Block #277,419

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 1:47:24 PM · Difficulty 9.9662 · 6,532,265 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40aa2d63c5e7dc9bee8f12592c2f1a86359fc6b9aa2a5a3ff5df5d532e6a4e1a

View on Chainz ↗

Height

#277,419

Difficulty

9.966208

Transactions

Size

721 B

Version

Bits

09f75961

Nonce

294,121

Timestamp

11/27/2013, 1:47:24 PM

Confirmations

6,532,265

Mined by

⛏️ P2SHALUbmsaMaFj42zmZQ4tXuWoMXPEhMYDZ5H

Merkle Root

1c84d87e9354b68361a45141c4ead3a0cb2596fc5df20a5f5ac7c50067df02c5

Transactions (2)

Coinbase9c44387c19b64e…2b33443345ac98

1 in → 1 out10.0600 XPM109 B

ALUbmsaM…EhMYDZ5H

3feeba0682545c…88fc68be7d1ba4

3 in → 2 out318.0817 XPM521 B

AUWoYWf7…Lra7sH3n AXJwiTie…uQMiabMK

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.

3.640 × 10⁹⁶(97-digit number)

36400287449052431703…20253710385715559679

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

3.640 × 10⁹⁶(97-digit number)

36400287449052431703…20253710385715559679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.640 × 10⁹⁶(97-digit number)

36400287449052431703…20253710385715559681

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

7.280 × 10⁹⁶(97-digit number)

72800574898104863406…40507420771431119359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.280 × 10⁹⁶(97-digit number)

72800574898104863406…40507420771431119361

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

1.456 × 10⁹⁷(98-digit number)

14560114979620972681…81014841542862238719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.456 × 10⁹⁷(98-digit number)

14560114979620972681…81014841542862238721

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

2.912 × 10⁹⁷(98-digit number)

29120229959241945362…62029683085724477439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.912 × 10⁹⁷(98-digit number)

29120229959241945362…62029683085724477441

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

5.824 × 10⁹⁷(98-digit number)

58240459918483890724…24059366171448954879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.824 × 10⁹⁷(98-digit number)

58240459918483890724…24059366171448954881

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 #277,419

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