Block #292,421

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 5:36:31 PM · Difficulty 9.9903 · 6,502,989 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cb833bfafd14fcd32730d03895b8c47e81c28875eb15ba58bca84eecace828b2

View on Chainz ↗

Height

#292,421

Difficulty

9.990289

Transactions

Size

1003 B

Version

Bits

09fd8397

Nonce

331,480

Timestamp

12/3/2013, 5:36:31 PM

Confirmations

6,502,989

Mined by

⛏️ EvaREfAZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

78051745c92148fd5ad76eda5cb6b654fba5ed5769d0812e6a73bee172109b89

Transactions (1)

Coinbase78051745c92148…73bee172109b89

1 in → 25 out10.0000 XPM913 B

AZninDSu…FvgDMwC4 Ad9pSzHt…cpJ3y2zz AKde1i4d…88R1bw6g Aa9yRYxd…t5ZDhWf3 AXxoVg7k…T5ujGMdn

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.

6.629 × 10⁹⁵(96-digit number)

66297206759883940645…53959227048186782719

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

6.629 × 10⁹⁵(96-digit number)

66297206759883940645…53959227048186782719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.629 × 10⁹⁵(96-digit number)

66297206759883940645…53959227048186782721

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

1.325 × 10⁹⁶(97-digit number)

13259441351976788129…07918454096373565439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.325 × 10⁹⁶(97-digit number)

13259441351976788129…07918454096373565441

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

2.651 × 10⁹⁶(97-digit number)

26518882703953576258…15836908192747130879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.651 × 10⁹⁶(97-digit number)

26518882703953576258…15836908192747130881

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

5.303 × 10⁹⁶(97-digit number)

53037765407907152516…31673816385494261759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.303 × 10⁹⁶(97-digit number)

53037765407907152516…31673816385494261761

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

1.060 × 10⁹⁷(98-digit number)

10607553081581430503…63347632770988523519

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