Block #191,007

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/2/2013, 8:25:53 PM · Difficulty 9.8756 · 6,604,649 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c36da30cbfb5da62b562dfb294341b9a8dfc45941a99ca4b79dc1675a47e6c4d

View on Chainz ↗

Height

#191,007

Difficulty

9.875641

Transactions

Size

3.46 KB

Version

Bits

09e02a02

Nonce

1,164,756,380

Timestamp

10/2/2013, 8:25:53 PM

Confirmations

6,604,649

Mined by

⛏️ RLAeFbzyLv5ch8d2B5wvK7wTRYmmuL8iw1RZ

Merkle Root

823073d95cbb2dc471feec7728e09fd57ea05b5ef1a9304954f8b8e3042d3389

Transactions (2)

Coinbase283eb1fee7c157…8d6c78ca7d36b6

1 in → 94 out10.2100 XPM3.18 KB

AeFbzyLv…uL8iw1RZ AKoHGbXL…AMALbdsK AXEf9r4a…54V7EYi4 AP7ZfMBN…n8aVFt5X AVp5teGi…6zMrJdp7

0e045d5a779ecd…4db5179ca4d445

1 in → 2 out10.3000 XPM193 B

AJTXn9Z5…CmQqReSu ALRDixNE…vCoYGXar

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.

5.333 × 10⁹⁵(96-digit number)

53337373371068767063…43740786707875760639

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

5.333 × 10⁹⁵(96-digit number)

53337373371068767063…43740786707875760639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.333 × 10⁹⁵(96-digit number)

53337373371068767063…43740786707875760641

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

1.066 × 10⁹⁶(97-digit number)

10667474674213753412…87481573415751521279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.066 × 10⁹⁶(97-digit number)

10667474674213753412…87481573415751521281

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

2.133 × 10⁹⁶(97-digit number)

21334949348427506825…74963146831503042559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.133 × 10⁹⁶(97-digit number)

21334949348427506825…74963146831503042561

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

4.266 × 10⁹⁶(97-digit number)

42669898696855013650…49926293663006085119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.266 × 10⁹⁶(97-digit number)

42669898696855013650…49926293663006085121

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

8.533 × 10⁹⁶(97-digit number)

85339797393710027301…99852587326012170239

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