Block #465,378

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/29/2014, 9:59:38 AM · Difficulty 10.4266 · 6,344,416 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

07c81904a61af76beeabe6028d055a58ed48d773a0cfb6bfdbb74664cb1c4fac

View on Chainz ↗

Height

#465,378

Difficulty

10.426584

Transactions

Size

2.11 KB

Version

Bits

0a6d34a0

Nonce

152,351

Timestamp

3/29/2014, 9:59:38 AM

Confirmations

6,344,416

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

5bed82bf4e70cfd7a63a8e8cd205c7c2666f3747c753e9cd4a3cde75935181fb

Transactions (5)

Coinbase754993f3ed11e8…ae6f19b0b63563

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

34f23f523a5a02…ffcc8b20a69e7c

7 in → 10 out27.9627 XPM1.25 KB

AWusGT5L…b5tk19df ANddBzjT…uicYUSMF ALo6jyqD…xLBCAeaV AJphiNRy…qY3wyDiF ALy7Ra4p…8KLmryJG

e8f8edffdce814…4f848f9d906cb8

1 in → 2 out5.1424 XPM226 B

AHo8XDfT…9Q47nCef APCza2xF…NYW1bK7F

4d56b52e951af9…e1b18e10d59ef5

1 in → 2 out3.0967 XPM225 B

Aaffr4EL…bJQCxKCY Abe3irN2…JjM7x6cz

1d23754807ebea…3611b16eee794e

1 in → 2 out5.1458 XPM227 B

AG5A1FH9…Dchs8rRx AMaFDmxv…Ncfnt9H3

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.

2.251 × 10¹⁰¹(102-digit number)

22511130984352543427…27426373094879150079

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

2.251 × 10¹⁰¹(102-digit number)

22511130984352543427…27426373094879150079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.251 × 10¹⁰¹(102-digit number)

22511130984352543427…27426373094879150081

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

4.502 × 10¹⁰¹(102-digit number)

45022261968705086855…54852746189758300159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.502 × 10¹⁰¹(102-digit number)

45022261968705086855…54852746189758300161

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

9.004 × 10¹⁰¹(102-digit number)

90044523937410173710…09705492379516600319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.004 × 10¹⁰¹(102-digit number)

90044523937410173710…09705492379516600321

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

1.800 × 10¹⁰²(103-digit number)

18008904787482034742…19410984759033200639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.800 × 10¹⁰²(103-digit number)

18008904787482034742…19410984759033200641

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

3.601 × 10¹⁰²(103-digit number)

36017809574964069484…38821969518066401279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.601 × 10¹⁰²(103-digit number)

36017809574964069484…38821969518066401281

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

Block #465,378

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