Block #428,937

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/4/2014, 11:03:33 AM · Difficulty 10.3432 · 6,378,128 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d888d3bd07e745bf18b979fea2c6e38ad69c9e4410148b3b13dab471968f7955

View on Chainz ↗

Height

#428,937

Difficulty

10.343182

Transactions

Size

1.01 KB

Version

Bits

0a57dac3

Nonce

31,429

Timestamp

3/4/2014, 11:03:33 AM

Confirmations

6,378,128

Mined by

⛏️ aS>#AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

c6496691c3c482525ede23cabbb5c8af0ed377277c7940b4d5fcf79d72b3a17d

Transactions (1)

Coinbasec6496691c3c482…fcf79d72b3a17d

1 in → 26 out9.3300 XPM947 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 AMm3qeod…8PBiCMXU

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.

6.904 × 10⁹⁶(97-digit number)

69048819347699719256…11985823371849809919

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

6.904 × 10⁹⁶(97-digit number)

69048819347699719256…11985823371849809919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.904 × 10⁹⁶(97-digit number)

69048819347699719256…11985823371849809921

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

1.380 × 10⁹⁷(98-digit number)

13809763869539943851…23971646743699619839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.380 × 10⁹⁷(98-digit number)

13809763869539943851…23971646743699619841

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

2.761 × 10⁹⁷(98-digit number)

27619527739079887702…47943293487399239679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.761 × 10⁹⁷(98-digit number)

27619527739079887702…47943293487399239681

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

5.523 × 10⁹⁷(98-digit number)

55239055478159775405…95886586974798479359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.523 × 10⁹⁷(98-digit number)

55239055478159775405…95886586974798479361

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

1.104 × 10⁹⁸(99-digit number)

11047811095631955081…91773173949596958719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.104 × 10⁹⁸(99-digit number)

11047811095631955081…91773173949596958721

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 #428,937

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