Block #64,666

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 8:33:05 AM · Difficulty 8.9823 · 6,740,401 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1b84fb6a23e0de2cdd1c7c21b4646c421919175a1aedf5025740c2fc4364831b

View on Chainz ↗

Height

#64,666

Difficulty

8.982276

Transactions

Size

514 B

Version

Bits

08fb766b

Nonce

431

Timestamp

7/19/2013, 8:33:05 AM

Confirmations

6,740,401

Mined by

⛏️ P2SHAUQRfVPMio8ApjpPWcqjJwMwPCP5Te1SVR

Merkle Root

073185b0007f7445a79831bd8e385462fb072be9915c4e601be96615460350a2

Transactions (3)

Coinbaseead6260cf8a54d…ee8e76f965a404

1 in → 1 out12.4000 XPM110 B

AUQRfVPM…P5Te1SVR

582fc06d1a47d4…5cf99eea6693f5

1 in → 1 out12.4200 XPM157 B

AFqbAUg8…usozGxmw

0ce055fa7e2869…b3a10a75f1fb8f

1 in → 1 out12.3900 XPM158 B

AT3efowp…sgm6DVMF

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.

8.786 × 10⁹¹(92-digit number)

87862852194549046004…76438416610334157359

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

8.786 × 10⁹¹(92-digit number)

87862852194549046004…76438416610334157359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.786 × 10⁹¹(92-digit number)

87862852194549046004…76438416610334157361

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

1.757 × 10⁹²(93-digit number)

17572570438909809200…52876833220668314719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.757 × 10⁹²(93-digit number)

17572570438909809200…52876833220668314721

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

3.514 × 10⁹²(93-digit number)

35145140877819618401…05753666441336629439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.514 × 10⁹²(93-digit number)

35145140877819618401…05753666441336629441

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

7.029 × 10⁹²(93-digit number)

70290281755639236803…11507332882673258879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.029 × 10⁹²(93-digit number)

70290281755639236803…11507332882673258881

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

1.405 × 10⁹³(94-digit number)

14058056351127847360…23014665765346517759

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