Block #316,532

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/17/2013, 3:22:35 AM · Difficulty 10.1363 · 6,487,010 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7d80ea0e1e42472b7e2313bb2c9904bc238579a27eb8f810258b45526e733a4c

View on Chainz ↗

Height

#316,532

Difficulty

10.136334

Transactions

Size

971 B

Version

Bits

0a22e6c6

Nonce

182,898

Timestamp

12/17/2013, 3:22:35 AM

Confirmations

6,487,010

Mined by

⛏️ taR>AcC2zSodXYDeR5UsaoQ7rZcf2ArtWatH79

Merkle Root

b9298a18cd839b51a151a33854867c1d1a62cfa68bfeba7a06e7151b7ea5d2d5

Transactions (1)

Coinbaseb9298a18cd839b…e7151b7ea5d2d5

1 in → 24 out9.7200 XPM879 B

AcC2zSod…rtWatH79 Acskt6D1…Db4ci1L8 Aac9Hjdg…P4ktypc3 AYcLTeXR…bscgPops AZ2pPuKg…95SN2Yr7

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.

1.195 × 10¹⁰⁰(101-digit number)

11959010861708464655…97578584103282156759

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

1.195 × 10¹⁰⁰(101-digit number)

11959010861708464655…97578584103282156759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.195 × 10¹⁰⁰(101-digit number)

11959010861708464655…97578584103282156761

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

2.391 × 10¹⁰⁰(101-digit number)

23918021723416929311…95157168206564313519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.391 × 10¹⁰⁰(101-digit number)

23918021723416929311…95157168206564313521

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

4.783 × 10¹⁰⁰(101-digit number)

47836043446833858622…90314336413128627039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.783 × 10¹⁰⁰(101-digit number)

47836043446833858622…90314336413128627041

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

9.567 × 10¹⁰⁰(101-digit number)

95672086893667717244…80628672826257254079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.567 × 10¹⁰⁰(101-digit number)

95672086893667717244…80628672826257254081

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

1.913 × 10¹⁰¹(102-digit number)

19134417378733543448…61257345652514508159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.913 × 10¹⁰¹(102-digit number)

19134417378733543448…61257345652514508161

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