Block #65,449

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 12:20:20 PM · Difficulty 8.9841 · 6,744,243 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ace6035fd94bed1437ddd5c0b24ba0cc915e61ca29e84bbad1843cb9e92e0a49

View on Chainz ↗

Height

#65,449

Difficulty

8.984147

Transactions

Size

507 B

Version

Bits

08fbf117

Nonce

542

Timestamp

7/19/2013, 12:20:20 PM

Confirmations

6,744,243

Mined by

⛏️ P2SHAVtT2Qr8jB8iLcbtQ5Xh94Ro1LeQwncwVJ

Merkle Root

4d0d298dee9e12d42a3c38956e31e650a0b470844192d9a0cbbc847f1423a840

Transactions (2)

Coinbase666d683c4b3840…d36307d1dbecc5

1 in → 1 out12.3800 XPM110 B

AVtT2Qr8…eQwncwVJ

90f4e8ea249322…f91fc2a2d8233e

2 in → 1 out12.6800 XPM306 B

AMXsNzhq…BrHbfkEE

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.

1.083 × 10⁹⁸(99-digit number)

10839190135764324545…30583071423895790599

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

1.083 × 10⁹⁸(99-digit number)

10839190135764324545…30583071423895790599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.083 × 10⁹⁸(99-digit number)

10839190135764324545…30583071423895790601

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

2.167 × 10⁹⁸(99-digit number)

21678380271528649091…61166142847791581199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.167 × 10⁹⁸(99-digit number)

21678380271528649091…61166142847791581201

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

4.335 × 10⁹⁸(99-digit number)

43356760543057298183…22332285695583162399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.335 × 10⁹⁸(99-digit number)

43356760543057298183…22332285695583162401

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

8.671 × 10⁹⁸(99-digit number)

86713521086114596366…44664571391166324799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.671 × 10⁹⁸(99-digit number)

86713521086114596366…44664571391166324801

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

1.734 × 10⁹⁹(100-digit number)

17342704217222919273…89329142782332649599

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 #65,449

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