Block #79,405

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/23/2013, 11:11:15 AM · Difficulty 9.2454 · 6,712,148 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1120b2179e2f7fb0f69e0f77682711bc496580421c65473411bda30690a96823

View on Chainz ↗

Height

#79,405

Difficulty

9.245427

Transactions

Size

425 B

Version

Bits

093ed44d

Nonce

19,429

Timestamp

7/23/2013, 11:11:15 AM

Confirmations

6,712,148

Merkle Root

dd5478664722f083d538c2330422e11b5aeac68bf2ad56d478a49abdf334d6a6

Transactions (2)

Coinbase64543868a95928…9f71846865fc16

1 in → 1 out11.6900 XPM109 B

AJZRqHQF…TGGyufYJ

5ee5f3b99ea4ba…7f7b2968235ae1

1 in → 2 out99.9900 XPM227 B

AHybNPqR…EyTA2d3W AeNcNjer…5Y7RAAnE

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.

1.496 × 10⁹²(93-digit number)

14960391399123766121…93972463733755545949

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

1.496 × 10⁹²(93-digit number)

14960391399123766121…93972463733755545949

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.496 × 10⁹²(93-digit number)

14960391399123766121…93972463733755545951

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

2.992 × 10⁹²(93-digit number)

29920782798247532242…87944927467511091899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.992 × 10⁹²(93-digit number)

29920782798247532242…87944927467511091901

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

5.984 × 10⁹²(93-digit number)

59841565596495064485…75889854935022183799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.984 × 10⁹²(93-digit number)

59841565596495064485…75889854935022183801

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

1.196 × 10⁹³(94-digit number)

11968313119299012897…51779709870044367599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.196 × 10⁹³(94-digit number)

11968313119299012897…51779709870044367601

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

2.393 × 10⁹³(94-digit number)

23936626238598025794…03559419740088735199

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