Block #17,651

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/12/2013, 2:33:36 AM · Difficulty 7.8963 · 6,773,849 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

331a40347b13ab00f470cad31fc767a629e3d202d64e3ce11adbc78cffa99b49

View on Chainz ↗

Height

#17,651

Difficulty

7.896269

Transactions

Size

194 B

Version

Bits

07e571e9

Nonce

1,147

Timestamp

7/12/2013, 2:33:36 AM

Confirmations

6,773,849

Merkle Root

fda58005eaa9365fabbe05d6085f5ca44325c2da18e90b63e8feb0ed4a881e62

Transactions (1)

Coinbasefda58005eaa936…feb0ed4a881e62

1 in → 1 out16.0200 XPM108 B

AZ7H8eqt…Eq36y96i

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.

6.702 × 10⁸⁵(86-digit number)

67021754534028278896…58441193568304115499

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

6.702 × 10⁸⁵(86-digit number)

67021754534028278896…58441193568304115499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.702 × 10⁸⁵(86-digit number)

67021754534028278896…58441193568304115501

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

1.340 × 10⁸⁶(87-digit number)

13404350906805655779…16882387136608230999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.340 × 10⁸⁶(87-digit number)

13404350906805655779…16882387136608231001

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

2.680 × 10⁸⁶(87-digit number)

26808701813611311558…33764774273216461999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.680 × 10⁸⁶(87-digit number)

26808701813611311558…33764774273216462001

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

5.361 × 10⁸⁶(87-digit number)

53617403627222623117…67529548546432923999

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