Block #319,595

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/19/2013, 3:09:45 AM · Difficulty 10.1702 · 6,483,060 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a89859bb93e1245ee8f4b01c21be26fcefb631af6c19598e59df0e19de58c618

View on Chainz ↗

Height

#319,595

Difficulty

10.170224

Transactions

Size

3.60 KB

Version

Bits

0a2b93d0

Nonce

56,821

Timestamp

12/19/2013, 3:09:45 AM

Confirmations

6,483,060

Mined by

⛏️ kaRcyAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

ad8a0495646ab95eb15592d14f01f43b30630f62259194c1b0d4c07fab0dd147

Transactions (4)

Coinbase4327642115297d…61401dd0e80888

1 in → 28 out9.6300 XPM1015 B

Aac9Hjdg…P4ktypc3 AP5UvYhU…vLTDwkdA Ad9pSzHt…cpJ3y2zz AZemWJAo…6jhDtieG AdnG9gQ7…N9B7mA2p

ab1c79df8eaddd…3d3fb0905a56f0

11 in → 15 out43.9133 XPM1.96 KB

ASMW6cPd…trbBzwD7 AV5DKmQ7…saMvPYKs AJiimiQf…kMeQwnBW AGXK7b8o…SukAF8rV ALX3iX2q…1oQ8ea28

76605b95342070…8961ac7135dc10

2 in → 1 out2.0080 XPM340 B

AXozqPPN…9GDWncxG

c95aa00f2b2942…b6e343b2d7c241

1 in → 2 out24.9312 XPM227 B

AVvyhacf…VgfUiyaR AGKSadyJ…y8F48gsM

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.

3.305 × 10¹⁰⁰(101-digit number)

33053515320600939683…43114738799894508199

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

3.305 × 10¹⁰⁰(101-digit number)

33053515320600939683…43114738799894508199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.305 × 10¹⁰⁰(101-digit number)

33053515320600939683…43114738799894508201

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

6.610 × 10¹⁰⁰(101-digit number)

66107030641201879366…86229477599789016399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.610 × 10¹⁰⁰(101-digit number)

66107030641201879366…86229477599789016401

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

1.322 × 10¹⁰¹(102-digit number)

13221406128240375873…72458955199578032799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.322 × 10¹⁰¹(102-digit number)

13221406128240375873…72458955199578032801

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

2.644 × 10¹⁰¹(102-digit number)

26442812256480751746…44917910399156065599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.644 × 10¹⁰¹(102-digit number)

26442812256480751746…44917910399156065601

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

5.288 × 10¹⁰¹(102-digit number)

52885624512961503493…89835820798312131199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.288 × 10¹⁰¹(102-digit number)

52885624512961503493…89835820798312131201

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