Block #236,393

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 11:34:21 AM · Difficulty 9.9473 · 6,570,757 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

af58437b5bc8df38d0a247fd1933d2047cad184e640359fcf8d33502780b54a4

View on Chainz ↗

Height

#236,393

Difficulty

9.947326

Transactions

Size

1.84 KB

Version

Bits

09f283f8

Nonce

130,374

Timestamp

10/31/2013, 11:34:21 AM

Confirmations

6,570,757

Mined by

⛏️ iRr@ALdHh27brbEqnGMrZaaR18HaaAXNbqrvPf

Merkle Root

010411fb6f9196caca38e79b7be69d4dafca85974e236e445559ff362b1200ad

Transactions (1)

Coinbase010411fb6f9196…59ff362b1200ad

1 in → 51 out10.0700 XPM1.75 KB

ALdHh27b…XNbqrvPf AdnG9gQ7…N9B7mA2p ANuKx9Ke…wm7nrBRq AQtzUSwq…htAuF3yC Ac5sZcdP…kzV4eckG

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.

8.563 × 10⁹²(93-digit number)

85639383612932242198…96155790516135085599

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

8.563 × 10⁹²(93-digit number)

85639383612932242198…96155790516135085599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.563 × 10⁹²(93-digit number)

85639383612932242198…96155790516135085601

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

1.712 × 10⁹³(94-digit number)

17127876722586448439…92311581032270171199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.712 × 10⁹³(94-digit number)

17127876722586448439…92311581032270171201

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

3.425 × 10⁹³(94-digit number)

34255753445172896879…84623162064540342399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.425 × 10⁹³(94-digit number)

34255753445172896879…84623162064540342401

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

6.851 × 10⁹³(94-digit number)

68511506890345793759…69246324129080684799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.851 × 10⁹³(94-digit number)

68511506890345793759…69246324129080684801

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

1.370 × 10⁹⁴(95-digit number)

13702301378069158751…38492648258161369599

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

Block #236,393

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