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Home/Chain Registry/Block #2,645,765

Block #2,645,765

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/3/2018, 1:32:04 AM Β· Difficulty 11.7383 Β· 4,196,616 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6345f84865534e393648718cb4a81767fc201da08620c59d056981a6621ce51d
View on Chainz β†—

Difficulty

11.738280

Transactions

1

Size

201 B

Version

2

Bits

0bbcffe3

Nonce

1,395,660,998

Timestamp

5/3/2018, 1:32:04 AM

Confirmations

4,196,616

Merkle Root

367e5fd22b823f179162c57fb9b72edb80801a31ff11a3ea8cdd7303dee77593
Transactions (1)
Coinbase367e5fd22b823f…dd7303dee77593
1 in β†’ 1 out7.2500 XPM110 B
Adqah8zh…1WwoHJ9t
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.

3.829 Γ— 10⁹⁢(97-digit number)
38294114185196931232…70636884606217205760
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
3.829 Γ— 10⁹⁢(97-digit number)
38294114185196931232…70636884606217205759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.829 Γ— 10⁹⁢(97-digit number)
38294114185196931232…70636884606217205761
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
7.658 Γ— 10⁹⁢(97-digit number)
76588228370393862464…41273769212434411519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.658 Γ— 10⁹⁢(97-digit number)
76588228370393862464…41273769212434411521
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
1.531 Γ— 10⁹⁷(98-digit number)
15317645674078772492…82547538424868823039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.531 Γ— 10⁹⁷(98-digit number)
15317645674078772492…82547538424868823041
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
3.063 Γ— 10⁹⁷(98-digit number)
30635291348157544985…65095076849737646079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.063 Γ— 10⁹⁷(98-digit number)
30635291348157544985…65095076849737646081
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
6.127 Γ— 10⁹⁷(98-digit number)
61270582696315089971…30190153699475292159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.127 Γ— 10⁹⁷(98-digit number)
61270582696315089971…30190153699475292161
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
1.225 Γ— 10⁹⁸(99-digit number)
12254116539263017994…60380307398950584319
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 2645765

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 6345f84865534e393648718cb4a81767fc201da08620c59d056981a6621ce51d

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 #2,645,765 on Chainz β†—
Circulating Supply:57,983,456 XPMΒ·at block #6,842,380 Β· updates every 60s
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