Block #222,451

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/22/2013, 6:14:48 AM · Difficulty 9.9395 · 6,572,511 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6e59197bdeee37e105b04bd974f5e7f454a94048595f6814f78b2012767ec881

View on Chainz ↗

Height

#222,451

Difficulty

9.939464

Transactions

Size

1.90 KB

Version

Bits

09f080b7

Nonce

15,668

Timestamp

10/22/2013, 6:14:48 AM

Confirmations

6,572,511

Mined by

⛏️ dRf*AS6sRu1RZyNqYNxz1pTq4rDhZ6UpJKwm5m

Merkle Root

596ff318b2c071b84b43c2b8ae6561f2c23abfea2592b20bdad84b460103432d

Transactions (2)

Coinbase5968c07da08535…9149b50a096515

1 in → 33 out10.0900 XPM1.16 KB

AS6sRu1R…UpJKwm5m AKXeSXzu…yeuNjvhB AKFBsJ1Y…LYyU7TbU AcMPa5Yh…j5yHgkwm AScCYXya…oAz38X3p

1d91dfda757aa0…f026f3bdc7056c

4 in → 6 out40.4700 XPM671 B

ATbqyV1r…CJL2t9DA AYaaJuja…8dbpprfG AdToHhys…uNu3dqWo APd3tden…qhRE2ARG AbuU1HhS…JPwsJEbB

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.

8.333 × 10⁹⁵(96-digit number)

83335805255286827776…25413837261304995839

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

8.333 × 10⁹⁵(96-digit number)

83335805255286827776…25413837261304995839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.333 × 10⁹⁵(96-digit number)

83335805255286827776…25413837261304995841

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

1.666 × 10⁹⁶(97-digit number)

16667161051057365555…50827674522609991679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.666 × 10⁹⁶(97-digit number)

16667161051057365555…50827674522609991681

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

3.333 × 10⁹⁶(97-digit number)

33334322102114731110…01655349045219983359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.333 × 10⁹⁶(97-digit number)

33334322102114731110…01655349045219983361

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

6.666 × 10⁹⁶(97-digit number)

66668644204229462220…03310698090439966719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.666 × 10⁹⁶(97-digit number)

66668644204229462220…03310698090439966721

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

1.333 × 10⁹⁷(98-digit number)

13333728840845892444…06621396180879933439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.333 × 10⁹⁷(98-digit number)

13333728840845892444…06621396180879933441

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