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Home/Chain Registry/Block #2,826,938

Block #2,826,938

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/6/2018, 7:18:08 AM Β· Difficulty 11.7100 Β· 4,014,578 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
64e0ab2e97a6300c8ce5aa6f541d7f149691d01785aa12ce9ae02b47b7b15065
View on Chainz β†—

Difficulty

11.709988

Transactions

1

Size

200 B

Version

2

Bits

0bb5c1c3

Nonce

356,757,162

Timestamp

9/6/2018, 7:18:08 AM

Confirmations

4,014,578

Merkle Root

f3b004b3e1d9022765ea718234196b319d0583602d161c87c8aedb6441484b61
Transactions (1)
Coinbasef3b004b3e1d902…aedb6441484b61
1 in β†’ 1 out7.2800 XPM110 B
AXbFuHo3…9VoEtaRa
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.

5.916 Γ— 10⁹⁡(96-digit number)
59168205486368337961…31781416815908609600
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
5.916 Γ— 10⁹⁡(96-digit number)
59168205486368337961…31781416815908609599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.183 Γ— 10⁹⁢(97-digit number)
11833641097273667592…63562833631817219199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.366 Γ— 10⁹⁢(97-digit number)
23667282194547335184…27125667263634438399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.733 Γ— 10⁹⁢(97-digit number)
47334564389094670369…54251334527268876799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.466 Γ— 10⁹⁢(97-digit number)
94669128778189340739…08502669054537753599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.893 Γ— 10⁹⁷(98-digit number)
18933825755637868147…17005338109075507199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.786 Γ— 10⁹⁷(98-digit number)
37867651511275736295…34010676218151014399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.573 Γ— 10⁹⁷(98-digit number)
75735303022551472591…68021352436302028799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.514 Γ— 10⁹⁸(99-digit number)
15147060604510294518…36042704872604057599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.029 Γ— 10⁹⁸(99-digit number)
30294121209020589036…72085409745208115199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.058 Γ— 10⁹⁸(99-digit number)
60588242418041178073…44170819490416230399
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 2826938

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 64e0ab2e97a6300c8ce5aa6f541d7f149691d01785aa12ce9ae02b47b7b15065

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 #2,826,938 on Chainz β†—
Circulating Supply:57,976,509 XPMΒ·at block #6,841,515 Β· updates every 60s
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