Home/Chain Registry/Block #2,148,887

Block #2,148,887

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/6/2017, 6:03:38 PM · Difficulty 10.8962 · 4,695,739 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ffa031731666d00d4e5dc4420256bd8ba6814cf4788b49c20dd8477d0e63d8c6

View on Chainz ↗

Height

#2,148,887

Difficulty

10.896212

Transactions

Size

651 B

Version

Bits

0ae56e1e

Nonce

1,523,914,905

Timestamp

6/6/2017, 6:03:38 PM

Confirmations

4,695,739

Merkle Root

2d5300110968fc2fe8b5868212a9a34533635975949ef8c695e586b100b22235

Transactions (3)

Coinbasefc929a3d16f5b1…2041b9fa2c130f

1 in → 1 out8.4300 XPM109 B

ARxZXHes…2oqdtQaE

39865b4554f037…02f82227c2146c

1 in → 2 out125229.3740 XPM227 B

AcrAfJWy…zjMdYD4o AMtW2ofX…YwnrGRC2

70d2c37d18e778…8b8f4054e2cfc3

1 in → 2 out123645.3640 XPM225 B

AQnyyhNG…9wVzmPZC ALPdHZCV…Smf9JDAM

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.006 × 10⁹⁵(96-digit number)

30065234691428502882…71256808222830100480

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

3.006 × 10⁹⁵(96-digit number)

30065234691428502882…71256808222830100479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.006 × 10⁹⁵(96-digit number)

30065234691428502882…71256808222830100481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

6.013 × 10⁹⁵(96-digit number)

60130469382857005765…42513616445660200959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.013 × 10⁹⁵(96-digit number)

60130469382857005765…42513616445660200961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.202 × 10⁹⁶(97-digit number)

12026093876571401153…85027232891320401919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.202 × 10⁹⁶(97-digit number)

12026093876571401153…85027232891320401921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.405 × 10⁹⁶(97-digit number)

24052187753142802306…70054465782640803839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.405 × 10⁹⁶(97-digit number)

24052187753142802306…70054465782640803841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

4.810 × 10⁹⁶(97-digit number)

48104375506285604612…40108931565281607679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.810 × 10⁹⁶(97-digit number)

48104375506285604612…40108931565281607681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — 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 →

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 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 2148887

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 ffa031731666d00d4e5dc4420256bd8ba6814cf4788b49c20dd8477d0e63d8c6

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 → Debug Window → 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 #2,148,887 on Chainz ↗

Block #2,148,887

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