Block #319,593

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/19/2013, 3:10:39 AM · Difficulty 10.1702 · 6,494,621 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

057cd8e844d75f2e4883345ba8c1eda4b8c51df4cedde1dac74b544db32c8a5e

View on Chainz ↗

Height

#319,593

Difficulty

10.170227

Transactions

Size

1.05 KB

Version

Bits

0a2b93fb

Nonce

82,395

Timestamp

12/19/2013, 3:10:39 AM

Confirmations

6,494,621

Mined by

⛏️ iaRc9AU3PaCwFbpVpgvTtXyuzHhCqzG92DCmeEV

Merkle Root

c87a377df8cee2da8aa55f4f68268e2d2c1472ba8103df13085cfe02bffb80e7

Transactions (1)

Coinbasec87a377df8cee2…5cfe02bffb80e7

1 in → 27 out9.6500 XPM981 B

AU3PaCwF…92DCmeEV AcABUaNj…WXyu2did Aac9Hjdg…P4ktypc3 AZemWJAo…6jhDtieG AYcLTeXR…bscgPops

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.

1.371 × 10⁹⁹(100-digit number)

13713996178287063472…46940814126933637119

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

1.371 × 10⁹⁹(100-digit number)

13713996178287063472…46940814126933637119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.371 × 10⁹⁹(100-digit number)

13713996178287063472…46940814126933637121

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

2.742 × 10⁹⁹(100-digit number)

27427992356574126945…93881628253867274239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.742 × 10⁹⁹(100-digit number)

27427992356574126945…93881628253867274241

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

5.485 × 10⁹⁹(100-digit number)

54855984713148253890…87763256507734548479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.485 × 10⁹⁹(100-digit number)

54855984713148253890…87763256507734548481

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

1.097 × 10¹⁰⁰(101-digit number)

10971196942629650778…75526513015469096959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.097 × 10¹⁰⁰(101-digit number)

10971196942629650778…75526513015469096961

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

2.194 × 10¹⁰⁰(101-digit number)

21942393885259301556…51053026030938193919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.194 × 10¹⁰⁰(101-digit number)

21942393885259301556…51053026030938193921

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 #319,593

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