Block #193

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/7/2013, 9:24:17 PM · Difficulty 7.0043 · 6,788,711 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

58b5a0fad304e84da96e3a223df63a7fd34b7a0599fb8193f0c786b036edc572

View on Chainz ↗

Height

#193

Difficulty

7.004298

Transactions

Size

208 B

Version

Bits

070119b2

Nonce

342

Timestamp

7/7/2013, 9:24:17 PM

Confirmations

6,788,711

Merkle Root

9f04661341467db77cdfd79be3d1d59364cab007a56424aa84cdc529583a1f88

Transactions (1)

Coinbase9f04661341467d…cdc529583a1f88

1 in → 1 out20.3600 XPM108 B

AdV5Vw5N…owsi9s2P

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.

6.462 × 10¹¹⁸(119-digit number)

64623740268927598864…52083639735742881299

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

6.462 × 10¹¹⁸(119-digit number)

64623740268927598864…52083639735742881299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.462 × 10¹¹⁸(119-digit number)

64623740268927598864…52083639735742881301

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

1.292 × 10¹¹⁹(120-digit number)

12924748053785519772…04167279471485762599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.292 × 10¹¹⁹(120-digit number)

12924748053785519772…04167279471485762601

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

2.584 × 10¹¹⁹(120-digit number)

25849496107571039545…08334558942971525199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.584 × 10¹¹⁹(120-digit number)

25849496107571039545…08334558942971525201

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

5.169 × 10¹¹⁹(120-digit number)

51698992215142079091…16669117885943050399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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