Block #2,001,914

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/27/2017, 6:12:02 PM · Difficulty 10.7403 · 4,839,224 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

989233f1819a0f3019fb6d307b951c7592420fb478ef97f9418919fa6f4c71e9

View on Chainz ↗

Height

#2,001,914

Difficulty

10.740317

Transactions

Size

1.87 KB

Version

Bits

0abd8563

Nonce

300,736,930

Timestamp

2/27/2017, 6:12:02 PM

Confirmations

4,839,224

Mined by

⛏️ P2SHART6AT4bhMgQMzoSPq8hABxA81mMNAdBYa

Merkle Root

e5cad497bf01c0f8b2d9933d0f5bdcae9e7596a9e308a9bdf631641cbe935d1e

Transactions (2)

Coinbase9a2d6e5d64f897…d041591b7521b7

1 in → 1 out8.6800 XPM109 B

ART6AT4b…mMNAdBYa

6c9783ee89d977…6cd7d45ad92684

11 in → 2 out279.2291 XPM1.67 KB

AbfHPQRP…cc1QCTYa AXWhBn1M…KKxweWoX

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.

8.730 × 10⁹⁵(96-digit number)

87304677411031687374…43451785690183070719

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

8.730 × 10⁹⁵(96-digit number)

87304677411031687374…43451785690183070719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.730 × 10⁹⁵(96-digit number)

87304677411031687374…43451785690183070721

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

1.746 × 10⁹⁶(97-digit number)

17460935482206337474…86903571380366141439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.746 × 10⁹⁶(97-digit number)

17460935482206337474…86903571380366141441

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

3.492 × 10⁹⁶(97-digit number)

34921870964412674949…73807142760732282879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.492 × 10⁹⁶(97-digit number)

34921870964412674949…73807142760732282881

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

6.984 × 10⁹⁶(97-digit number)

69843741928825349899…47614285521464565759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.984 × 10⁹⁶(97-digit number)

69843741928825349899…47614285521464565761

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

1.396 × 10⁹⁷(98-digit number)

13968748385765069979…95228571042929131519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.396 × 10⁹⁷(98-digit number)

13968748385765069979…95228571042929131521

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.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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

Cross-reference on Chainz Explorer

Block #2,001,914

Cookie Preferences