Block #399,081

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/11/2014, 5:23:03 AM · Difficulty 10.4187 · 6,406,719 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9c11d9330e55e307c45f2fde72f88cc1b2b4146fc0b2a7626686affdebe21134

View on Chainz ↗

Height

#399,081

Difficulty

10.418692

Transactions

Size

1.46 KB

Version

Bits

0a6b2f6c

Nonce

50,625

Timestamp

2/11/2014, 5:23:03 AM

Confirmations

6,406,719

Mined by

⛏️ aR`AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

38e9fc8679c9ba58255722772ad95aacc5509441257d191e4924d493025fe382

Transactions (2)

Coinbasea1ff032930683b…7030c98c67b3e3

1 in → 24 out9.2000 XPM879 B

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

e3969fd8d73707…379a7bf05dbe51

3 in → 2 out0.9367 XPM523 B

AN9UcTZ3…f4cCMBbQ AMRKybp4…rW7YuPPp

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.

5.196 × 10⁹⁸(99-digit number)

51960527261707754913…75200669223682332499

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

5.196 × 10⁹⁸(99-digit number)

51960527261707754913…75200669223682332499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.196 × 10⁹⁸(99-digit number)

51960527261707754913…75200669223682332501

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

1.039 × 10⁹⁹(100-digit number)

10392105452341550982…50401338447364664999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.039 × 10⁹⁹(100-digit number)

10392105452341550982…50401338447364665001

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

2.078 × 10⁹⁹(100-digit number)

20784210904683101965…00802676894729329999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.078 × 10⁹⁹(100-digit number)

20784210904683101965…00802676894729330001

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

4.156 × 10⁹⁹(100-digit number)

41568421809366203930…01605353789458659999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.156 × 10⁹⁹(100-digit number)

41568421809366203930…01605353789458660001

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

8.313 × 10⁹⁹(100-digit number)

83136843618732407861…03210707578917319999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.313 × 10⁹⁹(100-digit number)

83136843618732407861…03210707578917320001

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