Block #343,868

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/4/2014, 10:55:35 PM · Difficulty 10.1856 · 6,450,421 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2b47f8e81bc81e91a100ba15a6d7e7f2641b9312c50cd2f7fc9d830f610c6c9b

View on Chainz ↗

Height

#343,868

Difficulty

10.185590

Transactions

Size

1.52 KB

Version

Bits

0a2f82d2

Nonce

35,899

Timestamp

1/4/2014, 10:55:35 PM

Confirmations

6,450,421

Merkle Root

58dcf191bb231913107cd111d2c995115a6ad468165f1844eb277be9751d3dc9

Transactions (4)

Coinbase5b6554882b889c…f569cb21709a5b

1 in → 1 out9.6500 XPM110 B

AeKNrjNj…1NEq95Ta

969a30ca50727b…bd78e30d94980a

4 in → 13 out39.4400 XPM905 B

AHb9D17o…rg9iXrZC AH8z3gEd…ENu7n9sN AGcGz2WX…8vNQDX3J APJ3F9Bt…hRmbyT7p AZgxPmzd…tMfZ5f7B

00a15032c80015…e0649905ee8ea8

1 in → 2 out5.6207 XPM226 B

ANyqyMn6…P5X2eSLP ARkZjbCM…Y3umdoPx

b0c6717c838ec6…2cc9c568ffb3dd

1 in → 2 out1.3712 XPM226 B

Ac2SYqWn…xQdYtCbf AWuVSyoy…pmBAv8ZP

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.

4.307 × 10¹⁰²(103-digit number)

43070735180975062162…81069900291235985919

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

4.307 × 10¹⁰²(103-digit number)

43070735180975062162…81069900291235985919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.307 × 10¹⁰²(103-digit number)

43070735180975062162…81069900291235985921

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

8.614 × 10¹⁰²(103-digit number)

86141470361950124325…62139800582471971839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.614 × 10¹⁰²(103-digit number)

86141470361950124325…62139800582471971841

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

1.722 × 10¹⁰³(104-digit number)

17228294072390024865…24279601164943943679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.722 × 10¹⁰³(104-digit number)

17228294072390024865…24279601164943943681

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

3.445 × 10¹⁰³(104-digit number)

34456588144780049730…48559202329887887359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.445 × 10¹⁰³(104-digit number)

34456588144780049730…48559202329887887361

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

6.891 × 10¹⁰³(104-digit number)

68913176289560099460…97118404659775774719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.891 × 10¹⁰³(104-digit number)

68913176289560099460…97118404659775774721

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