Block #161,092

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/12/2013, 10:16:44 AM · Difficulty 9.8596 · 6,637,459 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

32ce6a385305a06c32a820a2eaebdc6adb425e1567c2231966b77fceb249a9ce

View on Chainz ↗

Height

#161,092

Difficulty

9.859563

Transactions

Size

507 B

Version

Bits

09dc0c55

Nonce

34,475

Timestamp

9/12/2013, 10:16:44 AM

Confirmations

6,637,459

Mined by

⛏️ P2SHATcYY5nLzEMr6w59GbiSw4QQzJev5HLvsx

Merkle Root

473c034c94ac4057b305d970a1b08b87a954659bd166566cb932d0875a9e951a

Transactions (2)

Coinbase5e9459f18fc4b9…ed418f13054824

1 in → 1 out10.2800 XPM109 B

ATcYY5nL…ev5HLvsx

7c5af3fba15956…6a05453fbb86bb

2 in → 2 out20.6600 XPM307 B

ASPdVtvp…cRFDfco6 AJecGVPu…Ht4pNBpS

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.

1.935 × 10⁹⁶(97-digit number)

19358231485464864002…29677287334077781279

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

1.935 × 10⁹⁶(97-digit number)

19358231485464864002…29677287334077781279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.935 × 10⁹⁶(97-digit number)

19358231485464864002…29677287334077781281

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

3.871 × 10⁹⁶(97-digit number)

38716462970929728005…59354574668155562559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.871 × 10⁹⁶(97-digit number)

38716462970929728005…59354574668155562561

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

7.743 × 10⁹⁶(97-digit number)

77432925941859456010…18709149336311125119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.743 × 10⁹⁶(97-digit number)

77432925941859456010…18709149336311125121

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

1.548 × 10⁹⁷(98-digit number)

15486585188371891202…37418298672622250239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.548 × 10⁹⁷(98-digit number)

15486585188371891202…37418298672622250241

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

3.097 × 10⁹⁷(98-digit number)

30973170376743782404…74836597345244500479

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