Block #389,019

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2014, 5:55:22 AM · Difficulty 10.4131 · 6,416,074 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a754d2e668bd94e979f6505032b040515951ab3a0025e96bef62ac7611eb637e

View on Chainz ↗

Height

#389,019

Difficulty

10.413112

Transactions

Size

798 B

Version

Bits

0a69c1ba

Nonce

12,278

Timestamp

2/4/2014, 5:55:22 AM

Confirmations

6,416,074

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

d7af08a8797290ff945c6d4570d3d8a484602c2e64d578366db6c843bf8717c7

Transactions (1)

Coinbased7af08a8797290…b6c843bf8717c7

1 in → 19 out9.2100 XPM709 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AGKhfQo2…h7fBXLX6 AJzWx2VD…j4ZSMit5

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.

5.275 × 10⁹²(93-digit number)

52756688825751221829…80300757143881452959

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

5.275 × 10⁹²(93-digit number)

52756688825751221829…80300757143881452959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.275 × 10⁹²(93-digit number)

52756688825751221829…80300757143881452961

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

1.055 × 10⁹³(94-digit number)

10551337765150244365…60601514287762905919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.055 × 10⁹³(94-digit number)

10551337765150244365…60601514287762905921

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

2.110 × 10⁹³(94-digit number)

21102675530300488731…21203028575525811839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.110 × 10⁹³(94-digit number)

21102675530300488731…21203028575525811841

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

4.220 × 10⁹³(94-digit number)

42205351060600977463…42406057151051623679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.220 × 10⁹³(94-digit number)

42205351060600977463…42406057151051623681

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

8.441 × 10⁹³(94-digit number)

84410702121201954926…84812114302103247359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.441 × 10⁹³(94-digit number)

84410702121201954926…84812114302103247361

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