Block #218,293

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/19/2013, 8:39:12 PM · Difficulty 9.9301 · 6,588,051 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c2866df404ec51b0b5785340bee81db742c24a74f0890c87bf6e835c3c666357

View on Chainz ↗

Height

#218,293

Difficulty

9.930105

Transactions

Size

1.58 KB

Version

Bits

09ee1b61

Nonce

159,155

Timestamp

10/19/2013, 8:39:12 PM

Confirmations

6,588,051

Mined by

⛏️ TRbAeNjg8HA2JzrdQD3LcJMTkwYEE9AkdpcSC

Merkle Root

3a07378103b4b18cb45d9379b54463b18ef5abe4acd0ed363c962adf8cc5eb07

Transactions (1)

Coinbase3a07378103b4b1…962adf8cc5eb07

1 in → 43 out10.1100 XPM1.49 KB

AeNjg8HA…9AkdpcSC AbeUZSvK…ijGzuyjz AKXeSXzu…yeuNjvhB AKFBsJ1Y…LYyU7TbU ARpndEmc…Hg792kEk

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.

9.460 × 10⁹⁵(96-digit number)

94608894463415413101…75030825804473355199

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

9.460 × 10⁹⁵(96-digit number)

94608894463415413101…75030825804473355199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.460 × 10⁹⁵(96-digit number)

94608894463415413101…75030825804473355201

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

1.892 × 10⁹⁶(97-digit number)

18921778892683082620…50061651608946710399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.892 × 10⁹⁶(97-digit number)

18921778892683082620…50061651608946710401

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

3.784 × 10⁹⁶(97-digit number)

37843557785366165240…00123303217893420799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.784 × 10⁹⁶(97-digit number)

37843557785366165240…00123303217893420801

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

7.568 × 10⁹⁶(97-digit number)

75687115570732330480…00246606435786841599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.568 × 10⁹⁶(97-digit number)

75687115570732330480…00246606435786841601

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

1.513 × 10⁹⁷(98-digit number)

15137423114146466096…00493212871573683199

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 #218,293

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