Block #147,313

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/3/2013, 12:40:08 AM · Difficulty 9.8519 · 6,646,976 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3e005a518c23ba51247ba3591f2aee7aa72f9f0a496fa26e6351d9e2a6dfb967

View on Chainz ↗

Height

#147,313

Difficulty

9.851939

Transactions

Size

424 B

Version

Bits

09da18a5

Nonce

153,334

Timestamp

9/3/2013, 12:40:08 AM

Confirmations

6,646,976

Merkle Root

7952dc0c4089765372bfb18fc6ec08f2821d6d5aa39b4f189fb8560b65421fa1

Transactions (2)

Coinbase885c1a3480c61b…829d0f6dffe0fd

1 in → 1 out10.3000 XPM109 B

AJnfGiH6…Rom3PedH

7d491574059275…b4a85f1a188dcd

1 in → 2 out5.2541 XPM226 B

AcKk5ktG…W2GXmENL AN3GzQd8…kVvyzfjE

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.

4.065 × 10⁹¹(92-digit number)

40655912654588614985…64696027184619995039

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

4.065 × 10⁹¹(92-digit number)

40655912654588614985…64696027184619995039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.065 × 10⁹¹(92-digit number)

40655912654588614985…64696027184619995041

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

8.131 × 10⁹¹(92-digit number)

81311825309177229971…29392054369239990079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.131 × 10⁹¹(92-digit number)

81311825309177229971…29392054369239990081

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

1.626 × 10⁹²(93-digit number)

16262365061835445994…58784108738479980159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.626 × 10⁹²(93-digit number)

16262365061835445994…58784108738479980161

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

3.252 × 10⁹²(93-digit number)

32524730123670891988…17568217476959960319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.252 × 10⁹²(93-digit number)

32524730123670891988…17568217476959960321

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

6.504 × 10⁹²(93-digit number)

65049460247341783976…35136434953919920639

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