Block #190,379

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/2/2013, 11:19:45 AM · Difficulty 9.8735 · 6,604,169 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9d2753a6f90a6112347541ae10720e02163df0d49985da67a2328286f5328f9d

View on Chainz ↗

Height

#190,379

Difficulty

9.873457

Transactions

Size

3.70 KB

Version

Bits

09df9add

Nonce

1,164,869,139

Timestamp

10/2/2013, 11:19:45 AM

Confirmations

6,604,169

Mined by

⛏️ RL%AZYSPqZ9B1MyJ1B6CZFifWyiUNKsqVRLZX

Merkle Root

6880059ac7651b15986b3173db662aa8323dcaada408529f2165d8aa1d4c6b55

Transactions (1)

Coinbase6880059ac7651b…65d8aa1d4c6b55

1 in → 107 out10.2100 XPM3.61 KB

AZYSPqZ9…KsqVRLZX AJCCNvEZ…gX1b1gmx AWNQupAN…aZuvsT36 APuVQWHc…wmkgqriM AMtLvyhH…QzfLCpZS

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.

1.178 × 10⁹⁵(96-digit number)

11780034768018362584…08335784844452956159

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

1.178 × 10⁹⁵(96-digit number)

11780034768018362584…08335784844452956159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.178 × 10⁹⁵(96-digit number)

11780034768018362584…08335784844452956161

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

2.356 × 10⁹⁵(96-digit number)

23560069536036725169…16671569688905912319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.356 × 10⁹⁵(96-digit number)

23560069536036725169…16671569688905912321

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

4.712 × 10⁹⁵(96-digit number)

47120139072073450339…33343139377811824639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.712 × 10⁹⁵(96-digit number)

47120139072073450339…33343139377811824641

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

9.424 × 10⁹⁵(96-digit number)

94240278144146900679…66686278755623649279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.424 × 10⁹⁵(96-digit number)

94240278144146900679…66686278755623649281

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

1.884 × 10⁹⁶(97-digit number)

18848055628829380135…33372557511247298559

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