Block #293,437

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/4/2013, 7:47:28 AM · Difficulty 9.9906 · 6,515,029 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dcbe32ac8ac83cbdd7341be11f757046d1e5982df52cd67c5587c0ea31d859a3

View on Chainz ↗

Height

#293,437

Difficulty

9.990632

Transactions

Size

1.18 KB

Version

Bits

09fd9a17

Nonce

82,063

Timestamp

12/4/2013, 7:47:28 AM

Confirmations

6,515,029

Mined by

⛏️ =zaRAZ2pPuKgN7GXPJPBLxtm9bkWcE95SN2Yr7

Merkle Root

576be7eef47adf8d82fb5900ed30902121fb628232c1edc853ec1a0720dc1dd3

Transactions (1)

Coinbase576be7eef47adf…ec1a0720dc1dd3

1 in → 31 out9.9800 XPM1.09 KB

AZ2pPuKg…95SN2Yr7 Ad9pSzHt…cpJ3y2zz ARzXge7S…CEjL5oYm APFsQ3Fo…xoFKrF12 AN63YyQR…1tfe566A

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.

2.108 × 10⁹²(93-digit number)

21080088061568715990…89968645909753879039

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

2.108 × 10⁹²(93-digit number)

21080088061568715990…89968645909753879039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.108 × 10⁹²(93-digit number)

21080088061568715990…89968645909753879041

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

4.216 × 10⁹²(93-digit number)

42160176123137431980…79937291819507758079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.216 × 10⁹²(93-digit number)

42160176123137431980…79937291819507758081

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

8.432 × 10⁹²(93-digit number)

84320352246274863961…59874583639015516159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.432 × 10⁹²(93-digit number)

84320352246274863961…59874583639015516161

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

1.686 × 10⁹³(94-digit number)

16864070449254972792…19749167278031032319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.686 × 10⁹³(94-digit number)

16864070449254972792…19749167278031032321

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

3.372 × 10⁹³(94-digit number)

33728140898509945584…39498334556062064639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.372 × 10⁹³(94-digit number)

33728140898509945584…39498334556062064641

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 #293,437

Cookie Preferences