Block #72,313

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 11:24:22 PM · Difficulty 8.9940 · 6,717,629 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f6e934abed8f1c78dcef61eb87e6be0ae0132f62da71c1502f751716f4dc2888

View on Chainz ↗

Height

#72,313

Difficulty

8.993976

Transactions

Size

200 B

Version

Bits

08fe752e

Nonce

644

Timestamp

7/20/2013, 11:24:22 PM

Confirmations

6,717,629

Merkle Root

b5f39bfa0ab406f2f5058d3c17bc9033285f5d8f8c94b94fc14b7c6d7588dd47

Transactions (1)

Coinbaseb5f39bfa0ab406…4b7c6d7588dd47

1 in → 1 out12.3400 XPM110 B

AK1JUKWL…oPR4rN5o

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.

1.181 × 10⁹⁵(96-digit number)

11817385997979238332…94854674583026975669

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

1.181 × 10⁹⁵(96-digit number)

11817385997979238332…94854674583026975669

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.181 × 10⁹⁵(96-digit number)

11817385997979238332…94854674583026975671

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

2.363 × 10⁹⁵(96-digit number)

23634771995958476665…89709349166053951339

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.363 × 10⁹⁵(96-digit number)

23634771995958476665…89709349166053951341

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

4.726 × 10⁹⁵(96-digit number)

47269543991916953330…79418698332107902679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.726 × 10⁹⁵(96-digit number)

47269543991916953330…79418698332107902681

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

9.453 × 10⁹⁵(96-digit number)

94539087983833906660…58837396664215805359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.453 × 10⁹⁵(96-digit number)

94539087983833906660…58837396664215805361

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

1.890 × 10⁹⁶(97-digit number)

18907817596766781332…17674793328431610719

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