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Home/Chain Registry/Block #2,796,305

Block #2,796,305

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/16/2018, 8:23:07 AM Β· Difficulty 11.6813 Β· 4,049,351 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
11e9e536903edbe05f101e41c64c32f3c697d902d663989ee360ab83c7667ad5
View on Chainz β†—

Difficulty

11.681331

Transactions

1

Size

200 B

Version

2

Bits

0bae6bb9

Nonce

922,568,498

Timestamp

8/16/2018, 8:23:07 AM

Confirmations

4,049,351

Merkle Root

c0b018763759679edf5d7565487c6cd25143f559f3821f34e654ea4fde2927f8
Transactions (1)
Coinbasec0b01876375967…54ea4fde2927f8
1 in β†’ 1 out7.3200 XPM110 B
AS5GFpcr…1w7eZtbi
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.

5.277 Γ— 10⁹⁴(95-digit number)
52777654464470177663…39492786553917329450
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
5.277 Γ— 10⁹⁴(95-digit number)
52777654464470177663…39492786553917329451
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.055 Γ— 10⁹⁡(96-digit number)
10555530892894035532…78985573107834658901
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.111 Γ— 10⁹⁡(96-digit number)
21111061785788071065…57971146215669317801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.222 Γ— 10⁹⁡(96-digit number)
42222123571576142130…15942292431338635601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.444 Γ— 10⁹⁡(96-digit number)
84444247143152284261…31884584862677271201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.688 Γ— 10⁹⁢(97-digit number)
16888849428630456852…63769169725354542401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.377 Γ— 10⁹⁢(97-digit number)
33777698857260913704…27538339450709084801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.755 Γ— 10⁹⁢(97-digit number)
67555397714521827409…55076678901418169601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.351 Γ— 10⁹⁷(98-digit number)
13511079542904365481…10153357802836339201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.702 Γ— 10⁹⁷(98-digit number)
27022159085808730963…20306715605672678401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.404 Γ— 10⁹⁷(98-digit number)
54044318171617461927…40613431211345356801
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 2796305

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 11e9e536903edbe05f101e41c64c32f3c697d902d663989ee360ab83c7667ad5

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 #2,796,305 on Chainz β†—
Circulating Supply:58,009,697 XPMΒ·at block #6,845,655 Β· updates every 60s
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