Block #216,084

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 1:05:29 PM · Difficulty 9.9255 · 6,596,733 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

015e9be3c7a21981013327dff8cbabfa776303247b95387224a490cbb2074a66

View on Chainz ↗

Height

#216,084

Difficulty

9.925472

Transactions

Size

2.30 KB

Version

Bits

09ecebba

Nonce

32,693

Timestamp

10/18/2013, 1:05:29 PM

Confirmations

6,596,733

Mined by

⛏️ P2SHAJQrZiJWuMLN6yZnW94F5KnujNcuF4ugC9

Merkle Root

85e888655a272441748a4ef2f3698bdeadf2f8b5210cbcbd0afba09875a67334

Transactions (2)

Coinbasee07ff7a5457f67…839c08afa16e26

1 in → 1 out10.1700 XPM109 B

AJQrZiJW…cuF4ugC9

4db66195bcfb20…10799c831ddce8

14 in → 2 out330.0000 XPM2.10 KB

AFnJWFCi…9uTg8xNn AKp7HBuw…rpdbf1Jt

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.

5.567 × 10⁹⁶(97-digit number)

55673892990210283909…40226463367743081559

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

5.567 × 10⁹⁶(97-digit number)

55673892990210283909…40226463367743081559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.567 × 10⁹⁶(97-digit number)

55673892990210283909…40226463367743081561

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

1.113 × 10⁹⁷(98-digit number)

11134778598042056781…80452926735486163119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.113 × 10⁹⁷(98-digit number)

11134778598042056781…80452926735486163121

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

2.226 × 10⁹⁷(98-digit number)

22269557196084113563…60905853470972326239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.226 × 10⁹⁷(98-digit number)

22269557196084113563…60905853470972326241

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

4.453 × 10⁹⁷(98-digit number)

44539114392168227127…21811706941944652479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.453 × 10⁹⁷(98-digit number)

44539114392168227127…21811706941944652481

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

8.907 × 10⁹⁷(98-digit number)

89078228784336454255…43623413883889304959

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 #216,084

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