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Home/Chain Registry/Block #2,557,780

Block #2,557,780

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/9/2018, 11:31:04 PM Β· Difficulty 10.9915 Β· 4,273,967 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ed9df10419949b82e72f8555e694681a8e6b23aebd38eccfcf59927656357840
View on Chainz β†—

Difficulty

10.991483

Transactions

1

Size

200 B

Version

2

Bits

0afdd1d2

Nonce

21,004,591

Timestamp

3/9/2018, 11:31:04 PM

Confirmations

4,273,967

Merkle Root

baa8e06f73d6794f8850b29b525a9db1a313c8acde93dd42e6c70a4063e85109
Transactions (1)
Coinbasebaa8e06f73d679…c70a4063e85109
1 in β†’ 1 out8.2600 XPM109 B
ALQGpaT6…9dLVU1B9
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.

7.140 Γ— 10⁹⁢(97-digit number)
71400895724505744919…07708554334912942080
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
7.140 Γ— 10⁹⁢(97-digit number)
71400895724505744919…07708554334912942079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.140 Γ— 10⁹⁢(97-digit number)
71400895724505744919…07708554334912942081
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
1.428 Γ— 10⁹⁷(98-digit number)
14280179144901148983…15417108669825884159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.428 Γ— 10⁹⁷(98-digit number)
14280179144901148983…15417108669825884161
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
2.856 Γ— 10⁹⁷(98-digit number)
28560358289802297967…30834217339651768319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.856 Γ— 10⁹⁷(98-digit number)
28560358289802297967…30834217339651768321
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
5.712 Γ— 10⁹⁷(98-digit number)
57120716579604595935…61668434679303536639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.712 Γ— 10⁹⁷(98-digit number)
57120716579604595935…61668434679303536641
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
1.142 Γ— 10⁹⁸(99-digit number)
11424143315920919187…23336869358607073279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.142 Γ— 10⁹⁸(99-digit number)
11424143315920919187…23336869358607073281
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
2.284 Γ— 10⁹⁸(99-digit number)
22848286631841838374…46673738717214146559
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 2557780

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 ed9df10419949b82e72f8555e694681a8e6b23aebd38eccfcf59927656357840

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 #2,557,780 on Chainz β†—
Circulating Supply:57,898,083 XPMΒ·at block #6,831,746 Β· updates every 60s
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