Block #64,242

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 6:29:06 AM · Difficulty 8.9812 · 6,725,698 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

414d8d3d79a7a31ced1574abf3f89dfdf755066b319356cc269f024b24886e03

View on Chainz ↗

Height

#64,242

Difficulty

8.981176

Transactions

Size

199 B

Version

Bits

08fb2e62

Nonce

118

Timestamp

7/19/2013, 6:29:06 AM

Confirmations

6,725,698

Merkle Root

54f040f7afca991f265c13c3b9ee75f793c4c5d36dc9123e8c8af30202771e15

Transactions (1)

Coinbase54f040f7afca99…8af30202771e15

1 in → 1 out12.3800 XPM110 B

AK1JUKWL…oPR4rN5o

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.

2.093 × 10⁹³(94-digit number)

20931608595572155913…29409174302138098279

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

2.093 × 10⁹³(94-digit number)

20931608595572155913…29409174302138098279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.093 × 10⁹³(94-digit number)

20931608595572155913…29409174302138098281

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

4.186 × 10⁹³(94-digit number)

41863217191144311827…58818348604276196559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.186 × 10⁹³(94-digit number)

41863217191144311827…58818348604276196561

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

8.372 × 10⁹³(94-digit number)

83726434382288623654…17636697208552393119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.372 × 10⁹³(94-digit number)

83726434382288623654…17636697208552393121

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

1.674 × 10⁹⁴(95-digit number)

16745286876457724730…35273394417104786239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.674 × 10⁹⁴(95-digit number)

16745286876457724730…35273394417104786241

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

3.349 × 10⁹⁴(95-digit number)

33490573752915449461…70546788834209572479

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