Block #234,715

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/30/2013, 12:05:21 PM · Difficulty 9.9445 · 6,559,622 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d6e80895f1361573d1b711c749f8bcd0fe87a3573c60d21aaee03067a4be5445

View on Chainz ↗

Height

#234,715

Difficulty

9.944457

Transactions

Size

1.68 KB

Version

Bits

09f1c7f2

Nonce

62,133

Timestamp

10/30/2013, 12:05:21 PM

Confirmations

6,559,622

Merkle Root

d1e7469406f1a2532eeebc188aa9f3655acb31955e412d414edcd0254969aa6a

Transactions (1)

Coinbased1e7469406f1a2…dcd0254969aa6a

1 in → 46 out10.0800 XPM1.59 KB

AFqKfjez…qX9Ace3g AabHNb1B…GRoingRy AeZmMFY8…mjAy5Mi4 AXDu24HR…L9o8sC5D ARpndEmc…Hg792kEk

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.

2.236 × 10⁹⁸(99-digit number)

22366947952658291232…29747254062539688959

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

2.236 × 10⁹⁸(99-digit number)

22366947952658291232…29747254062539688959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.236 × 10⁹⁸(99-digit number)

22366947952658291232…29747254062539688961

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

4.473 × 10⁹⁸(99-digit number)

44733895905316582465…59494508125079377919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.473 × 10⁹⁸(99-digit number)

44733895905316582465…59494508125079377921

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

8.946 × 10⁹⁸(99-digit number)

89467791810633164931…18989016250158755839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.946 × 10⁹⁸(99-digit number)

89467791810633164931…18989016250158755841

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

1.789 × 10⁹⁹(100-digit number)

17893558362126632986…37978032500317511679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.789 × 10⁹⁹(100-digit number)

17893558362126632986…37978032500317511681

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

3.578 × 10⁹⁹(100-digit number)

35787116724253265972…75956065000635023359

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