Block #639,432

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/19/2014, 9:28:33 AM · Difficulty 10.9597 · 6,155,736 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6ad7521306f8302165bfaac395ee7f7c18db000a9cf0176b94a305c986335ef8

View on Chainz ↗

Height

#639,432

Difficulty

10.959712

Transactions

Size

733 B

Version

Bits

0af5afb4

Nonce

660,884

Timestamp

7/19/2014, 9:28:33 AM

Confirmations

6,155,736

Mined by

⛏️ aS:,AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

8bb6ae4c8572fa87a8a4e53849f5f18878bed963b9b1cd876fbdd7ebccba83ec

Transactions (1)

Coinbase8bb6ae4c8572fa…bdd7ebccba83ec

1 in → 17 out8.3100 XPM641 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AQyr8Lw3…hs4nt3Pn AR6Bo1f6…bC66D1z4 AXBL3gqC…y7uPRbRC

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.

1.736 × 10⁹⁹(100-digit number)

17364458730462768495…75497035571407516799

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

1.736 × 10⁹⁹(100-digit number)

17364458730462768495…75497035571407516799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.736 × 10⁹⁹(100-digit number)

17364458730462768495…75497035571407516801

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

3.472 × 10⁹⁹(100-digit number)

34728917460925536991…50994071142815033599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.472 × 10⁹⁹(100-digit number)

34728917460925536991…50994071142815033601

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

6.945 × 10⁹⁹(100-digit number)

69457834921851073982…01988142285630067199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.945 × 10⁹⁹(100-digit number)

69457834921851073982…01988142285630067201

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

1.389 × 10¹⁰⁰(101-digit number)

13891566984370214796…03976284571260134399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.389 × 10¹⁰⁰(101-digit number)

13891566984370214796…03976284571260134401

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

2.778 × 10¹⁰⁰(101-digit number)

27783133968740429593…07952569142520268799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.778 × 10¹⁰⁰(101-digit number)

27783133968740429593…07952569142520268801

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