Block #391,403

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/5/2014, 7:00:26 PM · Difficulty 10.4318 · 6,398,431 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

12b6988bac29649fd7dd357fcfc57e3331dc957c9cf9279b55ba7bf56914cd1c

View on Chainz ↗

Height

#391,403

Difficulty

10.431767

Transactions

Size

1.08 KB

Version

Bits

0a6e8850

Nonce

130,267

Timestamp

2/5/2014, 7:00:26 PM

Confirmations

6,398,431

Merkle Root

d3a29c5fbbe4667efdb0d9087824a30c2a8b96ddde8640f81f49c854d26ab30f

Transactions (5)

Coinbase105b820488829a…490eb5ed2cf80d

1 in → 1 out9.2200 XPM109 B

AZv7gMUK…CbiASjGW

e499550377e683…fd47dd20e868b4

1 in → 2 out5.0666 XPM226 B

ASSHj3vx…dkmEpGSF AaNbdZKG…ih5PNwLu

ab1f762ae5abd7…444e490f52dccf

1 in → 2 out8.1527 XPM226 B

APbAeZoX…APPRfKtU AQQ4QXJG…5oSH58gp

e07de6acb10242…4f40f28b1e3e18

1 in → 2 out6.1770 XPM226 B

ARijjV4A…TpVV5Jq7 AJgDEz2n…ui8LcpXg

2237ef5d4df251…d1fc464aeae46f

1 in → 2 out3.9921 XPM227 B

AXxp24rY…yi3yUFBu AUy13NxD…Mg2mPuMi

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.

2.386 × 10⁹⁶(97-digit number)

23862719789933437600…44667702981028956879

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

2.386 × 10⁹⁶(97-digit number)

23862719789933437600…44667702981028956879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.386 × 10⁹⁶(97-digit number)

23862719789933437600…44667702981028956881

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

4.772 × 10⁹⁶(97-digit number)

47725439579866875201…89335405962057913759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.772 × 10⁹⁶(97-digit number)

47725439579866875201…89335405962057913761

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

9.545 × 10⁹⁶(97-digit number)

95450879159733750402…78670811924115827519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.545 × 10⁹⁶(97-digit number)

95450879159733750402…78670811924115827521

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

1.909 × 10⁹⁷(98-digit number)

19090175831946750080…57341623848231655039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.909 × 10⁹⁷(98-digit number)

19090175831946750080…57341623848231655041

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

3.818 × 10⁹⁷(98-digit number)

38180351663893500160…14683247696463310079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.818 × 10⁹⁷(98-digit number)

38180351663893500160…14683247696463310081

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