Block #219,966

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/20/2013, 6:45:36 PM · Difficulty 9.9348 · 6,579,372 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f9eb1f936060564afa230c1bb9ea1dca6630e01d9fd8e70083cf275d2934dbd2

View on Chainz ↗

Height

#219,966

Difficulty

9.934834

Transactions

Size

1.41 KB

Version

Bits

09ef5150

Nonce

41,237

Timestamp

10/20/2013, 6:45:36 PM

Confirmations

6,579,372

Mined by

AHo7y676AfFQ6SvV4xk8W7pEhQHnay4JgM

Merkle Root

54571e4abe5b0d3b521f2de180ed77c68cb0e64438ed1bd6235bdcd24341c07f

Transactions (1)

Coinbase54571e4abe5b0d…5bdcd24341c07f

1 in → 38 out10.1000 XPM1.32 KB

AHo7y676…Hnay4JgM AbeUZSvK…ijGzuyjz AKXeSXzu…yeuNjvhB AXpmXsTH…1zkdde3r AKDTDDtx…iqvw9cdY

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.

1.729 × 10⁹¹(92-digit number)

17291456448733682216…78024370307660031999

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

1.729 × 10⁹¹(92-digit number)

17291456448733682216…78024370307660031999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.729 × 10⁹¹(92-digit number)

17291456448733682216…78024370307660032001

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

3.458 × 10⁹¹(92-digit number)

34582912897467364432…56048740615320063999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.458 × 10⁹¹(92-digit number)

34582912897467364432…56048740615320064001

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

6.916 × 10⁹¹(92-digit number)

69165825794934728864…12097481230640127999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.916 × 10⁹¹(92-digit number)

69165825794934728864…12097481230640128001

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

1.383 × 10⁹²(93-digit number)

13833165158986945772…24194962461280255999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.383 × 10⁹²(93-digit number)

13833165158986945772…24194962461280256001

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

2.766 × 10⁹²(93-digit number)

27666330317973891545…48389924922560511999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.766 × 10⁹²(93-digit number)

27666330317973891545…48389924922560512001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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