Block #421,829

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/27/2014, 7:53:13 AM · Difficulty 10.3756 · 6,383,860 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

370782d7747dabddc846f30351c37e0e8fd82429cb1935a66dbb15f12e707958

View on Chainz ↗

Height

#421,829

Difficulty

10.375595

Transactions

Size

1.17 KB

Version

Bits

0a602703

Nonce

50,151

Timestamp

2/27/2014, 7:53:13 AM

Confirmations

6,383,860

Mined by

⛏️ oaSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

41e4cff12be701b917fb95661a6bd83d0598fdf4fc42b24a5779bcfbca7615f4

Transactions (2)

Coinbaseabb70034796b91…d544b96d601719

1 in → 25 out9.2700 XPM913 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AGD4yZQw…hGzM2XAx AGKhfQo2…h7fBXLX6

cd5cf5b6720ce6…01fdde3a36655a

1 in → 1 out0.2900 XPM191 B

Ab2WDWkw…Qj57yySt

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.

7.555 × 10⁹³(94-digit number)

75558617976348222749…00944734279746953919

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

7.555 × 10⁹³(94-digit number)

75558617976348222749…00944734279746953919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.555 × 10⁹³(94-digit number)

75558617976348222749…00944734279746953921

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

1.511 × 10⁹⁴(95-digit number)

15111723595269644549…01889468559493907839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.511 × 10⁹⁴(95-digit number)

15111723595269644549…01889468559493907841

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

3.022 × 10⁹⁴(95-digit number)

30223447190539289099…03778937118987815679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.022 × 10⁹⁴(95-digit number)

30223447190539289099…03778937118987815681

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

6.044 × 10⁹⁴(95-digit number)

60446894381078578199…07557874237975631359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.044 × 10⁹⁴(95-digit number)

60446894381078578199…07557874237975631361

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

1.208 × 10⁹⁵(96-digit number)

12089378876215715639…15115748475951262719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.208 × 10⁹⁵(96-digit number)

12089378876215715639…15115748475951262721

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