Block #277,335

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 1:06:26 PM · Difficulty 9.9659 · 6,532,727 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4a6f854edcd0fa3ba488636d7e98db0c368880b6f3a501226db4010f6132b0f5

View on Chainz ↗

Height

#277,335

Difficulty

9.965908

Transactions

Size

1.18 KB

Version

Bits

09f745c2

Nonce

33,971

Timestamp

11/27/2013, 1:06:26 PM

Confirmations

6,532,727

Mined by

⛏️ W;aRZAWGQhzDNqt1A9FGXDdvgYQjDXoRDYvugUy

Merkle Root

c6826e350e30e0171a2eafb1e5edd15d4454ef7d2040d685e13a38c50de4f1a4

Transactions (1)

Coinbasec6826e350e30e0…3a38c50de4f1a4

1 in → 31 out10.0300 XPM1.09 KB

AWGQhzDN…RDYvugUy AQ7ar5wG…hBCAeEwD ARkHWBbk…NFGu7Vm7 AJwNHVNN…Gx7HjrBw AVSRHCfX…pYML2Mhc

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.

5.327 × 10⁹⁶(97-digit number)

53278222929490090233…36924083192722539209

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

5.327 × 10⁹⁶(97-digit number)

53278222929490090233…36924083192722539209

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.327 × 10⁹⁶(97-digit number)

53278222929490090233…36924083192722539211

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

1.065 × 10⁹⁷(98-digit number)

10655644585898018046…73848166385445078419

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.065 × 10⁹⁷(98-digit number)

10655644585898018046…73848166385445078421

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

2.131 × 10⁹⁷(98-digit number)

21311289171796036093…47696332770890156839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.131 × 10⁹⁷(98-digit number)

21311289171796036093…47696332770890156841

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

4.262 × 10⁹⁷(98-digit number)

42622578343592072186…95392665541780313679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.262 × 10⁹⁷(98-digit number)

42622578343592072186…95392665541780313681

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

8.524 × 10⁹⁷(98-digit number)

85245156687184144373…90785331083560627359

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 #277,335

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