Block #160,152

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/11/2013, 5:14:03 PM · Difficulty 9.8618 · 6,636,367 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a1886cfb934faee2fcd7c0972a6c11bcb700065b2501a3f3b2a03f38caabb992

View on Chainz ↗

Height

#160,152

Difficulty

9.861797

Transactions

Size

719 B

Version

Bits

09dc9ec0

Nonce

18,015

Timestamp

9/11/2013, 5:14:03 PM

Confirmations

6,636,367

Mined by

⛏️ P2SHAG2RnfCTr1D6FVnVLRXGQAAYYdeBNNSXNf

Merkle Root

10cfb20ba6f3f37fad2839c02a069c1c39319dcda1cb077ad9623c46e3295510

Transactions (2)

Coinbase266aecd6f5cdee…b8fa638114c91c

1 in → 1 out10.2800 XPM109 B

AG2RnfCT…eBNNSXNf

3dd467a0d60066…6a8ae539505a6d

3 in → 2 out200.0122 XPM520 B

AUKkWYqh…Exn95uPd AM6mGFgp…6mPzfFFP

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.

3.170 × 10⁹⁴(95-digit number)

31708803547145742431…11055439652173143039

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

3.170 × 10⁹⁴(95-digit number)

31708803547145742431…11055439652173143039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.170 × 10⁹⁴(95-digit number)

31708803547145742431…11055439652173143041

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

6.341 × 10⁹⁴(95-digit number)

63417607094291484862…22110879304346286079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.341 × 10⁹⁴(95-digit number)

63417607094291484862…22110879304346286081

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

1.268 × 10⁹⁵(96-digit number)

12683521418858296972…44221758608692572159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.268 × 10⁹⁵(96-digit number)

12683521418858296972…44221758608692572161

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

2.536 × 10⁹⁵(96-digit number)

25367042837716593945…88443517217385144319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.536 × 10⁹⁵(96-digit number)

25367042837716593945…88443517217385144321

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

5.073 × 10⁹⁵(96-digit number)

50734085675433187890…76887034434770288639

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