Block #18,673

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/12/2013, 6:11:25 AM · Difficulty 7.9116 · 6,774,017 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

55f3fc34b095ffa49e1de51be0c655ccc334478ddf90046cca9815f641905d4a

View on Chainz ↗

Height

#18,673

Difficulty

7.911602

Transactions

Size

2.34 KB

Version

Bits

07e95ebe

Nonce

181

Timestamp

7/12/2013, 6:11:25 AM

Confirmations

6,774,017

Merkle Root

b40a9931609ca6dda47b21ab3f74f58979cd834075197ce48485f40430d4d091

Transactions (4)

Coinbaseeba48b63b4e7d5…1d783e349646c9

1 in → 1 out16.0000 XPM109 B

AGpo8L7e…keBwR2mo

d8f2e95090035a…1764f581cefc58

7 in → 2 out100.0800 XPM912 B

AVMYgRrt…xtpNkUTL AYxoT5K3…VLfpXK9w

2c454771deddc6…856d85f722a363

3 in → 1 out48.6000 XPM385 B

AVm6CvLW…GmiytmRn

396a8f1e959c82…92992ad01ee493

6 in → 1 out146.9900 XPM900 B

AMm2NR1w…19uBFzE6

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.

2.901 × 10¹⁰³(104-digit number)

29012812848004403467…43058520573882893979

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

2.901 × 10¹⁰³(104-digit number)

29012812848004403467…43058520573882893979

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.901 × 10¹⁰³(104-digit number)

29012812848004403467…43058520573882893981

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

5.802 × 10¹⁰³(104-digit number)

58025625696008806935…86117041147765787959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.802 × 10¹⁰³(104-digit number)

58025625696008806935…86117041147765787961

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

1.160 × 10¹⁰⁴(105-digit number)

11605125139201761387…72234082295531575919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.160 × 10¹⁰⁴(105-digit number)

11605125139201761387…72234082295531575921

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

2.321 × 10¹⁰⁴(105-digit number)

23210250278403522774…44468164591063151839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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