Block #428,163

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2014, 9:22:59 PM · Difficulty 10.3484 · 6,380,927 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e9cdbbc5e5bd18a4da0ac94ea1296ffb3b173b2aa7a89c46670eaee792ec84c4

View on Chainz ↗

Height

#428,163

Difficulty

10.348356

Transactions

Size

833 B

Version

Bits

0a592dd7

Nonce

33,051

Timestamp

3/3/2014, 9:22:59 PM

Confirmations

6,380,927

Mined by

⛏️ aSKAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e834f1d298a6cb3a24219501681fa7d0ff43aef12afbcfa8171a089f78ecc741

Transactions (1)

Coinbasee834f1d298a6cb…1a089f78ecc741

1 in → 20 out9.3200 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

3.911 × 10⁹⁴(95-digit number)

39113351685987136865…71512543682650711679

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

3.911 × 10⁹⁴(95-digit number)

39113351685987136865…71512543682650711679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.911 × 10⁹⁴(95-digit number)

39113351685987136865…71512543682650711681

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

7.822 × 10⁹⁴(95-digit number)

78226703371974273731…43025087365301423359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.822 × 10⁹⁴(95-digit number)

78226703371974273731…43025087365301423361

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

1.564 × 10⁹⁵(96-digit number)

15645340674394854746…86050174730602846719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.564 × 10⁹⁵(96-digit number)

15645340674394854746…86050174730602846721

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

3.129 × 10⁹⁵(96-digit number)

31290681348789709492…72100349461205693439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.129 × 10⁹⁵(96-digit number)

31290681348789709492…72100349461205693441

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

6.258 × 10⁹⁵(96-digit number)

62581362697579418985…44200698922411386879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.258 × 10⁹⁵(96-digit number)

62581362697579418985…44200698922411386881

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 #428,163

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