Block #216,069

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 12:52:01 PM · Difficulty 9.9254 · 6,590,191 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8e93291424eb4afe1cd3ea3f6505b55fbc30f55992de53eb5407f6436280ed1f

View on Chainz ↗

Height

#216,069

Difficulty

9.925424

Transactions

Size

1.07 KB

Version

Bits

09ece89d

Nonce

130,469

Timestamp

10/18/2013, 12:52:01 PM

Confirmations

6,590,191

Mined by

⛏️ P2SHAVDWXkeYRc1J7RNt5eSeqHs4JbEigwWXVy

Merkle Root

497be1cf60d8af5b581623257be5c3776909627da10dfe42026a438acfd64f01

Transactions (3)

Coinbased6717872147f88…9394d6f410253d

1 in → 1 out10.1600 XPM109 B

AVDWXkeY…EigwWXVy

4449a44b3d8f99…d32246e3998179

2 in → 2 out20.2900 XPM373 B

ASuoUi24…FwBoFbxd AM7p9oUk…1nbGivy8

8c0dd476650dda…91c81778650de8

3 in → 2 out11.3283 XPM522 B

AP5jQRRy…kUEyPFi2 AHyHEeYQ…XuELsExj

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.

7.355 × 10⁹⁵(96-digit number)

73554118955351161101…37706496958027582319

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

7.355 × 10⁹⁵(96-digit number)

73554118955351161101…37706496958027582319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.355 × 10⁹⁵(96-digit number)

73554118955351161101…37706496958027582321

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

1.471 × 10⁹⁶(97-digit number)

14710823791070232220…75412993916055164639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.471 × 10⁹⁶(97-digit number)

14710823791070232220…75412993916055164641

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

2.942 × 10⁹⁶(97-digit number)

29421647582140464440…50825987832110329279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.942 × 10⁹⁶(97-digit number)

29421647582140464440…50825987832110329281

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

5.884 × 10⁹⁶(97-digit number)

58843295164280928881…01651975664220658559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.884 × 10⁹⁶(97-digit number)

58843295164280928881…01651975664220658561

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

1.176 × 10⁹⁷(98-digit number)

11768659032856185776…03303951328441317119

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 #216,069

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