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Home/Chain Registry/Block #2,876,975

Block #2,876,975

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/11/2018, 5:17:07 PM Β· Difficulty 11.6510 Β· 3,968,367 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e3bd2cad31f600c51eb9b433d79815e1bf238c04982e158d1bf965e922b40de2
View on Chainz β†—

Difficulty

11.651042

Transactions

1

Size

198 B

Version

2

Bits

0ba6aaaf

Nonce

1,355,705,755

Timestamp

10/11/2018, 5:17:07 PM

Confirmations

3,968,367

Merkle Root

7614939e7b888d9878138732b8ecd4a4f341f4b7c88f5b097dbc2b5750d762d5
Transactions (1)
Coinbase7614939e7b888d…bc2b5750d762d5
1 in β†’ 1 out7.3500 XPM109 B
Aeshfi3x…AtcNugit
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.

4.100 Γ— 10⁹¹(92-digit number)
41005815467979813976…68030554004540205180
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
4.100 Γ— 10⁹¹(92-digit number)
41005815467979813976…68030554004540205181
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.201 Γ— 10⁹¹(92-digit number)
82011630935959627953…36061108009080410361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.640 Γ— 10⁹²(93-digit number)
16402326187191925590…72122216018160820721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.280 Γ— 10⁹²(93-digit number)
32804652374383851181…44244432036321641441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.560 Γ— 10⁹²(93-digit number)
65609304748767702363…88488864072643282881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.312 Γ— 10⁹³(94-digit number)
13121860949753540472…76977728145286565761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.624 Γ— 10⁹³(94-digit number)
26243721899507080945…53955456290573131521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.248 Γ— 10⁹³(94-digit number)
52487443799014161890…07910912581146263041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.049 Γ— 10⁹⁴(95-digit number)
10497488759802832378…15821825162292526081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.099 Γ— 10⁹⁴(95-digit number)
20994977519605664756…31643650324585052161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.198 Γ— 10⁹⁴(95-digit number)
41989955039211329512…63287300649170104321
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 2876975

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 e3bd2cad31f600c51eb9b433d79815e1bf238c04982e158d1bf965e922b40de2

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 #2,876,975 on Chainz β†—
Circulating Supply:58,007,177 XPMΒ·at block #6,845,341 Β· updates every 60s
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