Block #159,627

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/11/2013, 6:52:42 AM · Difficulty 9.8644 · 6,648,120 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

88b29ded17b33c76006817b87315fdebe5e10c530981b0a55a4e34461f293b7b

View on Chainz ↗

Height

#159,627

Difficulty

9.864375

Transactions

Size

1.07 KB

Version

Bits

09dd47b0

Nonce

68,549

Timestamp

9/11/2013, 6:52:42 AM

Confirmations

6,648,120

Mined by

⛏️ P2SHAHRFvx36vyE9FMonomDAzUXBKj6eM8gwQQ

Merkle Root

37727fb4fc04e8c953b12043c0865f1d0df194227e6228411b6b8df554e0e6e8

Transactions (3)

Coinbasee6457ad5523822…97a693130e4697

1 in → 1 out10.2800 XPM109 B

AHRFvx36…6eM8gwQQ

996459f5844e75…58a8c3e936579c

2 in → 2 out499.8339 XPM374 B

AVLT1CYV…4YGHZ2Fv AakGxn9J…d7mTfZVK

35ea42dfd48fe2…0269a7a8299ee4

3 in → 2 out20.3000 XPM522 B

AWj8vqaT…rByoonvB AKyXFqFn…hyELWgyd

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.

1.508 × 10⁹³(94-digit number)

15083371628318986988…76334880512792100559

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

1.508 × 10⁹³(94-digit number)

15083371628318986988…76334880512792100559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.508 × 10⁹³(94-digit number)

15083371628318986988…76334880512792100561

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

3.016 × 10⁹³(94-digit number)

30166743256637973977…52669761025584201119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.016 × 10⁹³(94-digit number)

30166743256637973977…52669761025584201121

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

6.033 × 10⁹³(94-digit number)

60333486513275947955…05339522051168402239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.033 × 10⁹³(94-digit number)

60333486513275947955…05339522051168402241

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

1.206 × 10⁹⁴(95-digit number)

12066697302655189591…10679044102336804479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.206 × 10⁹⁴(95-digit number)

12066697302655189591…10679044102336804481

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

2.413 × 10⁹⁴(95-digit number)

24133394605310379182…21358088204673608959

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 #159,627

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