Block #254,277

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/10/2013, 3:08:07 PM · Difficulty 9.9730 · 6,562,143 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a4ebbbe9152e018e595572116faf84a9ea10784b70d777e4e6b3d0b4e8db61f0

View on Chainz ↗

Height

#254,277

Difficulty

9.973024

Transactions

Size

2.45 KB

Version

Bits

09f91821

Nonce

80,488

Timestamp

11/10/2013, 3:08:07 PM

Confirmations

6,562,143

Mined by

⛏️ EaR+=ANmkKL2U9tSUyN8ojZRwqDzhmbjPxj1Qs3

Merkle Root

3946f9ad32acd64a63e5b069364a58dbfb1926b05ccef896ddd8f8cf2e88660c

Transactions (2)

Coinbase37fa4a30ff0b1b…db500591e33c3a

1 in → 54 out10.0200 XPM1.85 KB

ANmkKL2U…jPxj1Qs3 AQtzUSwq…htAuF3yC AKDTDDtx…iqvw9cdY AJzWx2VD…j4ZSMit5 ARR7aRH6…ne3DXGXZ

1563cf08d15f4a…0d37e5be81dde0

3 in → 2 out120.0138 XPM520 B

AM4YCePq…xsxPm6nK AHTaM2G7…DizHHzNE

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.

5.431 × 10⁸⁸(89-digit number)

54312007569795364682…82763886451792147349

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

5.431 × 10⁸⁸(89-digit number)

54312007569795364682…82763886451792147349

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.431 × 10⁸⁸(89-digit number)

54312007569795364682…82763886451792147351

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

1.086 × 10⁸⁹(90-digit number)

10862401513959072936…65527772903584294699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.086 × 10⁸⁹(90-digit number)

10862401513959072936…65527772903584294701

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

2.172 × 10⁸⁹(90-digit number)

21724803027918145872…31055545807168589399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.172 × 10⁸⁹(90-digit number)

21724803027918145872…31055545807168589401

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

4.344 × 10⁸⁹(90-digit number)

43449606055836291745…62111091614337178799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.344 × 10⁸⁹(90-digit number)

43449606055836291745…62111091614337178801

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

8.689 × 10⁸⁹(90-digit number)

86899212111672583491…24222183228674357599

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

Block #254,277

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