Block #398,930

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/11/2014, 2:39:31 AM · Difficulty 10.4195 · 6,406,681 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0a1e4ef77f209431bb7f63ce6b1c88324e9d2784094bf08bf1db4668b16bb74c

View on Chainz ↗

Height

#398,930

Difficulty

10.419514

Transactions

Size

968 B

Version

Bits

0a6b654c

Nonce

7,092

Timestamp

2/11/2014, 2:39:31 AM

Confirmations

6,406,681

Mined by

⛏️ RaRAGKhfQo2gx6heCfNgerzn5qmLLh7fBXLX6

Merkle Root

a4ae68711f7d49b26ab3518273ff5294d458cee6373d85dd910794bfa856d49b

Transactions (1)

Coinbasea4ae68711f7d49…0794bfa856d49b

1 in → 24 out9.2000 XPM879 B

AGKhfQo2…h7fBXLX6 Aac9Hjdg…P4ktypc3 ALqxX1WA…hsKjbnXn AZV4TwxQ…8JnQqSoH Af76ewER…EzGhbQ6S

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.

2.673 × 10⁹³(94-digit number)

26733463636034977475…83920003545580799199

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

2.673 × 10⁹³(94-digit number)

26733463636034977475…83920003545580799199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.673 × 10⁹³(94-digit number)

26733463636034977475…83920003545580799201

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

5.346 × 10⁹³(94-digit number)

53466927272069954950…67840007091161598399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.346 × 10⁹³(94-digit number)

53466927272069954950…67840007091161598401

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

1.069 × 10⁹⁴(95-digit number)

10693385454413990990…35680014182323196799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.069 × 10⁹⁴(95-digit number)

10693385454413990990…35680014182323196801

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

2.138 × 10⁹⁴(95-digit number)

21386770908827981980…71360028364646393599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.138 × 10⁹⁴(95-digit number)

21386770908827981980…71360028364646393601

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

4.277 × 10⁹⁴(95-digit number)

42773541817655963960…42720056729292787199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.277 × 10⁹⁴(95-digit number)

42773541817655963960…42720056729292787201

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