Block #292,622

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 8:26:16 PM · Difficulty 9.9904 · 6,498,410 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9157cd2fc97bc61ba04bc3bc057f10efc2b66c4bfbbb2a6428bb79d7db010318

View on Chainz ↗

Height

#292,622

Difficulty

9.990355

Transactions

Size

720 B

Version

Bits

09fd87ed

Nonce

17,573

Timestamp

12/3/2013, 8:26:16 PM

Confirmations

6,498,410

Merkle Root

1788247d27aa31d9a46429a1080b4e57ceb341c4421611ec55bb9a9ba8048b43

Transactions (2)

Coinbasef447d4734bd912…ec92c960703581

1 in → 1 out10.0100 XPM109 B

ARYuCmXb…HnxRmwtf

ce8f8ec79718a3…eabab5eebe0038

3 in → 2 out271.7414 XPM520 B

AMWuZuxu…cr7jDxMK AJjFSP52…2N1pwg4X

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.

8.721 × 10⁹⁶(97-digit number)

87211537718296787131…19323027030878356039

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

8.721 × 10⁹⁶(97-digit number)

87211537718296787131…19323027030878356039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.721 × 10⁹⁶(97-digit number)

87211537718296787131…19323027030878356041

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

1.744 × 10⁹⁷(98-digit number)

17442307543659357426…38646054061756712079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.744 × 10⁹⁷(98-digit number)

17442307543659357426…38646054061756712081

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

3.488 × 10⁹⁷(98-digit number)

34884615087318714852…77292108123513424159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.488 × 10⁹⁷(98-digit number)

34884615087318714852…77292108123513424161

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

6.976 × 10⁹⁷(98-digit number)

69769230174637429705…54584216247026848319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.976 × 10⁹⁷(98-digit number)

69769230174637429705…54584216247026848321

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

1.395 × 10⁹⁸(99-digit number)

13953846034927485941…09168432494053696639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.395 × 10⁹⁸(99-digit number)

13953846034927485941…09168432494053696641

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