Block #222,651

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/22/2013, 9:16:09 AM · Difficulty 9.9396 · 6,604,716 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

078353b5b985b8e5c1d7d79bdb2ab7c0f8ee0bf590a9dad807620fcf48e1c510

View on Chainz ↗

Height

#222,651

Difficulty

9.939640

Transactions

Size

1.91 KB

Version

Bits

09f08c38

Nonce

176,974

Timestamp

10/22/2013, 9:16:09 AM

Confirmations

6,604,716

Mined by

⛏️ P2SHAN9wYGUaA8h6buBp3sKay4zYKeFesDUDTc

Merkle Root

8340d056bd6c645c4e46730b128d7c1bf471ce66c955d9b0a4c590b6d0b00059

Transactions (5)

Coinbase289af610ff4920…8db2a8b77b9d65

1 in → 1 out10.1500 XPM109 B

AN9wYGUa…FesDUDTc

327241dc6cf058…5a07586f7cf520

6 in → 2 out734.3587 XPM967 B

AVizQs7o…bfnncJc8 AY3HnEc4…X7gmrnjY

cd54f9ac770e9a…fe991c507bcca0

1 in → 2 out10.1200 XPM192 B

AYaY7xkf…rLt5C2w6 AFz9fXym…wh4UqpkL

ac440888fb40f6…bf4b862e65abfa

2 in → 2 out15.2119 XPM374 B

ALWw5pne…DsdpGzi5 AN6ca7CP…yUBqykmo

120656948b0046…311a6c10e6d6c4

1 in → 2 out2.0473 XPM226 B

ASnSjgQg…fewAaNPL AKLNh1KW…vXa3TJTN

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.

9.555 × 10⁹¹(92-digit number)

95554471866316933147…37813356945718115219

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

9.555 × 10⁹¹(92-digit number)

95554471866316933147…37813356945718115219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.555 × 10⁹¹(92-digit number)

95554471866316933147…37813356945718115221

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

1.911 × 10⁹²(93-digit number)

19110894373263386629…75626713891436230439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.911 × 10⁹²(93-digit number)

19110894373263386629…75626713891436230441

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

3.822 × 10⁹²(93-digit number)

38221788746526773259…51253427782872460879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.822 × 10⁹²(93-digit number)

38221788746526773259…51253427782872460881

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

7.644 × 10⁹²(93-digit number)

76443577493053546518…02506855565744921759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.644 × 10⁹²(93-digit number)

76443577493053546518…02506855565744921761

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

1.528 × 10⁹³(94-digit number)

15288715498610709303…05013711131489843519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.528 × 10⁹³(94-digit number)

15288715498610709303…05013711131489843521

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

Block #222,651

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