Block #79,808

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/23/2013, 6:11:00 PM · Difficulty 9.2435 · 6,712,770 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9b91a83b0b607a8d097eb1d762db20363284b3240e6fabd218837fe17dc968bb

View on Chainz ↗

Height

#79,808

Difficulty

9.243520

Transactions

Size

1.51 KB

Version

Bits

093e5752

Nonce

Timestamp

7/23/2013, 6:11:00 PM

Confirmations

6,712,770

Merkle Root

224a193fae1f45e9f6ca01f2487e9132874088948e958aa4f03409500cd012f2

Transactions (3)

Coinbase6ac4a3f4e0c224…086324564588f4

1 in → 1 out11.7100 XPM110 B

AcUGDGA2…7xWrMsWf

2d1d89aa5fd280…519e0dc26b5e8f

2 in → 2 out98.0135 XPM375 B

APLcNg81…1WSfUexs AP6mrFkf…AbQY7Uw9

70548cd262a02f…a52cc8f566930b

6 in → 2 out49.9106 XPM968 B

ASKMAhku…7wZHy27U AP6mrFkf…AbQY7Uw9

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.

5.597 × 10⁹⁵(96-digit number)

55971592228182885455…62913729925769448869

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

5.597 × 10⁹⁵(96-digit number)

55971592228182885455…62913729925769448869

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.597 × 10⁹⁵(96-digit number)

55971592228182885455…62913729925769448871

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

1.119 × 10⁹⁶(97-digit number)

11194318445636577091…25827459851538897739

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.119 × 10⁹⁶(97-digit number)

11194318445636577091…25827459851538897741

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

2.238 × 10⁹⁶(97-digit number)

22388636891273154182…51654919703077795479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.238 × 10⁹⁶(97-digit number)

22388636891273154182…51654919703077795481

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

4.477 × 10⁹⁶(97-digit number)

44777273782546308364…03309839406155590959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.477 × 10⁹⁶(97-digit number)

44777273782546308364…03309839406155590961

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

8.955 × 10⁹⁶(97-digit number)

89554547565092616729…06619678812311181919

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