Block #363,303

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/17/2014, 8:08:09 AM · Difficulty 10.4124 · 6,447,515 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7cf584e4b9d46779a37004bc4697bf1bfbabc633a627517b3f45f0b09c9637e8

View on Chainz ↗

Height

#363,303

Difficulty

10.412376

Transactions

Size

1.30 KB

Version

Bits

0a699175

Nonce

3,745

Timestamp

1/17/2014, 8:08:09 AM

Confirmations

6,447,515

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

94d39544e80ced9c6f7a1d6dd64ce8cf9646d3bf45067db37c679d9389b99cff

Transactions (4)

Coinbasea7f85e28d854ae…ceff542a5cf3b7

1 in → 1 out9.2400 XPM116 B

AbwWkWZt…kawDhufa

37c20c2e54dce2…c0b13bac2f09ec

1 in → 2 out8.1422 XPM227 B

AJTdvrta…GmpZ7rgo AK5C6SYw…snxXW3u2

1f5889e811accf…dfbfee98bfec1e

1 in → 2 out6.0120 XPM225 B

AeiN1MQq…Rv5BvW48 ALnb9Xiy…jogyqnj9

f1ca6b0545788f…73faf8777166e6

4 in → 2 out1.0309 XPM669 B

AeW1rttf…s9QpwuSL AUxbTrVE…W8WU52ti

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.

1.685 × 10⁹⁴(95-digit number)

16853479910963076009…95559890059809360959

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

1.685 × 10⁹⁴(95-digit number)

16853479910963076009…95559890059809360959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.685 × 10⁹⁴(95-digit number)

16853479910963076009…95559890059809360961

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

3.370 × 10⁹⁴(95-digit number)

33706959821926152019…91119780119618721919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.370 × 10⁹⁴(95-digit number)

33706959821926152019…91119780119618721921

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

6.741 × 10⁹⁴(95-digit number)

67413919643852304038…82239560239237443839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.741 × 10⁹⁴(95-digit number)

67413919643852304038…82239560239237443841

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

1.348 × 10⁹⁵(96-digit number)

13482783928770460807…64479120478474887679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.348 × 10⁹⁵(96-digit number)

13482783928770460807…64479120478474887681

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

2.696 × 10⁹⁵(96-digit number)

26965567857540921615…28958240956949775359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.696 × 10⁹⁵(96-digit number)

26965567857540921615…28958240956949775361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.393 × 10⁹⁵(96-digit number)

53931135715081843231…57916481913899550719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #363,303

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