Block #150,044

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/4/2013, 6:38:20 PM · Difficulty 9.8583 · 6,660,550 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f50a52c0e874476e1286b59ef7b865ab3c7de58a8c0c854dd52fbb5e867af860

View on Chainz ↗

Height

#150,044

Difficulty

9.858325

Transactions

Size

1.08 KB

Version

Bits

09dbbb28

Nonce

222,902

Timestamp

9/4/2013, 6:38:20 PM

Confirmations

6,660,550

Mined by

⛏️ P2SHAbWNYvpMPTr5yNMC9jYji7WgMb89n1NEAp

Merkle Root

77650ae4b37f9265079b22284c54528dc289999af776ba4aaaacb5edb3082af4

Transactions (5)

Coinbasee8b06f4c9b6cca…a321930455c910

1 in → 1 out10.3100 XPM109 B

AbWNYvpM…89n1NEAp

9fbcec2b607229…d86944a5b90026

1 in → 2 out10.2800 XPM227 B

AP2J7nwT…UQN2sX6s ANjE4rRU…gZ9FpSTJ

fb71bab8a92481…a163eef0f9c9e7

1 in → 2 out10.2800 XPM225 B

AXEk2gxD…43WBsB78 AZehgMKn…xPe3PbU3

22a2c232dd31fb…b3d677a5b3fe61

1 in → 2 out10.2800 XPM226 B

AcMfUmHy…mb9H82gQ AZB2k4uv…CGPNm7PB

bcdc14ecec746c…bc980efa2e0ea7

1 in → 2 out5.2402 XPM226 B

AQ4m6H6s…Dd3a3smu AQFBW6Ev…RQ4H4EFe

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.

1.050 × 10⁹²(93-digit number)

10501229122330933235…08037176833703923199

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

1.050 × 10⁹²(93-digit number)

10501229122330933235…08037176833703923199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.050 × 10⁹²(93-digit number)

10501229122330933235…08037176833703923201

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

2.100 × 10⁹²(93-digit number)

21002458244661866471…16074353667407846399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.100 × 10⁹²(93-digit number)

21002458244661866471…16074353667407846401

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

4.200 × 10⁹²(93-digit number)

42004916489323732943…32148707334815692799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.200 × 10⁹²(93-digit number)

42004916489323732943…32148707334815692801

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

8.400 × 10⁹²(93-digit number)

84009832978647465887…64297414669631385599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.400 × 10⁹²(93-digit number)

84009832978647465887…64297414669631385601

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

1.680 × 10⁹³(94-digit number)

16801966595729493177…28594829339262771199

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

Block #150,044

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