Block #147,977

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/3/2013, 10:46:55 AM · Difficulty 9.8537 · 6,655,333 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a8fa6332a2d3babed94eb877b28b29a92b8671129778f8a53b3b3826de09cfc8

View on Chainz ↗

Height

#147,977

Difficulty

9.853736

Transactions

Size

1.27 KB

Version

Bits

09da8e76

Nonce

178,343

Timestamp

9/3/2013, 10:46:55 AM

Confirmations

6,655,333

Mined by

⛏️ P2SHARZhi1acyuuS34Xqs7kFqCGBvATa6T9Mew

Merkle Root

5b95a319eb2351f35de8548b573c8ae045ba247be26fe69596adb9c3172b558b

Transactions (3)

Coinbaseeac80ef39267b5…f755672ad34690

1 in → 1 out10.3000 XPM109 B

ARZhi1ac…Ta6T9Mew

efbeb4d1fd1598…86cd047d49a9fc

3 in → 1 out31.0500 XPM386 B

Abg9b4kX…im9CLs7g

2ecf4404a913a4…50099a6257f158

5 in → 2 out31.0190 XPM718 B

AFz9fXym…wh4UqpkL AeAGzLgM…cBkXk3U8

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.

1.149 × 10⁹²(93-digit number)

11493135965985667678…86130283543798884159

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

1.149 × 10⁹²(93-digit number)

11493135965985667678…86130283543798884159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.149 × 10⁹²(93-digit number)

11493135965985667678…86130283543798884161

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

2.298 × 10⁹²(93-digit number)

22986271931971335356…72260567087597768319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.298 × 10⁹²(93-digit number)

22986271931971335356…72260567087597768321

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

4.597 × 10⁹²(93-digit number)

45972543863942670713…44521134175195536639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.597 × 10⁹²(93-digit number)

45972543863942670713…44521134175195536641

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

9.194 × 10⁹²(93-digit number)

91945087727885341427…89042268350391073279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.194 × 10⁹²(93-digit number)

91945087727885341427…89042268350391073281

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

1.838 × 10⁹³(94-digit number)

18389017545577068285…78084536700782146559

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