Block #2,610,765

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/12/2018, 1:56:42 PM · Difficulty 11.2185 · 4,220,208 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

565f6d8724497c751734cfb7d8b2c3920e9ad90fae579417e6981dff3148cca8

View on Chainz ↗

Height

#2,610,765

Difficulty

11.218478

Transactions

Size

1.04 KB

Version

Bits

0b37ee2e

Nonce

1,430,962,601

Timestamp

4/12/2018, 1:56:42 PM

Confirmations

4,220,208

Mined by

⛏️ P2SHAGbSnjkXYJyKuUp7wJGAg5SgjrZgLqzHvW

Merkle Root

61fc0a0bff87386c8b49e735293718e600a80627ee04404040db0b0a43135b48

Transactions (3)

Coinbase0db12919c9d4b6…21436b6347dfb3

1 in → 1 out7.9500 XPM109 B

AGbSnjkX…ZgLqzHvW

487ea6346b058f…07de211069348f

4 in → 2 out24.6112 XPM671 B

AW5pvoHn…6Yu9oQpC AUbcfGpc…S3vN8WbG

35cace2a56a56e…e60b5354fd85f5

1 in → 1 out3.9900 XPM192 B

AZfrnjXa…iW3cj5BL

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.

1.644 × 10⁹⁵(96-digit number)

16449728184742107680…12609488560405007999

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

1.644 × 10⁹⁵(96-digit number)

16449728184742107680…12609488560405007999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.644 × 10⁹⁵(96-digit number)

16449728184742107680…12609488560405008001

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

3.289 × 10⁹⁵(96-digit number)

32899456369484215360…25218977120810015999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.289 × 10⁹⁵(96-digit number)

32899456369484215360…25218977120810016001

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

6.579 × 10⁹⁵(96-digit number)

65798912738968430720…50437954241620031999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.579 × 10⁹⁵(96-digit number)

65798912738968430720…50437954241620032001

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

1.315 × 10⁹⁶(97-digit number)

13159782547793686144…00875908483240063999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.315 × 10⁹⁶(97-digit number)

13159782547793686144…00875908483240064001

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

2.631 × 10⁹⁶(97-digit number)

26319565095587372288…01751816966480127999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.631 × 10⁹⁶(97-digit number)

26319565095587372288…01751816966480128001

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

5.263 × 10⁹⁶(97-digit number)

52639130191174744576…03503633932960255999

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 #2,610,765

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