Block #74,329

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 10:28:58 AM · Difficulty 8.9954 · 6,721,194 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

22e0f891d1d1329ef466183df02f7a93c506387708f08f902641dfa143e864f9

View on Chainz ↗

Height

#74,329

Difficulty

8.995440

Transactions

Size

207 B

Version

Bits

08fed521

Nonce

138

Timestamp

7/21/2013, 10:28:58 AM

Confirmations

6,721,194

Mined by

⛏️ P2SHAcaEggwWoKPiukDE42MjnUbDgotD6Y7rL7

Merkle Root

d1ccdc03af216fa19d743857a177b22b0b7a6144a6623459f76089d0142996c1

Transactions (1)

Coinbased1ccdc03af216f…6089d0142996c1

1 in → 1 out12.3400 XPM110 B

AcaEggwW…tD6Y7rL7

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.

6.931 × 10¹¹⁰(111-digit number)

69315985540108803945…63277319792222358559

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

6.931 × 10¹¹⁰(111-digit number)

69315985540108803945…63277319792222358559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.931 × 10¹¹⁰(111-digit number)

69315985540108803945…63277319792222358561

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

1.386 × 10¹¹¹(112-digit number)

13863197108021760789…26554639584444717119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.386 × 10¹¹¹(112-digit number)

13863197108021760789…26554639584444717121

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

2.772 × 10¹¹¹(112-digit number)

27726394216043521578…53109279168889434239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.772 × 10¹¹¹(112-digit number)

27726394216043521578…53109279168889434241

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

5.545 × 10¹¹¹(112-digit number)

55452788432087043156…06218558337778868479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.545 × 10¹¹¹(112-digit number)

55452788432087043156…06218558337778868481

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

1.109 × 10¹¹²(113-digit number)

11090557686417408631…12437116675557736959

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