Block #403,847

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/14/2014, 10:56:17 AM · Difficulty 10.4327 · 6,402,218 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5c91e721f3d95e86315fe0f438fdee58004677f570fc34558d0e0fdca6ece33c

View on Chainz ↗

Height

#403,847

Difficulty

10.432659

Transactions

Size

969 B

Version

Bits

0a6ec2c2

Nonce

95,342

Timestamp

2/14/2014, 10:56:17 AM

Confirmations

6,402,218

Mined by

⛏️ aR~AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

1533f67f636d1a09b9c4e7db2029697755fc06c7cf16695782bff691d2fd4eac

Transactions (1)

Coinbase1533f67f636d1a…bff691d2fd4eac

1 in → 24 out9.1700 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AYRvXuTr…CkbwFeLY AGKhfQo2…h7fBXLX6 AXFYLKrL…HmfBXJJP

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.

1.556 × 10⁹⁵(96-digit number)

15565127458981804257…26994433456197601279

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

1.556 × 10⁹⁵(96-digit number)

15565127458981804257…26994433456197601279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.556 × 10⁹⁵(96-digit number)

15565127458981804257…26994433456197601281

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

3.113 × 10⁹⁵(96-digit number)

31130254917963608515…53988866912395202559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.113 × 10⁹⁵(96-digit number)

31130254917963608515…53988866912395202561

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

6.226 × 10⁹⁵(96-digit number)

62260509835927217031…07977733824790405119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.226 × 10⁹⁵(96-digit number)

62260509835927217031…07977733824790405121

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

1.245 × 10⁹⁶(97-digit number)

12452101967185443406…15955467649580810239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.245 × 10⁹⁶(97-digit number)

12452101967185443406…15955467649580810241

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

2.490 × 10⁹⁶(97-digit number)

24904203934370886812…31910935299161620479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.490 × 10⁹⁶(97-digit number)

24904203934370886812…31910935299161620481

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