Block #76,230

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 10:43:14 PM · Difficulty 9.0824 · 6,727,109 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5be6ab2c34c4ac9ab3ac6775a6cc47acbf60be5799f059c81ac3c242a4a90ab7

View on Chainz ↗

Height

#76,230

Difficulty

9.082400

Transactions

Size

210 B

Version

Bits

09151825

Nonce

451

Timestamp

7/21/2013, 10:43:14 PM

Confirmations

6,727,109

Mined by

⛏️ P2SHANey87HKeHbF7P31ach44cVFqNMGUx5bYr

Merkle Root

226298caa2f329c4ee1662fca3926397a2157127cf54bd833ff8784697ae78ba

Transactions (1)

Coinbase226298caa2f329…f8784697ae78ba

1 in → 1 out12.1100 XPM110 B

ANey87HK…MGUx5bYr

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.

3.163 × 10¹¹⁸(119-digit number)

31635162421207242628…12173267960983924599

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

3.163 × 10¹¹⁸(119-digit number)

31635162421207242628…12173267960983924599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.163 × 10¹¹⁸(119-digit number)

31635162421207242628…12173267960983924601

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

6.327 × 10¹¹⁸(119-digit number)

63270324842414485256…24346535921967849199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.327 × 10¹¹⁸(119-digit number)

63270324842414485256…24346535921967849201

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

1.265 × 10¹¹⁹(120-digit number)

12654064968482897051…48693071843935698399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.265 × 10¹¹⁹(120-digit number)

12654064968482897051…48693071843935698401

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

2.530 × 10¹¹⁹(120-digit number)

25308129936965794102…97386143687871396799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.530 × 10¹¹⁹(120-digit number)

25308129936965794102…97386143687871396801

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

5.061 × 10¹¹⁹(120-digit number)

50616259873931588205…94772287375742793599

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