit number)
74686191395994343703…99646511827929688481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.493 Γ— 10⁹⁡(96-digit number)
14937238279198868740…99293023655859376961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.987 Γ— 10⁹⁡(96-digit number)
29874476558397737481…98586047311718753921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.974 Γ— 10⁹⁡(96-digit number)
59748953116795474962…97172094623437507841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.194 Γ— 10⁹⁢(97-digit number)
11949790623359094992…94344189246875015681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.389 Γ— 10⁹⁢(97-digit number)
23899581246718189985…88688378493750031361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.779 Γ— 10⁹⁢(97-digit number)
47799162493436379970…77376756987500062721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.559 Γ— 10⁹⁢(97-digit number)
95598324986872759940…54753513975000125441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.911 Γ— 10⁹⁷(98-digit number)
19119664997374551988…09507027950000250881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.823 Γ— 10⁹⁷(98-digit number)
38239329994749103976…19014055900000501761
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 2642493

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 6e674255d3758f2e36574bca7bd8dc0b417ccdbe3c20b6585ab6e444bd5775e6

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 #2,642,493 on Chainz β†—
Circulating Supply:57,900,094 XPMΒ·at block #6,831,995 Β· updates every 60s
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