Block #95,970

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/3/2013, 11:20:41 PM · Difficulty 9.2481 · 6,695,276 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

25663ee765518ee3047f706c34e53ffcd54afaec2b0ec3e489c923097b466f52

View on Chainz ↗

Height

#95,970

Difficulty

9.248052

Transactions

Size

579 B

Version

Bits

093f805b

Nonce

4,961

Timestamp

8/3/2013, 11:20:41 PM

Confirmations

6,695,276

Merkle Root

14c942b243af0716ebc7a00ca469eb6126ed536cc83b485f73123fbafeebf188

Transactions (2)

Coinbase3ef734e8553f92…3ff8f964132392

1 in → 1 out11.6900 XPM109 B

ANvaFfst…dDNhJGZ9

5c27df17022db8…0838c04206a7e6

2 in → 2 out360.1100 XPM374 B

ATDg1wpK…dc5kwZ3e AUYwKdeS…qtj2rLnH

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.

7.373 × 10¹⁰⁸(109-digit number)

73739005982270935953…36269098706380869919

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

7.373 × 10¹⁰⁸(109-digit number)

73739005982270935953…36269098706380869919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.373 × 10¹⁰⁸(109-digit number)

73739005982270935953…36269098706380869921

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

1.474 × 10¹⁰⁹(110-digit number)

14747801196454187190…72538197412761739839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.474 × 10¹⁰⁹(110-digit number)

14747801196454187190…72538197412761739841

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

2.949 × 10¹⁰⁹(110-digit number)

29495602392908374381…45076394825523479679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.949 × 10¹⁰⁹(110-digit number)

29495602392908374381…45076394825523479681

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

5.899 × 10¹⁰⁹(110-digit number)

58991204785816748762…90152789651046959359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.899 × 10¹⁰⁹(110-digit number)

58991204785816748762…90152789651046959361

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

1.179 × 10¹¹⁰(111-digit number)

11798240957163349752…80305579302093918719

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