Block #465,765

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/29/2014, 4:59:51 PM · Difficulty 10.4228 · 6,336,048 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d65650e2437ed29227cfce2d8875728ccea3f3f2acebeca6ead674adbb68c37c

View on Chainz ↗

Height

#465,765

Difficulty

10.422834

Transactions

Size

653 B

Version

Bits

0a6c3ed7

Nonce

24,041,192

Timestamp

3/29/2014, 4:59:51 PM

Confirmations

6,336,048

Mined by

⛏️ P2SHAQRURqLzRFofV9gMex9CNtKizcmA7NC3qU

Merkle Root

607beaf85102b678d509cf15606ee93abd393f7398a1c6b7c039efa7d3b59658

Transactions (3)

Coinbase2cc435efad82e5…f2512f404caf0c

1 in → 1 out9.2100 XPM109 B

AQRURqLz…mA7NC3qU

2a564f40a48cf3…4f8e2dce750720

1 in → 2 out1.4111 XPM227 B

AQNphPHf…8aE1rie4 AdW3EJYA…dSAh6TKR

7315e582d70cce…7fa819db225e6a

1 in → 2 out1.0879 XPM226 B

APCza2xF…NYW1bK7F AYw4eWHD…KC51umpS

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.

1.002 × 10⁹⁶(97-digit number)

10020762187547729493…68487730039863542399

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

1.002 × 10⁹⁶(97-digit number)

10020762187547729493…68487730039863542399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.002 × 10⁹⁶(97-digit number)

10020762187547729493…68487730039863542401

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

2.004 × 10⁹⁶(97-digit number)

20041524375095458987…36975460079727084799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.004 × 10⁹⁶(97-digit number)

20041524375095458987…36975460079727084801

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

4.008 × 10⁹⁶(97-digit number)

40083048750190917975…73950920159454169599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.008 × 10⁹⁶(97-digit number)

40083048750190917975…73950920159454169601

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

8.016 × 10⁹⁶(97-digit number)

80166097500381835951…47901840318908339199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.016 × 10⁹⁶(97-digit number)

80166097500381835951…47901840318908339201

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

1.603 × 10⁹⁷(98-digit number)

16033219500076367190…95803680637816678399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.603 × 10⁹⁷(98-digit number)

16033219500076367190…95803680637816678401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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