Block #141,186

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/30/2013, 3:34:11 AM · Difficulty 9.8349 · 6,650,623 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a22b8079924467fdafc5cdece99e9eb561ceebafb79d68ef391c75f961bba8df

View on Chainz ↗

Height

#141,186

Difficulty

9.834941

Transactions

Size

200 B

Version

Bits

09d5beb6

Nonce

95,307

Timestamp

8/30/2013, 3:34:11 AM

Confirmations

6,650,623

Merkle Root

99612a7478c8a626590cdcd7e14a86c799a6d2b4e2c9b44de482614d897a1686

Transactions (1)

Coinbase99612a7478c8a6…82614d897a1686

1 in → 1 out10.3200 XPM109 B

AKhaGKFX…KjeAXtBv

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.

8.574 × 10⁹⁶(97-digit number)

85741079216008250404…70017533506784289279

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

8.574 × 10⁹⁶(97-digit number)

85741079216008250404…70017533506784289279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.574 × 10⁹⁶(97-digit number)

85741079216008250404…70017533506784289281

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

1.714 × 10⁹⁷(98-digit number)

17148215843201650080…40035067013568578559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.714 × 10⁹⁷(98-digit number)

17148215843201650080…40035067013568578561

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

3.429 × 10⁹⁷(98-digit number)

34296431686403300161…80070134027137157119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.429 × 10⁹⁷(98-digit number)

34296431686403300161…80070134027137157121

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

6.859 × 10⁹⁷(98-digit number)

68592863372806600323…60140268054274314239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.859 × 10⁹⁷(98-digit number)

68592863372806600323…60140268054274314241

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

1.371 × 10⁹⁸(99-digit number)

13718572674561320064…20280536108548628479

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