Block #433,793

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/7/2014, 7:41:59 PM · Difficulty 10.3483 · 6,375,571 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

30afae6fb46083c559177327c3553610bdd7b3721c0eee6bb7e488da7c016a01

View on Chainz ↗

Height

#433,793

Difficulty

10.348273

Transactions

Size

1006 B

Version

Bits

0a592870

Nonce

6,696

Timestamp

3/7/2014, 7:41:59 PM

Confirmations

6,375,571

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

5e9c33a5e935c662d854ecb51fcca687a7527f9660e5d5e01d6519edce48ffb9

Transactions (1)

Coinbase5e9c33a5e935c6…6519edce48ffb9

1 in → 25 out9.3200 XPM913 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AGKhfQo2…h7fBXLX6

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.

4.756 × 10¹⁰⁰(101-digit number)

47566875084624389635…60918199197166766079

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

4.756 × 10¹⁰⁰(101-digit number)

47566875084624389635…60918199197166766079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.756 × 10¹⁰⁰(101-digit number)

47566875084624389635…60918199197166766081

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

9.513 × 10¹⁰⁰(101-digit number)

95133750169248779271…21836398394333532159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.513 × 10¹⁰⁰(101-digit number)

95133750169248779271…21836398394333532161

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

1.902 × 10¹⁰¹(102-digit number)

19026750033849755854…43672796788667064319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.902 × 10¹⁰¹(102-digit number)

19026750033849755854…43672796788667064321

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

3.805 × 10¹⁰¹(102-digit number)

38053500067699511708…87345593577334128639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.805 × 10¹⁰¹(102-digit number)

38053500067699511708…87345593577334128641

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

7.610 × 10¹⁰¹(102-digit number)

76107000135399023417…74691187154668257279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.610 × 10¹⁰¹(102-digit number)

76107000135399023417…74691187154668257281

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 #433,793

Cookie Preferences