Block #80,599

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/24/2013, 6:18:06 AM · Difficulty 9.2527 · 6,710,394 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3f5c75a3d2e4dca084a7937e9bf37e84f4b32819a6c2c6e62cf9d64f7300205f

View on Chainz ↗

Height

#80,599

Difficulty

9.252652

Transactions

Size

579 B

Version

Bits

0940adcb

Nonce

332,640

Timestamp

7/24/2013, 6:18:06 AM

Confirmations

6,710,394

Merkle Root

6fd098ef1ee7feff3c13dc2de4409d99b8c998cc5a5506a679eb5fb2024b8bf8

Transactions (2)

Coinbase98c895360174bc…10540979f98cd6

1 in → 1 out11.6700 XPM109 B

AbE9HrtY…XycDQ7ri

78f7957772f562…325c5b8bceba3f

2 in → 2 out56.0100 XPM372 B

AJjd86cP…Dgm9xPM4 AQ8SQnEZ…vLSf77FF

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.

7.237 × 10¹¹⁴(115-digit number)

72378020294119236639…32577992527263245479

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

7.237 × 10¹¹⁴(115-digit number)

72378020294119236639…32577992527263245479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.237 × 10¹¹⁴(115-digit number)

72378020294119236639…32577992527263245481

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

1.447 × 10¹¹⁵(116-digit number)

14475604058823847327…65155985054526490959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.447 × 10¹¹⁵(116-digit number)

14475604058823847327…65155985054526490961

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

2.895 × 10¹¹⁵(116-digit number)

28951208117647694655…30311970109052981919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.895 × 10¹¹⁵(116-digit number)

28951208117647694655…30311970109052981921

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

5.790 × 10¹¹⁵(116-digit number)

57902416235295389311…60623940218105963839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.790 × 10¹¹⁵(116-digit number)

57902416235295389311…60623940218105963841

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

1.158 × 10¹¹⁶(117-digit number)

11580483247059077862…21247880436211927679

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