Block #89,198

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/30/2013, 4:48:05 AM · Difficulty 9.2606 · 6,702,460 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

79e416b71e2d6066e702e5fbf4b51a0d9df0b2eef0fabae04938293367771855

View on Chainz ↗

Height

#89,198

Difficulty

9.260559

Transactions

Size

2.61 KB

Version

Bits

0942b3fd

Nonce

293,165

Timestamp

7/30/2013, 4:48:05 AM

Confirmations

6,702,460

Merkle Root

a31ed0601707e435d657b82b77d7f76be88dbd360943cfead5b07fb6eb2d530e

Transactions (3)

Coinbase40e900fa3c640e…bc9d39108a55ec

1 in → 1 out11.6800 XPM109 B

ASxK3vzM…RLNUrHoW

c402d728e8f279…d8b29fb9f17b08

2 in → 1 out23.2400 XPM272 B

Af4gn3KP…wykeRBrf

98c647e37d4042…a7cff664eff9fa

18 in → 3 out201.8100 XPM2.15 KB

AGfz3APU…kNJNtgfb AezV1WN3…3eFh9Nfm AQ9VkUy6…TuxTAEug

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.

1.873 × 10⁹⁶(97-digit number)

18738574905239439407…89512790372866172839

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

1.873 × 10⁹⁶(97-digit number)

18738574905239439407…89512790372866172839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.873 × 10⁹⁶(97-digit number)

18738574905239439407…89512790372866172841

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

3.747 × 10⁹⁶(97-digit number)

37477149810478878815…79025580745732345679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.747 × 10⁹⁶(97-digit number)

37477149810478878815…79025580745732345681

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

7.495 × 10⁹⁶(97-digit number)

74954299620957757630…58051161491464691359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.495 × 10⁹⁶(97-digit number)

74954299620957757630…58051161491464691361

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

1.499 × 10⁹⁷(98-digit number)

14990859924191551526…16102322982929382719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.499 × 10⁹⁷(98-digit number)

14990859924191551526…16102322982929382721

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

2.998 × 10⁹⁷(98-digit number)

29981719848383103052…32204645965858765439

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