Block #3,020,442

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/22/2019, 10:42:25 AM · Difficulty 11.1632 · 3,823,147 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1227efbbfdbbf8242579ee25b5f9c7d77d40dda11171c317ec57498237a9210f

View on Chainz ↗

Height

#3,020,442

Difficulty

11.163242

Transactions

Size

1.04 KB

Version

Bits

0b29ca36

Nonce

567,673,528

Timestamp

1/22/2019, 10:42:25 AM

Confirmations

3,823,147

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

5f935016e820e6c604bfdc721627da3cfba2187e211cd258b15537ecd1e15b17

Transactions (3)

Coinbasefad724dc85e1cd…4a4a043535a7df

1 in → 1 out8.0300 XPM109 B

AUMQRepm…tAfKmdW1

1a05f80f221f14…a997f6c1115ea8

1 in → 2 out7.9900 XPM191 B

AbXwmGxD…4XXYP765 ATgjv9bW…5PDCqVRW

3db764c6160b42…3fbaae514ff5c1

4 in → 2 out1.0217 XPM670 B

AbXwmGxD…4XXYP765 AGaku26r…JYV3fSSU

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.

5.759 × 10⁹⁴(95-digit number)

57592384368843726973…01001566672058306559

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

5.759 × 10⁹⁴(95-digit number)

57592384368843726973…01001566672058306559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.759 × 10⁹⁴(95-digit number)

57592384368843726973…01001566672058306561

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

1.151 × 10⁹⁵(96-digit number)

11518476873768745394…02003133344116613119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.151 × 10⁹⁵(96-digit number)

11518476873768745394…02003133344116613121

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

2.303 × 10⁹⁵(96-digit number)

23036953747537490789…04006266688233226239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.303 × 10⁹⁵(96-digit number)

23036953747537490789…04006266688233226241

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

4.607 × 10⁹⁵(96-digit number)

46073907495074981578…08012533376466452479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.607 × 10⁹⁵(96-digit number)

46073907495074981578…08012533376466452481

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

9.214 × 10⁹⁵(96-digit number)

92147814990149963157…16025066752932904959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.214 × 10⁹⁵(96-digit number)

92147814990149963157…16025066752932904961

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

1.842 × 10⁹⁶(97-digit number)

18429562998029992631…32050133505865809919

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 #3,020,442

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