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Home/Chain Registry/Block #2,796,707

Block #2,796,707

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/16/2018, 3:58:17 PM Β· Difficulty 11.6780 Β· 4,039,969 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d9e59b68555bfa401492e3ca7ea6f5d5126e287a2a49343035891fb16607a8af
View on Chainz β†—

Difficulty

11.677981

Transactions

1

Size

200 B

Version

2

Bits

0bad902a

Nonce

1,654,178,899

Timestamp

8/16/2018, 3:58:17 PM

Confirmations

4,039,969

Merkle Root

0a0f1d4cba602f9ab5250bd1dabf847944a5ed1f59cfca19c95e5f7f2607674d
Transactions (1)
Coinbase0a0f1d4cba602f…5e5f7f2607674d
1 in β†’ 1 out7.3200 XPM110 B
AWQYPn6Y…m6cjQ4aD
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.

2.661 Γ— 10⁹⁴(95-digit number)
26616962310420009246…71201257315760102000
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
2.661 Γ— 10⁹⁴(95-digit number)
26616962310420009246…71201257315760101999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.323 Γ— 10⁹⁴(95-digit number)
53233924620840018492…42402514631520203999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.064 Γ— 10⁹⁡(96-digit number)
10646784924168003698…84805029263040407999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.129 Γ— 10⁹⁡(96-digit number)
21293569848336007396…69610058526080815999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.258 Γ— 10⁹⁡(96-digit number)
42587139696672014793…39220117052161631999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.517 Γ— 10⁹⁡(96-digit number)
85174279393344029587…78440234104323263999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.703 Γ— 10⁹⁢(97-digit number)
17034855878668805917…56880468208646527999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.406 Γ— 10⁹⁢(97-digit number)
34069711757337611835…13760936417293055999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.813 Γ— 10⁹⁢(97-digit number)
68139423514675223670…27521872834586111999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.362 Γ— 10⁹⁷(98-digit number)
13627884702935044734…55043745669172223999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.725 Γ— 10⁹⁷(98-digit number)
27255769405870089468…10087491338344447999
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 2796707

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 d9e59b68555bfa401492e3ca7ea6f5d5126e287a2a49343035891fb16607a8af

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 #2,796,707 on Chainz β†—
Circulating Supply:57,937,688 XPMΒ·at block #6,836,675 Β· updates every 60s
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