Block #155,994

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/8/2013, 4:28:34 PM · Difficulty 9.8672 · 6,634,946 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

644d91074fad876cc3691455c124d407644a67f4bec010295fc0c7dc31e820ae

View on Chainz ↗

Height

#155,994

Difficulty

9.867212

Transactions

Size

356 B

Version

Bits

09de01a2

Nonce

81,660

Timestamp

9/8/2013, 4:28:34 PM

Confirmations

6,634,946

Merkle Root

dd98ade8ad2c26f36cb4cbaf9c8eb0c13b960522ffc9236647a40d6ceb454985

Transactions (2)

Coinbase85a862bd6a5448…8fedd7431e05e4

1 in → 1 out10.2700 XPM109 B

ARjqnoYd…FsP3c6ZD

092c4ac61b173b…7dd39c600c79ab

1 in → 1 out10.2600 XPM157 B

AcWWWPc4…NKmGSdQs

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.

2.117 × 10⁹⁴(95-digit number)

21179273265967277881…30499743337152753279

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

2.117 × 10⁹⁴(95-digit number)

21179273265967277881…30499743337152753279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.117 × 10⁹⁴(95-digit number)

21179273265967277881…30499743337152753281

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

4.235 × 10⁹⁴(95-digit number)

42358546531934555762…60999486674305506559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.235 × 10⁹⁴(95-digit number)

42358546531934555762…60999486674305506561

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

8.471 × 10⁹⁴(95-digit number)

84717093063869111525…21998973348611013119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.471 × 10⁹⁴(95-digit number)

84717093063869111525…21998973348611013121

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

1.694 × 10⁹⁵(96-digit number)

16943418612773822305…43997946697222026239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.694 × 10⁹⁵(96-digit number)

16943418612773822305…43997946697222026241

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

3.388 × 10⁹⁵(96-digit number)

33886837225547644610…87995893394444052479

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