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Home/Chain Registry/Block #2,814,021

Block #2,814,021

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2018, 4:15:35 PM Β· Difficulty 11.6797 Β· 4,028,104 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
afa0b489f51d1e860b4fa2a4f8d0ab7aae7f07e9b0126d4fdac93abe369784ba
View on Chainz β†—

Difficulty

11.679697

Transactions

1

Size

201 B

Version

2

Bits

0bae009e

Nonce

115,798,001

Timestamp

8/28/2018, 4:15:35 PM

Confirmations

4,028,104

Merkle Root

5c854eeca2ee8f95cf51fd8612f94e0bd840212c28dca5af84f11db1f5c6bd2d
Transactions (1)
Coinbase5c854eeca2ee8f…f11db1f5c6bd2d
1 in β†’ 1 out7.3200 XPM110 B
AZtxQr2F…7grUWrUz
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.

9.994 Γ— 10⁹⁷(98-digit number)
99949309824901165174…49504403924071936000
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
9.994 Γ— 10⁹⁷(98-digit number)
99949309824901165174…49504403924071935999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.994 Γ— 10⁹⁷(98-digit number)
99949309824901165174…49504403924071936001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.998 Γ— 10⁹⁸(99-digit number)
19989861964980233034…99008807848143871999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.998 Γ— 10⁹⁸(99-digit number)
19989861964980233034…99008807848143872001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
3.997 Γ— 10⁹⁸(99-digit number)
39979723929960466069…98017615696287743999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.997 Γ— 10⁹⁸(99-digit number)
39979723929960466069…98017615696287744001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
7.995 Γ— 10⁹⁸(99-digit number)
79959447859920932139…96035231392575487999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.995 Γ— 10⁹⁸(99-digit number)
79959447859920932139…96035231392575488001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.599 Γ— 10⁹⁹(100-digit number)
15991889571984186427…92070462785150975999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.599 Γ— 10⁹⁹(100-digit number)
15991889571984186427…92070462785150976001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
3.198 Γ— 10⁹⁹(100-digit number)
31983779143968372855…84140925570301951999
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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 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 2814021

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 afa0b489f51d1e860b4fa2a4f8d0ab7aae7f07e9b0126d4fdac93abe369784ba

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 #2,814,021 on Chainz β†—
Circulating Supply:57,981,388 XPMΒ·at block #6,842,124 Β· updates every 60s
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