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Block #2,992,880

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/2/2019, 8:08:55 PM Β· Difficulty 11.2667 Β· 3,839,832 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
19119d96f80d5e7dfdfddc01fad148592841e66ca43b45c5bf0695ff3622f2d0
View on Chainz β†—

Difficulty

11.266673

Transactions

1

Size

200 B

Version

2

Bits

0b4444ae

Nonce

387,991,837

Timestamp

1/2/2019, 8:08:55 PM

Confirmations

3,839,832

Merkle Root

e99c75d875f030cfb862419111f72ae1d883e54732b0b46127f9f9af9a18009c
Transactions (1)
Coinbasee99c75d875f030…f9f9af9a18009c
1 in β†’ 1 out7.8600 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.

7.187 Γ— 10⁹⁴(95-digit number)
71873874641018306761…47400043379514194640
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
7.187 Γ— 10⁹⁴(95-digit number)
71873874641018306761…47400043379514194641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.437 Γ— 10⁹⁡(96-digit number)
14374774928203661352…94800086759028389281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.874 Γ— 10⁹⁡(96-digit number)
28749549856407322704…89600173518056778561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.749 Γ— 10⁹⁡(96-digit number)
57499099712814645408…79200347036113557121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.149 Γ— 10⁹⁢(97-digit number)
11499819942562929081…58400694072227114241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.299 Γ— 10⁹⁢(97-digit number)
22999639885125858163…16801388144454228481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.599 Γ— 10⁹⁢(97-digit number)
45999279770251716327…33602776288908456961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.199 Γ— 10⁹⁢(97-digit number)
91998559540503432654…67205552577816913921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.839 Γ— 10⁹⁷(98-digit number)
18399711908100686530…34411105155633827841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.679 Γ— 10⁹⁷(98-digit number)
36799423816201373061…68822210311267655681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.359 Γ— 10⁹⁷(98-digit number)
73598847632402746123…37644420622535311361
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 2992880

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 19119d96f80d5e7dfdfddc01fad148592841e66ca43b45c5bf0695ff3622f2d0

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 #2,992,880 on Chainz β†—
Circulating Supply:57,905,855 XPMΒ·at block #6,832,711 Β· updates every 60s
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