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Home/Chain Registry/Block #2,766,816

Block #2,766,816

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/27/2018, 12:50:37 AM Β· Difficulty 11.6651 Β· 4,071,830 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d8295d33b205c157cb6bc6ab856adaf1795974fcfdc59cb1cbba4367c14f77bd
View on Chainz β†—

Difficulty

11.665101

Transactions

1

Size

200 B

Version

2

Bits

0baa440a

Nonce

1,907,338,394

Timestamp

7/27/2018, 12:50:37 AM

Confirmations

4,071,830

Merkle Root

4fcb81dcd8a593e6f6f0b907de43da22df50322f39cf42bef3ea4c7cc0690ea7
Transactions (1)
Coinbase4fcb81dcd8a593…ea4c7cc0690ea7
1 in β†’ 1 out7.3400 XPM110 B
AYpWWuov…QwmisJj2
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.

8.595 Γ— 10⁹⁴(95-digit number)
85955455556200107155…30201342596978784800
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
8.595 Γ— 10⁹⁴(95-digit number)
85955455556200107155…30201342596978784801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.719 Γ— 10⁹⁡(96-digit number)
17191091111240021431…60402685193957569601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.438 Γ— 10⁹⁡(96-digit number)
34382182222480042862…20805370387915139201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.876 Γ— 10⁹⁡(96-digit number)
68764364444960085724…41610740775830278401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.375 Γ— 10⁹⁢(97-digit number)
13752872888992017144…83221481551660556801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.750 Γ— 10⁹⁢(97-digit number)
27505745777984034289…66442963103321113601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.501 Γ— 10⁹⁢(97-digit number)
55011491555968068579…32885926206642227201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.100 Γ— 10⁹⁷(98-digit number)
11002298311193613715…65771852413284454401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.200 Γ— 10⁹⁷(98-digit number)
22004596622387227431…31543704826568908801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.400 Γ— 10⁹⁷(98-digit number)
44009193244774454863…63087409653137817601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.801 Γ— 10⁹⁷(98-digit number)
88018386489548909727…26174819306275635201
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 2766816

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 d8295d33b205c157cb6bc6ab856adaf1795974fcfdc59cb1cbba4367c14f77bd

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 #2,766,816 on Chainz β†—
Circulating Supply:57,953,433 XPMΒ·at block #6,838,645 Β· updates every 60s
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