Block #131,451

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/24/2013, 7:04:39 AM · Difficulty 9.7858 · 6,673,602 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1ecdb680d77a70a3e3a53d2c17cf60533d41f9a74e1c9c2246f80d2fa28f19da

View on Chainz ↗

Height

#131,451

Difficulty

9.785750

Transactions

Size

1.00 KB

Version

Bits

09c926f1

Nonce

178,767

Timestamp

8/24/2013, 7:04:39 AM

Confirmations

6,673,602

Mined by

⛏️ P2SHAMiZByGri59c7eDiEa5jQCLJS7nXNRp9VS

Merkle Root

a777db2ec3b6d161786132e9306426e49773cf44a0af836ec5461cb10b5254ed

Transactions (4)

Coinbasebcfe728fc84d4e…ab0f14828f0758

1 in → 1 out10.4600 XPM109 B

AMiZByGr…nXNRp9VS

1f8fef8ae29f3b…b34f9f1eb5407b

2 in → 2 out20.8500 XPM374 B

AcxZqits…NQeGY4jo AZ2HVrvK…1zcwkaFn

fba01287716064…453133d3f8906c

1 in → 2 out6.3410 XPM225 B

AJm1RVcf…uid9DkuU AX7htKtJ…uM6fYMgg

2491bf7c5be41d…de1fb4d0010d83

1 in → 2 out3.6254 XPM226 B

AK6DLNgv…M4GgceQx ATuGnP64…yMkJKPrK

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.

3.476 × 10⁹⁷(98-digit number)

34767763613616986346…09124772272998317399

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

3.476 × 10⁹⁷(98-digit number)

34767763613616986346…09124772272998317399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.476 × 10⁹⁷(98-digit number)

34767763613616986346…09124772272998317401

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

6.953 × 10⁹⁷(98-digit number)

69535527227233972693…18249544545996634799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.953 × 10⁹⁷(98-digit number)

69535527227233972693…18249544545996634801

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

1.390 × 10⁹⁸(99-digit number)

13907105445446794538…36499089091993269599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.390 × 10⁹⁸(99-digit number)

13907105445446794538…36499089091993269601

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

2.781 × 10⁹⁸(99-digit number)

27814210890893589077…72998178183986539199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.781 × 10⁹⁸(99-digit number)

27814210890893589077…72998178183986539201

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

5.562 × 10⁹⁸(99-digit number)

55628421781787178154…45996356367973078399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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