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Block #2,994,534

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/3/2019, 10:56:10 PM Β· Difficulty 11.2734 Β· 3,845,144 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
db38911431cadc4e1c114b48aaef0dcaa0ec70d6926ece1399d6913036148640
View on Chainz β†—

Difficulty

11.273439

Transactions

1

Size

201 B

Version

2

Bits

0b46001b

Nonce

296,721,406

Timestamp

1/3/2019, 10:56:10 PM

Confirmations

3,845,144

Merkle Root

63468a30de8314acca18c801e1d75ebcea5e06df9d0a0f2972186447887e5a72
Transactions (1)
Coinbase63468a30de8314…186447887e5a72
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.

8.761 Γ— 10⁹⁷(98-digit number)
87619824432456504454…80401629542153953280
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
8.761 Γ— 10⁹⁷(98-digit number)
87619824432456504454…80401629542153953281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.752 Γ— 10⁹⁸(99-digit number)
17523964886491300890…60803259084307906561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.504 Γ— 10⁹⁸(99-digit number)
35047929772982601781…21606518168615813121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.009 Γ— 10⁹⁸(99-digit number)
70095859545965203563…43213036337231626241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.401 Γ— 10⁹⁹(100-digit number)
14019171909193040712…86426072674463252481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.803 Γ— 10⁹⁹(100-digit number)
28038343818386081425…72852145348926504961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.607 Γ— 10⁹⁹(100-digit number)
56076687636772162850…45704290697853009921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.121 Γ— 10¹⁰⁰(101-digit number)
11215337527354432570…91408581395706019841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.243 Γ— 10¹⁰⁰(101-digit number)
22430675054708865140…82817162791412039681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.486 Γ— 10¹⁰⁰(101-digit number)
44861350109417730280…65634325582824079361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.972 Γ— 10¹⁰⁰(101-digit number)
89722700218835460561…31268651165648158721
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 2994534

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 db38911431cadc4e1c114b48aaef0dcaa0ec70d6926ece1399d6913036148640

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 #2,994,534 on Chainz β†—
Circulating Supply:57,961,712 XPMΒ·at block #6,839,677 Β· updates every 60s
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