Block #792,718

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/1/2014, 8:55:38 PM · Difficulty 10.9738 · 6,020,118 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fcfe66e0c0a3d0a669d6ae02cfbcf4615961a0694f968ec50270b2a7e5b617cc

View on Chainz ↗

Height

#792,718

Difficulty

10.973777

Transactions

Size

1.23 KB

Version

Bits

0af94970

Nonce

2,396,930,003

Timestamp

11/1/2014, 8:55:38 PM

Confirmations

6,020,118

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cd9a9f95eaa19796e38f48cf33fae39c4760ee67b3110d8eb9feac0c49798d4e

Transactions (5)

Coinbasedc9adc75e4377d…e034c41b22abf0

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

8b558af80e7ded…1c5c566ae92ed8

1 in → 2 out4.6338 XPM226 B

AGXqJki6…YNiMZGMN AagYXpwp…imQfY7ZY

870dcd16b3deb0…d87151f02821cc

1 in → 2 out1.4003 XPM226 B

AMoJsji6…a13Bp22Q APyk8PFL…QbYgn7Yy

a3fbc1557d9e2f…32d53d3ec19f7d

1 in → 2 out1.0309 XPM227 B

AGdWVjRk…LFVsqCnK ALqw1EQn…oqzwxra5

a0dc623aa4cbe4…979e5f7ef03b5a

2 in → 2 out1.1305 XPM375 B

ATxoEAVm…o1hPnNf4 AYxjiY9w…pyyEbxUP

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.

4.096 × 10⁹⁶(97-digit number)

40964103658029359651…99629448868901523199

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

4.096 × 10⁹⁶(97-digit number)

40964103658029359651…99629448868901523199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.096 × 10⁹⁶(97-digit number)

40964103658029359651…99629448868901523201

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

8.192 × 10⁹⁶(97-digit number)

81928207316058719302…99258897737803046399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.192 × 10⁹⁶(97-digit number)

81928207316058719302…99258897737803046401

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

1.638 × 10⁹⁷(98-digit number)

16385641463211743860…98517795475606092799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.638 × 10⁹⁷(98-digit number)

16385641463211743860…98517795475606092801

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

3.277 × 10⁹⁷(98-digit number)

32771282926423487721…97035590951212185599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.277 × 10⁹⁷(98-digit number)

32771282926423487721…97035590951212185601

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

6.554 × 10⁹⁷(98-digit number)

65542565852846975442…94071181902424371199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.554 × 10⁹⁷(98-digit number)

65542565852846975442…94071181902424371201

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

Block #792,718

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