Block #160,236

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/11/2013, 6:44:05 PM · Difficulty 9.8618 · 6,637,580 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d6368a21e42ab9ff42bc8f750e302e0d6b5ff6f440164fee0dc22cb3d51b1eca

View on Chainz ↗

Height

#160,236

Difficulty

9.861750

Transactions

Size

67.38 KB

Version

Bits

09dc9ba6

Nonce

59,230

Timestamp

9/11/2013, 6:44:05 PM

Confirmations

6,637,580

Mined by

⛏️ P2SHAW7csDjrkyTy6fADU41S7MnvGqWLLrBTmA

Merkle Root

3dfcb0d85b87fc244fb6bfa3e36e50db0f8691037895f48ea1176528b6843828

Transactions (3)

Coinbase936b5b682cefd3…cf72c57936e5d1

1 in → 1 out10.9600 XPM109 B

AW7csDjr…WLLrBTmA

33d45c6f89674c…185d7320c6db30

595 in → 1 out6900.0000 XPM66.39 KB

AWqrmbWo…ZcSjTJTw

5b53399b102c44…3502ef269d6c96

5 in → 2 out19.5126 XPM817 B

APYgGDLH…fvJ498W4 AeY9JR7w…quc3g9Mk

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.

4.577 × 10⁹⁴(95-digit number)

45771370309706523767…73672732745413233919

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

4.577 × 10⁹⁴(95-digit number)

45771370309706523767…73672732745413233919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.577 × 10⁹⁴(95-digit number)

45771370309706523767…73672732745413233921

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

9.154 × 10⁹⁴(95-digit number)

91542740619413047535…47345465490826467839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.154 × 10⁹⁴(95-digit number)

91542740619413047535…47345465490826467841

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

1.830 × 10⁹⁵(96-digit number)

18308548123882609507…94690930981652935679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.830 × 10⁹⁵(96-digit number)

18308548123882609507…94690930981652935681

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

3.661 × 10⁹⁵(96-digit number)

36617096247765219014…89381861963305871359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.661 × 10⁹⁵(96-digit number)

36617096247765219014…89381861963305871361

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

7.323 × 10⁹⁵(96-digit number)

73234192495530438028…78763723926611742719

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