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Home/Chain Registry/Block #2,642,995

Block #2,642,995

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/1/2018, 10:46:41 PM Β· Difficulty 11.6702 Β· 4,193,367 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4cda9a0e76d4f12a2b7d1b7bc822b5870f2d71dd21383ae9c2b03d42b1a673c4
View on Chainz β†—

Difficulty

11.670187

Transactions

1

Size

200 B

Version

2

Bits

0bab9164

Nonce

1,230,549,754

Timestamp

5/1/2018, 10:46:41 PM

Confirmations

4,193,367

Merkle Root

69475b2a11a635d555fbae8d45f834640fc1c9ef8b66ca632721e8788f712f4b
Transactions (1)
Coinbase69475b2a11a635…21e8788f712f4b
1 in β†’ 1 out7.3300 XPM110 B
Adqah8zh…1WwoHJ9t
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.

5.682 Γ— 10⁹⁡(96-digit number)
56821842033255524283…81193367909582208000
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
5.682 Γ— 10⁹⁡(96-digit number)
56821842033255524283…81193367909582207999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.136 Γ— 10⁹⁢(97-digit number)
11364368406651104856…62386735819164415999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.272 Γ— 10⁹⁢(97-digit number)
22728736813302209713…24773471638328831999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.545 Γ— 10⁹⁢(97-digit number)
45457473626604419427…49546943276657663999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.091 Γ— 10⁹⁢(97-digit number)
90914947253208838854…99093886553315327999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.818 Γ— 10⁹⁷(98-digit number)
18182989450641767770…98187773106630655999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.636 Γ— 10⁹⁷(98-digit number)
36365978901283535541…96375546213261311999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.273 Γ— 10⁹⁷(98-digit number)
72731957802567071083…92751092426522623999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.454 Γ— 10⁹⁸(99-digit number)
14546391560513414216…85502184853045247999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.909 Γ— 10⁹⁸(99-digit number)
29092783121026828433…71004369706090495999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.818 Γ— 10⁹⁸(99-digit number)
58185566242053656866…42008739412180991999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2642995

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 4cda9a0e76d4f12a2b7d1b7bc822b5870f2d71dd21383ae9c2b03d42b1a673c4

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 #2,642,995 on Chainz β†—
Circulating Supply:57,935,155 XPMΒ·at block #6,836,361 Β· updates every 60s
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