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Block #2,580,268

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/23/2018, 3:05:19 AM Β· Difficulty 11.0365 Β· 4,259,531 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f5e8d76a3428b8ca5a3d07dda908422edc470c9d8cb068a8eba05f2bef51f5b0
View on Chainz β†—

Difficulty

11.036518

Transactions

2

Size

8.07 KB

Version

2

Bits

0b095938

Nonce

625,735,070

Timestamp

3/23/2018, 3:05:19 AM

Confirmations

4,259,531

Merkle Root

c8bd47bca996267222ac89c177ccdf11affa549fd290ab9bfde050449ce629b9
Transactions (2)
Coinbase44d3a66136824f…f9953c8575877b
1 in β†’ 1 out8.2900 XPM109 B
Adqah8zh…1WwoHJ9t
979138471374ea…72bc7a8b547c8a
54 in β†’ 2 out271.4739 XPM7.88 KB
AS7LRS8s…iaW2W6juAKGxoSP8…8oH3hVLd
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.

1.803 Γ— 10⁹⁡(96-digit number)
18039627750751502365…47861854878773958400
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
1.803 Γ— 10⁹⁡(96-digit number)
18039627750751502365…47861854878773958399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.803 Γ— 10⁹⁡(96-digit number)
18039627750751502365…47861854878773958401
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
3.607 Γ— 10⁹⁡(96-digit number)
36079255501503004731…95723709757547916799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.607 Γ— 10⁹⁡(96-digit number)
36079255501503004731…95723709757547916801
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
7.215 Γ— 10⁹⁡(96-digit number)
72158511003006009462…91447419515095833599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.215 Γ— 10⁹⁡(96-digit number)
72158511003006009462…91447419515095833601
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
1.443 Γ— 10⁹⁢(97-digit number)
14431702200601201892…82894839030191667199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.443 Γ— 10⁹⁢(97-digit number)
14431702200601201892…82894839030191667201
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
2.886 Γ— 10⁹⁢(97-digit number)
28863404401202403785…65789678060383334399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.886 Γ— 10⁹⁢(97-digit number)
28863404401202403785…65789678060383334401
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
5.772 Γ— 10⁹⁢(97-digit number)
57726808802404807570…31579356120766668799
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 2580268

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 f5e8d76a3428b8ca5a3d07dda908422edc470c9d8cb068a8eba05f2bef51f5b0

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 #2,580,268 on Chainz β†—
Circulating Supply:57,962,684 XPMΒ·at block #6,839,798 Β· updates every 60s
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