Block #315,986

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/16/2013, 7:46:17 PM · Difficulty 10.1205 · 6,474,958 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

50938503d99e4f680cc63c02084e379f03465bb6d5156a7b361a9429c77fbd56

View on Chainz ↗

Height

#315,986

Difficulty

10.120515

Transactions

Size

576 B

Version

Bits

0a1eda0a

Nonce

14,275

Timestamp

12/16/2013, 7:46:17 PM

Confirmations

6,474,958

Merkle Root

adbba9d1a3c9fcd56c2827fb72055d0d9837c8a3c753db7ba03eb68f3e19a52a

Transactions (2)

Coinbase4b2381d763250c…ac78937774e177

1 in → 1 out9.7600 XPM110 B

AeKNrjNj…1NEq95Ta

65aa3715353254…0a998bf05dd77a

2 in → 2 out47.3100 XPM373 B

AHMjJGmz…9tP7sLaW AQfF8HQm…aFKwtyPG

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.

5.406 × 10¹⁰¹(102-digit number)

54060169279278146872…39530669106897872399

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

5.406 × 10¹⁰¹(102-digit number)

54060169279278146872…39530669106897872399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.406 × 10¹⁰¹(102-digit number)

54060169279278146872…39530669106897872401

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

1.081 × 10¹⁰²(103-digit number)

10812033855855629374…79061338213795744799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.081 × 10¹⁰²(103-digit number)

10812033855855629374…79061338213795744801

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

2.162 × 10¹⁰²(103-digit number)

21624067711711258749…58122676427591489599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.162 × 10¹⁰²(103-digit number)

21624067711711258749…58122676427591489601

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

4.324 × 10¹⁰²(103-digit number)

43248135423422517498…16245352855182979199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.324 × 10¹⁰²(103-digit number)

43248135423422517498…16245352855182979201

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

8.649 × 10¹⁰²(103-digit number)

86496270846845034996…32490705710365958399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.649 × 10¹⁰²(103-digit number)

86496270846845034996…32490705710365958401

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