Block #73,913

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 8:27:56 AM · Difficulty 8.9952 · 6,717,571 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

af41a6d7bb4e0360ecc6355f209430010ebb24e18c27f63eef04881e5cb7cc17

View on Chainz ↗

Height

#73,913

Difficulty

8.995152

Transactions

Size

201 B

Version

Bits

08fec250

Nonce

Timestamp

7/21/2013, 8:27:56 AM

Confirmations

6,717,571

Merkle Root

ed05e92b40dd8386e35295c471736c2f19e5a6c3e451a6fdcd428e5f7485ffea

Transactions (1)

Coinbaseed05e92b40dd83…428e5f7485ffea

1 in → 1 out12.3400 XPM110 B

AcBadmkp…GmhL921o

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.

1.666 × 10⁹⁷(98-digit number)

16663844460337105040…44222955179167957159

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

1.666 × 10⁹⁷(98-digit number)

16663844460337105040…44222955179167957159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.666 × 10⁹⁷(98-digit number)

16663844460337105040…44222955179167957161

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

3.332 × 10⁹⁷(98-digit number)

33327688920674210080…88445910358335914319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.332 × 10⁹⁷(98-digit number)

33327688920674210080…88445910358335914321

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

6.665 × 10⁹⁷(98-digit number)

66655377841348420161…76891820716671828639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.665 × 10⁹⁷(98-digit number)

66655377841348420161…76891820716671828641

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

1.333 × 10⁹⁸(99-digit number)

13331075568269684032…53783641433343657279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.333 × 10⁹⁸(99-digit number)

13331075568269684032…53783641433343657281

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

2.666 × 10⁹⁸(99-digit number)

26662151136539368064…07567282866687314559

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