Block #3,077,810

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/4/2019, 8:24:55 AM · Difficulty 11.0047 · 3,763,855 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

67c17a187cc462aa29d4a16ce7e294a91fc70d12061c4dbd156f83bbed1821de

View on Chainz ↗

Height

#3,077,810

Difficulty

11.004716

Transactions

Size

425 B

Version

Bits

0b01350d

Nonce

938,630,663

Timestamp

3/4/2019, 8:24:55 AM

Confirmations

3,763,855

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

364ab76221cc1cd38f724a6b3fa775ffbb35ad69c9fa8498c585e128f164031e

Transactions (2)

Coinbasea4697b6297f570…1ad30f4c5b1d9a

1 in → 1 out8.2500 XPM110 B

AbXwmGxD…4XXYP765

107df7ef7f3900…8c2e647ae21f61

1 in → 2 out7.1770 XPM225 B

AbXwmGxD…4XXYP765 ALxskxzJ…mwRWwWjn

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.

4.583 × 10⁹⁴(95-digit number)

45833700471686753355…10510058982711780959

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

4.583 × 10⁹⁴(95-digit number)

45833700471686753355…10510058982711780959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.583 × 10⁹⁴(95-digit number)

45833700471686753355…10510058982711780961

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

9.166 × 10⁹⁴(95-digit number)

91667400943373506710…21020117965423561919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.166 × 10⁹⁴(95-digit number)

91667400943373506710…21020117965423561921

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

1.833 × 10⁹⁵(96-digit number)

18333480188674701342…42040235930847123839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.833 × 10⁹⁵(96-digit number)

18333480188674701342…42040235930847123841

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

3.666 × 10⁹⁵(96-digit number)

36666960377349402684…84080471861694247679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.666 × 10⁹⁵(96-digit number)

36666960377349402684…84080471861694247681

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

7.333 × 10⁹⁵(96-digit number)

73333920754698805368…68160943723388495359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.333 × 10⁹⁵(96-digit number)

73333920754698805368…68160943723388495361

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

1.466 × 10⁹⁶(97-digit number)

14666784150939761073…36321887446776990719

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 #3,077,810

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