Block #319,994

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/19/2013, 9:09:58 AM · Difficulty 10.1768 · 6,475,957 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6a77cbc3fe604df01cf0668b812f2972701f8485c97b7039eabaa7e1b440878e

View on Chainz ↗

Height

#319,994

Difficulty

10.176803

Transactions

Size

1.05 KB

Version

Bits

0a2d42f2

Nonce

16,792

Timestamp

12/19/2013, 9:09:58 AM

Confirmations

6,475,957

Mined by

⛏️ aR|Ad9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

d4dea20985a66c66ba810c219343677301f4a1285eace927a6c34c62dd76ef9e

Transactions (1)

Coinbased4dea20985a66c…c34c62dd76ef9e

1 in → 27 out9.6400 XPM981 B

Ad9pSzHt…cpJ3y2zz Aac9Hjdg…P4ktypc3 AZemWJAo…6jhDtieG AG5YAjec…VhA4Aeh1 AMiJebLB…rK2iN8iS

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.

1.244 × 10⁹⁹(100-digit number)

12446417596063760307…88706679252391658719

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

1.244 × 10⁹⁹(100-digit number)

12446417596063760307…88706679252391658719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.244 × 10⁹⁹(100-digit number)

12446417596063760307…88706679252391658721

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

2.489 × 10⁹⁹(100-digit number)

24892835192127520614…77413358504783317439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.489 × 10⁹⁹(100-digit number)

24892835192127520614…77413358504783317441

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

4.978 × 10⁹⁹(100-digit number)

49785670384255041229…54826717009566634879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.978 × 10⁹⁹(100-digit number)

49785670384255041229…54826717009566634881

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

9.957 × 10⁹⁹(100-digit number)

99571340768510082459…09653434019133269759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.957 × 10⁹⁹(100-digit number)

99571340768510082459…09653434019133269761

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

1.991 × 10¹⁰⁰(101-digit number)

19914268153702016491…19306868038266539519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.991 × 10¹⁰⁰(101-digit number)

19914268153702016491…19306868038266539521

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