Block #150,336

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/4/2013, 11:03:39 PM · Difficulty 9.8590 · 6,651,481 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0cbae5f753e45b357394aad744f15e310175842b7241d8e571fe355385efe79b

View on Chainz ↗

Height

#150,336

Difficulty

9.859015

Transactions

Size

1014 B

Version

Bits

09dbe865

Nonce

11,096

Timestamp

9/4/2013, 11:03:39 PM

Confirmations

6,651,481

Mined by

⛏️ P2SHARwEjnekTmEd4gDgSnACXGZ9UNXN12RHSr

Merkle Root

80b677eec61712077dbe5d2d27ae0204fb06cc1ffde2e47e834269c5376178b9

Transactions (2)

Coinbase6e41d0fa0cee89…df676eea44596f

1 in → 1 out10.2800 XPM109 B

ARwEjnek…XN12RHSr

260db54e639a9d…41f91f3ed5dc37

5 in → 2 out31.9868 XPM816 B

AMiWnd27…iS25816M AP8NinHw…iWUFjnQn

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.

1.074 × 10⁹²(93-digit number)

10746621083045489926…41048770585670285639

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

1.074 × 10⁹²(93-digit number)

10746621083045489926…41048770585670285639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.074 × 10⁹²(93-digit number)

10746621083045489926…41048770585670285641

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

2.149 × 10⁹²(93-digit number)

21493242166090979853…82097541171340571279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.149 × 10⁹²(93-digit number)

21493242166090979853…82097541171340571281

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

4.298 × 10⁹²(93-digit number)

42986484332181959706…64195082342681142559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.298 × 10⁹²(93-digit number)

42986484332181959706…64195082342681142561

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

8.597 × 10⁹²(93-digit number)

85972968664363919413…28390164685362285119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.597 × 10⁹²(93-digit number)

85972968664363919413…28390164685362285121

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

1.719 × 10⁹³(94-digit number)

17194593732872783882…56780329370724570239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.719 × 10⁹³(94-digit number)

17194593732872783882…56780329370724570241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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