Block #390,608

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/5/2014, 6:56:10 AM · Difficulty 10.4236 · 6,418,496 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

02438265814eac5fbb74fc4d98a72ae17ce5ae941efb10e0298232af7cc943d7

View on Chainz ↗

Height

#390,608

Difficulty

10.423645

Transactions

Size

833 B

Version

Bits

0a6c7402

Nonce

24,726

Timestamp

2/5/2014, 6:56:10 AM

Confirmations

6,418,496

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

2b7c3b7d163258df91f3c52f4064acd2984643f47751d542de7f472e4090d09a

Transactions (1)

Coinbase2b7c3b7d163258…7f472e4090d09a

1 in → 20 out9.1900 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AZV4TwxQ…8JnQqSoH

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.

8.933 × 10⁹³(94-digit number)

89332090755242172870…30234951231752417039

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

8.933 × 10⁹³(94-digit number)

89332090755242172870…30234951231752417039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.933 × 10⁹³(94-digit number)

89332090755242172870…30234951231752417041

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

1.786 × 10⁹⁴(95-digit number)

17866418151048434574…60469902463504834079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.786 × 10⁹⁴(95-digit number)

17866418151048434574…60469902463504834081

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

3.573 × 10⁹⁴(95-digit number)

35732836302096869148…20939804927009668159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.573 × 10⁹⁴(95-digit number)

35732836302096869148…20939804927009668161

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

7.146 × 10⁹⁴(95-digit number)

71465672604193738296…41879609854019336319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.146 × 10⁹⁴(95-digit number)

71465672604193738296…41879609854019336321

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

1.429 × 10⁹⁵(96-digit number)

14293134520838747659…83759219708038672639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.429 × 10⁹⁵(96-digit number)

14293134520838747659…83759219708038672641

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 #390,608

Cookie Preferences