Block #217,708

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/19/2013, 12:37:07 PM · Difficulty 9.9287 · 6,598,327 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a77adda9926dc62a7aca50b33ae313b7bd58aa34bd8a38766b6a9f886cccc333

View on Chainz ↗

Height

#217,708

Difficulty

9.928685

Transactions

Size

2.03 KB

Version

Bits

09edbe4d

Nonce

85,868

Timestamp

10/19/2013, 12:37:07 PM

Confirmations

6,598,327

Mined by

⛏️ lRRb|4AS2SFsLgPK6fmxchsQK3r8huEcE7xGAcPN

Merkle Root

4c2722795ca67ab33f04ed1ebbb60c0419d97779b7b4a960d89d3ed082a0c551

Transactions (2)

Coinbasec3696dde453e2f…d36e3e89643fd7

1 in → 50 out10.1100 XPM1.72 KB

AS2SFsLg…E7xGAcPN AbeUZSvK…ijGzuyjz AKXeSXzu…yeuNjvhB AK61Jfjk…fenNk1MA ANuKx9Ke…wm7nrBRq

f7bd91ada4d294…c8309c44fda77f

1 in → 2 out10.1300 XPM226 B

AWvfe2Jc…g5zoRyhQ AJ6fv1Jh…AMeqVhoj

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.

8.760 × 10⁹¹(92-digit number)

87603792426703797331…63669375227237040899

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

8.760 × 10⁹¹(92-digit number)

87603792426703797331…63669375227237040899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.760 × 10⁹¹(92-digit number)

87603792426703797331…63669375227237040901

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

1.752 × 10⁹²(93-digit number)

17520758485340759466…27338750454474081799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.752 × 10⁹²(93-digit number)

17520758485340759466…27338750454474081801

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

3.504 × 10⁹²(93-digit number)

35041516970681518932…54677500908948163599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.504 × 10⁹²(93-digit number)

35041516970681518932…54677500908948163601

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

7.008 × 10⁹²(93-digit number)

70083033941363037865…09355001817896327199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.008 × 10⁹²(93-digit number)

70083033941363037865…09355001817896327201

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

1.401 × 10⁹³(94-digit number)

14016606788272607573…18710003635792654399

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

Block #217,708

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