Block #278,853

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 3:38:14 AM · Difficulty 9.9701 · 6,531,604 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8d92fc1856e157afb4729e0800a9232f983fe12bc0113ebaf6da7a899a3ade64

View on Chainz ↗

Height

#278,853

Difficulty

9.970071

Transactions

Size

1.18 KB

Version

Bits

09f85696

Nonce

2,182

Timestamp

11/28/2013, 3:38:14 AM

Confirmations

6,531,604

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

cfa1b504375dacc3ae99e9d6b92be60c900c05849b6efcec6836744c2fb00944

Transactions (4)

Coinbase9690ae028b53f2…f30663eddfe2cb

1 in → 2 out10.0800 XPM142 B

AKcbk49N…GJbKa7j1 AKNbfPoc…jfkpwAyL

3e707786ae400a…1d71ec5d65374b

2 in → 2 out135.6102 XPM374 B

AQUC7Hue…LL2XMoNY AWBJWw3D…WNxLLvQB

5b5bb4b332bc1f…c58a84e226e27e

1 in → 2 out6.9960 XPM225 B

ANTzoe41…j9B8DPmr AeGDbpNc…VCo8sdmA

f40d9001880b89…bc49b1544f6172

2 in → 2 out2.3102 XPM375 B

AW88HN4N…Hme4cfSL AHf6yJib…dtZWd2SG

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.

1.713 × 10¹⁰³(104-digit number)

17137544407018791840…28255224888420639999

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

1.713 × 10¹⁰³(104-digit number)

17137544407018791840…28255224888420639999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.713 × 10¹⁰³(104-digit number)

17137544407018791840…28255224888420640001

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

3.427 × 10¹⁰³(104-digit number)

34275088814037583680…56510449776841279999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.427 × 10¹⁰³(104-digit number)

34275088814037583680…56510449776841280001

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

6.855 × 10¹⁰³(104-digit number)

68550177628075167360…13020899553682559999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.855 × 10¹⁰³(104-digit number)

68550177628075167360…13020899553682560001

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

1.371 × 10¹⁰⁴(105-digit number)

13710035525615033472…26041799107365119999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.371 × 10¹⁰⁴(105-digit number)

13710035525615033472…26041799107365120001

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

2.742 × 10¹⁰⁴(105-digit number)

27420071051230066944…52083598214730239999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #278,853

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