Block #143,022

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/31/2013, 8:58:35 AM · Difficulty 9.8374 · 6,648,462 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

981347ca8d14f11540da79447cddf45931bca3bedfc49c5508c2d92903295663

View on Chainz ↗

Height

#143,022

Difficulty

9.837351

Transactions

Size

198 B

Version

Bits

09d65ca7

Nonce

203,538

Timestamp

8/31/2013, 8:58:35 AM

Confirmations

6,648,462

Merkle Root

783b944a4f340af3aae2525159b1623015fd233e48209419a35983e61cb92f74

Transactions (1)

Coinbase783b944a4f340a…5983e61cb92f74

1 in → 1 out10.3200 XPM109 B

AYqLJLrz…Z5fMNdEg

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.

4.712 × 10⁹²(93-digit number)

47122117756508266385…68538403511232347919

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

4.712 × 10⁹²(93-digit number)

47122117756508266385…68538403511232347919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.712 × 10⁹²(93-digit number)

47122117756508266385…68538403511232347921

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

9.424 × 10⁹²(93-digit number)

94244235513016532771…37076807022464695839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.424 × 10⁹²(93-digit number)

94244235513016532771…37076807022464695841

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

1.884 × 10⁹³(94-digit number)

18848847102603306554…74153614044929391679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.884 × 10⁹³(94-digit number)

18848847102603306554…74153614044929391681

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

3.769 × 10⁹³(94-digit number)

37697694205206613108…48307228089858783359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.769 × 10⁹³(94-digit number)

37697694205206613108…48307228089858783361

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

7.539 × 10⁹³(94-digit number)

75395388410413226217…96614456179717566719

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