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Home/Chain Registry/Block #2,887,118

Block #2,887,118

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/19/2018, 1:22:49 AM Β· Difficulty 11.6209 Β· 3,944,586 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f305f315ccf8df1e4f67b2b0cc7c8635982f8ac243cb3192f4b1c284b157736b
View on Chainz β†—

Difficulty

11.620886

Transactions

1

Size

200 B

Version

2

Bits

0b9ef266

Nonce

1,996,534,105

Timestamp

10/19/2018, 1:22:49 AM

Confirmations

3,944,586

Merkle Root

263723c76d8a97aa39b00fe9551e5d9e185a1235d085baecd6f273b8969f3298
Transactions (1)
Coinbase263723c76d8a97…f273b8969f3298
1 in β†’ 1 out7.3900 XPM110 B
AaCY6wY1…gDoE6Nrp
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.

5.491 Γ— 10⁹³(94-digit number)
54912366088688838552…52743075345587753920
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
5.491 Γ— 10⁹³(94-digit number)
54912366088688838552…52743075345587753921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.098 Γ— 10⁹⁴(95-digit number)
10982473217737767710…05486150691175507841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.196 Γ— 10⁹⁴(95-digit number)
21964946435475535420…10972301382351015681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.392 Γ— 10⁹⁴(95-digit number)
43929892870951070841…21944602764702031361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.785 Γ— 10⁹⁴(95-digit number)
87859785741902141683…43889205529404062721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.757 Γ— 10⁹⁡(96-digit number)
17571957148380428336…87778411058808125441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.514 Γ— 10⁹⁡(96-digit number)
35143914296760856673…75556822117616250881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.028 Γ— 10⁹⁡(96-digit number)
70287828593521713346…51113644235232501761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.405 Γ— 10⁹⁢(97-digit number)
14057565718704342669…02227288470465003521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.811 Γ— 10⁹⁢(97-digit number)
28115131437408685338…04454576940930007041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.623 Γ— 10⁹⁢(97-digit number)
56230262874817370677…08909153881860014081
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 2887118

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 f305f315ccf8df1e4f67b2b0cc7c8635982f8ac243cb3192f4b1c284b157736b

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 #2,887,118 on Chainz β†—
Circulating Supply:57,897,741 XPMΒ·at block #6,831,703 Β· updates every 60s
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