Block #397,480

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/10/2014, 3:23:35 AM · Difficulty 10.4123 · 6,408,201 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9a7aa7397f94a72492342f6b94d2d8fbc1de6ac4512d96e3238a3e3f4f27654e

View on Chainz ↗

Height

#397,480

Difficulty

10.412281

Transactions

Size

936 B

Version

Bits

0a698b3a

Nonce

92,818

Timestamp

2/10/2014, 3:23:35 AM

Confirmations

6,408,201

Mined by

⛏️ tAN9emqpK7dgr5Ubo53Xd9AuJhzWEnrfX7s

Merkle Root

7193589b3712831ece558845cf34b3286ba9f5c0b194d298fa863a0cf3019bba

Transactions (1)

Coinbase7193589b371283…863a0cf3019bba

1 in → 23 out9.2100 XPM845 B

AN9emqpK…WEnrfX7s Acs9SHrk…QJSB8SFG ATp4jJhs…TbSgR8Qb AZuKpVkB…HFoeLG6t AaATnZp9…zJjScSCc

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.

1.641 × 10⁹⁶(97-digit number)

16418801668812059181…97959942029660827519

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

1.641 × 10⁹⁶(97-digit number)

16418801668812059181…97959942029660827519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.641 × 10⁹⁶(97-digit number)

16418801668812059181…97959942029660827521

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

3.283 × 10⁹⁶(97-digit number)

32837603337624118363…95919884059321655039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.283 × 10⁹⁶(97-digit number)

32837603337624118363…95919884059321655041

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

6.567 × 10⁹⁶(97-digit number)

65675206675248236726…91839768118643310079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.567 × 10⁹⁶(97-digit number)

65675206675248236726…91839768118643310081

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

1.313 × 10⁹⁷(98-digit number)

13135041335049647345…83679536237286620159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.313 × 10⁹⁷(98-digit number)

13135041335049647345…83679536237286620161

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

2.627 × 10⁹⁷(98-digit number)

26270082670099294690…67359072474573240319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.627 × 10⁹⁷(98-digit number)

26270082670099294690…67359072474573240321

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