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Home/Chain Registry/Block #2,851,326

Block #2,851,326

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/23/2018, 12:58:53 AM Β· Difficulty 11.7269 Β· 3,986,742 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b97c386dd4836906258737fc069366af310afd9a682aa2066e5a8ee4bb5f712f
View on Chainz β†—

Difficulty

11.726911

Transactions

1

Size

200 B

Version

2

Bits

0bba16df

Nonce

1,147,298,141

Timestamp

9/23/2018, 12:58:53 AM

Confirmations

3,986,742

Merkle Root

9fe84b77db1e473e456a1160e87b41565e3632755322138917bf7d797f0fee7f
Transactions (1)
Coinbase9fe84b77db1e47…bf7d797f0fee7f
1 in β†’ 1 out7.2600 XPM110 B
ASuyBDwt…M9D8wSkt
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.

3.577 Γ— 10⁹³(94-digit number)
35774768928182846443…39701855250144944000
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
3.577 Γ— 10⁹³(94-digit number)
35774768928182846443…39701855250144944001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.154 Γ— 10⁹³(94-digit number)
71549537856365692886…79403710500289888001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.430 Γ— 10⁹⁴(95-digit number)
14309907571273138577…58807421000579776001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.861 Γ— 10⁹⁴(95-digit number)
28619815142546277154…17614842001159552001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.723 Γ— 10⁹⁴(95-digit number)
57239630285092554309…35229684002319104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.144 Γ— 10⁹⁡(96-digit number)
11447926057018510861…70459368004638208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.289 Γ— 10⁹⁡(96-digit number)
22895852114037021723…40918736009276416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.579 Γ— 10⁹⁡(96-digit number)
45791704228074043447…81837472018552832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.158 Γ— 10⁹⁡(96-digit number)
91583408456148086894…63674944037105664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.831 Γ— 10⁹⁢(97-digit number)
18316681691229617378…27349888074211328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.663 Γ— 10⁹⁢(97-digit number)
36633363382459234757…54699776148422656001
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 2851326

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 b97c386dd4836906258737fc069366af310afd9a682aa2066e5a8ee4bb5f712f

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 #2,851,326 on Chainz β†—
Circulating Supply:57,948,901 XPMΒ·at block #6,838,067 Β· updates every 60s
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