Block #292,315

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 4:09:13 PM · Difficulty 9.9902 · 6,513,243 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8fedb8b0e721238788dc1057430be838860a4a63b65655f4c0599e46de8993ea

View on Chainz ↗

Height

#292,315

Difficulty

9.990249

Transactions

Size

2.15 KB

Version

Bits

09fd80f3

Nonce

227,762

Timestamp

12/3/2013, 4:09:13 PM

Confirmations

6,513,243

Mined by

⛏️ uaRAZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

4e091797c4c3ca2be0b76b57de8b9befcbab4930a58e190920b765d10a335b7b

Transactions (4)

Coinbase8c95135ec98635…ff7a80eb54b0f0

1 in → 27 out9.9784 XPM981 B

AZninDSu…FvgDMwC4 AKJVXxCy…FKh3JPJL AdomdxDW…oCsqGzkd AcC2zSod…rtWatH79 AMdvB6BS…DPq9FYdA

b9567165454039…48d9287f44f05e

1 in → 1 out9.9900 XPM191 B

AMq4mqcW…bajwBaFY

70f8fc4a11408a…592e6c2c39d8e2

1 in → 1 out10.0000 XPM157 B

AUh2ojHo…DQDmEBQk

7215698c404939…6a278e5ccc1d7a

5 in → 1 out11.2094 XPM784 B

ANDfb1Yy…wpAPTGgt

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.

3.327 × 10⁹²(93-digit number)

33271959185868035691…14697402304779974799

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

3.327 × 10⁹²(93-digit number)

33271959185868035691…14697402304779974799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.327 × 10⁹²(93-digit number)

33271959185868035691…14697402304779974801

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

6.654 × 10⁹²(93-digit number)

66543918371736071382…29394804609559949599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.654 × 10⁹²(93-digit number)

66543918371736071382…29394804609559949601

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

1.330 × 10⁹³(94-digit number)

13308783674347214276…58789609219119899199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.330 × 10⁹³(94-digit number)

13308783674347214276…58789609219119899201

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

2.661 × 10⁹³(94-digit number)

26617567348694428552…17579218438239798399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.661 × 10⁹³(94-digit number)

26617567348694428552…17579218438239798401

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

5.323 × 10⁹³(94-digit number)

53235134697388857105…35158436876479596799

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