Block #247,564

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/6/2013, 8:24:45 PM · Difficulty 9.9650 · 6,569,675 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7e45b258da25d2fa33454ce612c22d5e63d1efb3f03fb7167161aa73d4bdabf1

View on Chainz ↗

Height

#247,564

Difficulty

9.965038

Transactions

Size

425 B

Version

Bits

09f70cc0

Nonce

27,409

Timestamp

11/6/2013, 8:24:45 PM

Confirmations

6,569,675

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

9ab4f28fd4e364b7a8d356cafb9f6777148fcbcae34aa89cddb6c79c80c292b0

Transactions (2)

Coinbase0f42ce2bef464d…4dc2192a41377a

1 in → 2 out10.0700 XPM142 B

AKcbk49N…GJbKa7j1 ALfEGCwh…VawujfMm

37fafd992bc7e8…f4e90014b519db

1 in → 1 out107.9354 XPM192 B

ATknEwpv…tz6xvy1e

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.

5.536 × 10⁹⁷(98-digit number)

55360905185670449863…54038685494778969919

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

5.536 × 10⁹⁷(98-digit number)

55360905185670449863…54038685494778969919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.536 × 10⁹⁷(98-digit number)

55360905185670449863…54038685494778969921

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

1.107 × 10⁹⁸(99-digit number)

11072181037134089972…08077370989557939839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.107 × 10⁹⁸(99-digit number)

11072181037134089972…08077370989557939841

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

2.214 × 10⁹⁸(99-digit number)

22144362074268179945…16154741979115879679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.214 × 10⁹⁸(99-digit number)

22144362074268179945…16154741979115879681

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

4.428 × 10⁹⁸(99-digit number)

44288724148536359890…32309483958231759359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.428 × 10⁹⁸(99-digit number)

44288724148536359890…32309483958231759361

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

8.857 × 10⁹⁸(99-digit number)

88577448297072719781…64618967916463518719

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 #247,564

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