Block #1,038,327

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/30/2015, 1:56:26 AM · Difficulty 10.7342 · 5,753,409 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8e89b517c487cbcbfcb52d25bc09e2a995e706199284e760949439708a107a1d

View on Chainz ↗

Height

#1,038,327

Difficulty

10.734172

Transactions

Size

1.01 KB

Version

Bits

0abbf2ad

Nonce

44,123,345

Timestamp

4/30/2015, 1:56:26 AM

Confirmations

5,753,409

Merkle Root

65dad4a9344c5bfc2d284a0a3520266ea6ef766977be1d0da65dbab0de17e066

Transactions (4)

Coinbaseaa40bed5657e53…1df33bdbb01b41

1 in → 1 out8.7000 XPM116 B

ANSXnLY2…Sd25TjkD

2a71c0dbdc8f70…b07bf58e16bd2a

2 in → 2 out11.1183 XPM374 B

Ad6DXCui…MgiEBNyM Ae9drWdk…FnLTm9Pn

a3fef54a43c011…70a99f33aaf733

1 in → 2 out7.5189 XPM225 B

Aa4PtTwK…H3ppZFzk AMN7iR4V…qxn9yFT1

38fc9f347c5202…0aeeffc0f72d5c

1 in → 2 out3.4281 XPM227 B

Af3aPj7K…cnGd5dnY Ad9vSZjd…j5LrVAJn

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.

2.221 × 10⁹⁵(96-digit number)

22218203619422661572…79926121554616718719

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

2.221 × 10⁹⁵(96-digit number)

22218203619422661572…79926121554616718719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.221 × 10⁹⁵(96-digit number)

22218203619422661572…79926121554616718721

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

4.443 × 10⁹⁵(96-digit number)

44436407238845323145…59852243109233437439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.443 × 10⁹⁵(96-digit number)

44436407238845323145…59852243109233437441

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

8.887 × 10⁹⁵(96-digit number)

88872814477690646291…19704486218466874879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.887 × 10⁹⁵(96-digit number)

88872814477690646291…19704486218466874881

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

1.777 × 10⁹⁶(97-digit number)

17774562895538129258…39408972436933749759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.777 × 10⁹⁶(97-digit number)

17774562895538129258…39408972436933749761

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

3.554 × 10⁹⁶(97-digit number)

35549125791076258516…78817944873867499519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.554 × 10⁹⁶(97-digit number)

35549125791076258516…78817944873867499521

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