Block #277,774

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 5:04:44 PM · Difficulty 9.9673 · 6,565,194 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8ebe599ec4631280c4369044627a9929afbb8cbba8f7bffd377b033bf37fd244

View on Chainz ↗

Height

#277,774

Difficulty

9.967259

Transactions

Size

1.33 KB

Version

Bits

09f79e4d

Nonce

1,793

Timestamp

11/27/2013, 5:04:44 PM

Confirmations

6,565,194

Mined by

⛏️ =aR&HAVss9H5FkXhhqqTXyhqhrXDK3UzXhyMijY

Merkle Root

7342d6d6af9826ec6a471a9f3fc31e7b6aea499ff1bc157cb9563148172e42f9

Transactions (2)

Coinbase8c0065424e4ae1…a012ce16b36eec

1 in → 29 out10.0300 XPM1.02 KB

AVss9H5F…zXhyMijY AWNm5iN2…RrkMw1vi AYrgZtF4…6oLCC7XK AWA5FEzr…x9RdPKTy APeshfYV…3PKcKMKH

7fd3dff2b70af6…c75556caa69b45

1 in → 2 out13029.3538 XPM226 B

ALJycUR4…9SqFPY7a AMpxNwqM…Q8UyocvD

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.

3.206 × 10⁹²(93-digit number)

32061592446538423718…60239611633272377759

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

3.206 × 10⁹²(93-digit number)

32061592446538423718…60239611633272377759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.206 × 10⁹²(93-digit number)

32061592446538423718…60239611633272377761

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

6.412 × 10⁹²(93-digit number)

64123184893076847436…20479223266544755519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.412 × 10⁹²(93-digit number)

64123184893076847436…20479223266544755521

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

1.282 × 10⁹³(94-digit number)

12824636978615369487…40958446533089511039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.282 × 10⁹³(94-digit number)

12824636978615369487…40958446533089511041

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

2.564 × 10⁹³(94-digit number)

25649273957230738974…81916893066179022079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.564 × 10⁹³(94-digit number)

25649273957230738974…81916893066179022081

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

5.129 × 10⁹³(94-digit number)

51298547914461477948…63833786132358044159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.129 × 10⁹³(94-digit number)

51298547914461477948…63833786132358044161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #277,774

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