Block #316,857

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/17/2013, 7:53:31 AM · Difficulty 10.1456 · 6,495,279 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9f822c533b3f8e1d619e6937ddc203ebee651d96c65681cd9e94799ddfcba27c

View on Chainz ↗

Height

#316,857

Difficulty

10.145554

Transactions

Size

1.08 KB

Version

Bits

0a25430d

Nonce

64,579

Timestamp

12/17/2013, 7:53:31 AM

Confirmations

6,495,279

Mined by

⛏️ aRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

e38e96ef2f7ee6c5379a6bfcc6dc6d9feb4f671a79ca8248e93b62d5c05e10b7

Transactions (1)

Coinbasee38e96ef2f7ee6…3b62d5c05e10b7

1 in → 28 out9.6800 XPM1015 B

Aac9Hjdg…P4ktypc3 AYJ68rmN…zHKL2WMU Ad9pSzHt…cpJ3y2zz APeshfYV…3PKcKMKH Ae58nAEb…GFUA15fv

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.

6.187 × 10¹⁰⁰(101-digit number)

61879990393703630128…49774355651275473439

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

6.187 × 10¹⁰⁰(101-digit number)

61879990393703630128…49774355651275473439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.187 × 10¹⁰⁰(101-digit number)

61879990393703630128…49774355651275473441

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

1.237 × 10¹⁰¹(102-digit number)

12375998078740726025…99548711302550946879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.237 × 10¹⁰¹(102-digit number)

12375998078740726025…99548711302550946881

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

2.475 × 10¹⁰¹(102-digit number)

24751996157481452051…99097422605101893759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.475 × 10¹⁰¹(102-digit number)

24751996157481452051…99097422605101893761

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

4.950 × 10¹⁰¹(102-digit number)

49503992314962904102…98194845210203787519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.950 × 10¹⁰¹(102-digit number)

49503992314962904102…98194845210203787521

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

9.900 × 10¹⁰¹(102-digit number)

99007984629925808204…96389690420407575039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.900 × 10¹⁰¹(102-digit number)

99007984629925808204…96389690420407575041

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 #316,857

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