Block #206,160

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/12/2013, 3:15:24 PM · Difficulty 9.9007 · 6,590,360 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d68e0aa74ea0bac9c65b48054f4648b60638fd65597574487edacf6b7cfdb1f7

View on Chainz ↗

Height

#206,160

Difficulty

9.900667

Transactions

Size

4.33 KB

Version

Bits

09e69220

Nonce

1,164,735,653

Timestamp

10/12/2013, 3:15:24 PM

Confirmations

6,590,360

Mined by

⛏️ P%RYgbAXx8WhsNAFDPw8gGrLzZNtV8uJi5uHr3Yv

Merkle Root

b125a44f038a5b5210233b55a6c60728e2968eb9a08b629417801a034837fd97

Transactions (1)

Coinbaseb125a44f038a5b…801a034837fd97

1 in → 126 out10.1400 XPM4.24 KB

AXx8WhsN…i5uHr3Yv AYckRkCF…TgDe5VSp AWWaDRnP…qR1zB7PV AehSbrXS…x2Vu99iu AeFbzyLv…uL8iw1RZ

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.

2.767 × 10⁹⁷(98-digit number)

27678944278862919073…72259551315732381459

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

2.767 × 10⁹⁷(98-digit number)

27678944278862919073…72259551315732381459

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.767 × 10⁹⁷(98-digit number)

27678944278862919073…72259551315732381461

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

5.535 × 10⁹⁷(98-digit number)

55357888557725838146…44519102631464762919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.535 × 10⁹⁷(98-digit number)

55357888557725838146…44519102631464762921

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

1.107 × 10⁹⁸(99-digit number)

11071577711545167629…89038205262929525839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.107 × 10⁹⁸(99-digit number)

11071577711545167629…89038205262929525841

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

2.214 × 10⁹⁸(99-digit number)

22143155423090335258…78076410525859051679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.214 × 10⁹⁸(99-digit number)

22143155423090335258…78076410525859051681

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

4.428 × 10⁹⁸(99-digit number)

44286310846180670516…56152821051718103359

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