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Home/Chain Registry/Block #2,982,039

Block #2,982,039

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/26/2018, 4:35:06 AM Β· Difficulty 11.2907 Β· 3,862,016 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
488a33bd4b214f9e78f096f542e2c2bc99e0b796b406c213d96b14d610ce1f01
View on Chainz β†—

Difficulty

11.290706

Transactions

1

Size

199 B

Version

2

Bits

0b4a6bbd

Nonce

29,548,183

Timestamp

12/26/2018, 4:35:06 AM

Confirmations

3,862,016

Merkle Root

3f501d8a93067f10f4cb4d80e1a2f62066bba72b2ba0e1b354b0dc563e012a1f
Transactions (1)
Coinbase3f501d8a93067f…b0dc563e012a1f
1 in β†’ 1 out7.8300 XPM109 B
AUMQRepm…tAfKmdW1
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.

1.062 Γ— 10⁹⁡(96-digit number)
10627851802681604127…43341069740494702080
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
1.062 Γ— 10⁹⁡(96-digit number)
10627851802681604127…43341069740494702081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.125 Γ— 10⁹⁡(96-digit number)
21255703605363208255…86682139480989404161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.251 Γ— 10⁹⁡(96-digit number)
42511407210726416511…73364278961978808321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.502 Γ— 10⁹⁡(96-digit number)
85022814421452833023…46728557923957616641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.700 Γ— 10⁹⁢(97-digit number)
17004562884290566604…93457115847915233281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.400 Γ— 10⁹⁢(97-digit number)
34009125768581133209…86914231695830466561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.801 Γ— 10⁹⁢(97-digit number)
68018251537162266418…73828463391660933121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.360 Γ— 10⁹⁷(98-digit number)
13603650307432453283…47656926783321866241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.720 Γ— 10⁹⁷(98-digit number)
27207300614864906567…95313853566643732481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.441 Γ— 10⁹⁷(98-digit number)
54414601229729813134…90627707133287464961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.088 Γ— 10⁹⁸(99-digit number)
10882920245945962626…81255414266574929921
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 2982039

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 488a33bd4b214f9e78f096f542e2c2bc99e0b796b406c213d96b14d610ce1f01

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 #2,982,039 on Chainz β†—
Circulating Supply:57,996,811 XPMΒ·at block #6,844,054 Β· updates every 60s
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