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Home/Chain Registry/Block #2,110,043

Block #2,110,043

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/10/2017, 12:47:15 PM Β· Difficulty 10.9020 Β· 4,726,822 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
257831f82638c19d09533e74e87dbbc62ed650cbaa669fed2f44fd28297946dd
View on Chainz β†—

Difficulty

10.901975

Transactions

1

Size

200 B

Version

2

Bits

0ae6e7d1

Nonce

1,140,260,526

Timestamp

5/10/2017, 12:47:15 PM

Confirmations

4,726,822

Merkle Root

255e344c7ec2f75427093cbba9c1f30129ba6ff5e02e5359a98c59c786516a24
Transactions (1)
Coinbase255e344c7ec2f7…8c59c786516a24
1 in β†’ 1 out8.4000 XPM110 B
AMt8uAoX…7cXUs2EF
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.

3.772 Γ— 10⁹⁴(95-digit number)
37720473892452109005…43373201431236902400
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
3.772 Γ— 10⁹⁴(95-digit number)
37720473892452109005…43373201431236902399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.772 Γ— 10⁹⁴(95-digit number)
37720473892452109005…43373201431236902401
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
7.544 Γ— 10⁹⁴(95-digit number)
75440947784904218011…86746402862473804799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.544 Γ— 10⁹⁴(95-digit number)
75440947784904218011…86746402862473804801
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
1.508 Γ— 10⁹⁡(96-digit number)
15088189556980843602…73492805724947609599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.508 Γ— 10⁹⁡(96-digit number)
15088189556980843602…73492805724947609601
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
3.017 Γ— 10⁹⁡(96-digit number)
30176379113961687204…46985611449895219199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.017 Γ— 10⁹⁡(96-digit number)
30176379113961687204…46985611449895219201
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
6.035 Γ— 10⁹⁡(96-digit number)
60352758227923374409…93971222899790438399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.035 Γ— 10⁹⁡(96-digit number)
60352758227923374409…93971222899790438401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
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 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 2110043

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 257831f82638c19d09533e74e87dbbc62ed650cbaa669fed2f44fd28297946dd

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 #2,110,043 on Chainz β†—
Circulating Supply:57,939,209 XPMΒ·at block #6,836,864 Β· updates every 60s
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