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Home/Chain Registry/Block #2,038,092

Block #2,038,092

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/25/2017, 4:06:42 PM Β· Difficulty 10.6766 Β· 4,803,377 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2431e50cf25ddd4da18f2dd7c5349d3cee245e551e21c3cee8d2ac69abd4b795
View on Chainz β†—

Difficulty

10.676606

Transactions

1

Size

200 B

Version

2

Bits

0aad3608

Nonce

352,996,364

Timestamp

3/25/2017, 4:06:42 PM

Confirmations

4,803,377

Merkle Root

86e9c3052eb994b5e8f7ea80c7f0f3b91245edca690d1eb88233bad99616e5ae
Transactions (1)
Coinbase86e9c3052eb994…33bad99616e5ae
1 in β†’ 1 out8.7600 XPM110 B
AS5Y4q49…Fnh9z2ku
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.

7.412 Γ— 10⁹⁴(95-digit number)
74120067867299397216…77358449856454185520
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
7.412 Γ— 10⁹⁴(95-digit number)
74120067867299397216…77358449856454185521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.482 Γ— 10⁹⁡(96-digit number)
14824013573459879443…54716899712908371041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.964 Γ— 10⁹⁡(96-digit number)
29648027146919758886…09433799425816742081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.929 Γ— 10⁹⁡(96-digit number)
59296054293839517772…18867598851633484161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.185 Γ— 10⁹⁢(97-digit number)
11859210858767903554…37735197703266968321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.371 Γ— 10⁹⁢(97-digit number)
23718421717535807109…75470395406533936641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.743 Γ— 10⁹⁢(97-digit number)
47436843435071614218…50940790813067873281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.487 Γ— 10⁹⁢(97-digit number)
94873686870143228436…01881581626135746561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.897 Γ— 10⁹⁷(98-digit number)
18974737374028645687…03763163252271493121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.794 Γ— 10⁹⁷(98-digit number)
37949474748057291374…07526326504542986241
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2038092

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 2431e50cf25ddd4da18f2dd7c5349d3cee245e551e21c3cee8d2ac69abd4b795

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 #2,038,092 on Chainz β†—
Circulating Supply:57,976,126 XPMΒ·at block #6,841,468 Β· updates every 60s
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