Block #3,053,397

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/15/2019, 3:58:54 AM · Difficulty 10.9961 · 3,773,011 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8a945caac0563dd6584f4e3054d81a55f7fc5262a97d3756c2eea4e72da2ce8f

View on Chainz ↗

Height

#3,053,397

Difficulty

10.996078

Transactions

Size

3.75 KB

Version

Bits

0afefefa

Nonce

1,256,251,078

Timestamp

2/15/2019, 3:58:54 AM

Confirmations

3,773,011

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

5bf526239e9d7d26969e0503b7156a4e8ebf0c17021bdfdf08c756118943734f

Transactions (2)

Coinbase3c6e058e0d221b…8b66243ff4e9fe

1 in → 1 out8.3000 XPM110 B

AUhjokok…k5m93PZR

9698960ffe5921…d8d25968f9cd29

24 in → 2 out5000.0100 XPM3.55 KB

AUWLiCGG…uTwceacQ ATbf4Kib…gW2uPDMp

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.

3.693 × 10⁹⁵(96-digit number)

36933264125805323848…96288245589356703999

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

3.693 × 10⁹⁵(96-digit number)

36933264125805323848…96288245589356703999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.693 × 10⁹⁵(96-digit number)

36933264125805323848…96288245589356704001

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

7.386 × 10⁹⁵(96-digit number)

73866528251610647697…92576491178713407999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.386 × 10⁹⁵(96-digit number)

73866528251610647697…92576491178713408001

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

1.477 × 10⁹⁶(97-digit number)

14773305650322129539…85152982357426815999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.477 × 10⁹⁶(97-digit number)

14773305650322129539…85152982357426816001

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

2.954 × 10⁹⁶(97-digit number)

29546611300644259078…70305964714853631999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.954 × 10⁹⁶(97-digit number)

29546611300644259078…70305964714853632001

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

5.909 × 10⁹⁶(97-digit number)

59093222601288518157…40611929429707263999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.909 × 10⁹⁶(97-digit number)

59093222601288518157…40611929429707264001

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

1.181 × 10⁹⁷(98-digit number)

11818644520257703631…81223858859414527999

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 #3,053,397

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