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Block #2,915,891

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/9/2018, 9:14:46 AM Β· Difficulty 11.4444 Β· 3,926,900 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4aafb2a11cf24bd6fd976a36ae0bec82bc5492e9205e70d0e195e90eaf72faea
View on Chainz β†—

Difficulty

11.444398

Transactions

1

Size

201 B

Version

2

Bits

0b71c40d

Nonce

180,376,471

Timestamp

11/9/2018, 9:14:46 AM

Confirmations

3,926,900

Merkle Root

af10b9e20670f145f37175d655fd24a15ca6ca7099fe37cfee34891fe4a19c09
Transactions (1)
Coinbaseaf10b9e20670f1…34891fe4a19c09
1 in β†’ 1 out7.6200 XPM110 B
AbXwmGxD…4XXYP765
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.

2.244 Γ— 10⁹⁢(97-digit number)
22447450182300030455…33383743881662992640
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
2.244 Γ— 10⁹⁢(97-digit number)
22447450182300030455…33383743881662992641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.489 Γ— 10⁹⁢(97-digit number)
44894900364600060910…66767487763325985281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.978 Γ— 10⁹⁢(97-digit number)
89789800729200121821…33534975526651970561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.795 Γ— 10⁹⁷(98-digit number)
17957960145840024364…67069951053303941121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.591 Γ— 10⁹⁷(98-digit number)
35915920291680048728…34139902106607882241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.183 Γ— 10⁹⁷(98-digit number)
71831840583360097456…68279804213215764481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.436 Γ— 10⁹⁸(99-digit number)
14366368116672019491…36559608426431528961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.873 Γ— 10⁹⁸(99-digit number)
28732736233344038982…73119216852863057921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.746 Γ— 10⁹⁸(99-digit number)
57465472466688077965…46238433705726115841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.149 Γ— 10⁹⁹(100-digit number)
11493094493337615593…92476867411452231681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.298 Γ— 10⁹⁹(100-digit number)
22986188986675231186…84953734822904463361
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 2915891

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 4aafb2a11cf24bd6fd976a36ae0bec82bc5492e9205e70d0e195e90eaf72faea

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 #2,915,891 on Chainz β†—
Circulating Supply:57,986,667 XPMΒ·at block #6,842,790 Β· updates every 60s
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