Block #277,176

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 11:35:50 AM · Difficulty 9.9654 · 6,533,928 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f668659877da69a5803c98ee837555f12a81398ce2e94401d6f75d6ac5ef3a3a

View on Chainz ↗

Height

#277,176

Difficulty

9.965442

Transactions

Size

1.39 KB

Version

Bits

09f72735

Nonce

70,606

Timestamp

11/27/2013, 11:35:50 AM

Confirmations

6,533,928

Mined by

⛏️ :aR4AaD5wr9WG1ZjzcTVAQ7xdzossNeU2RcM2H

Merkle Root

891d4accf623c42d1efc0336b30b12f810c33bf80b963d5c6105b2e47dc06d4c

Transactions (2)

Coinbase9c1a19ab396d67…2850f7b5a9614d

1 in → 9 out10.0500 XPM368 B

AaD5wr9W…eU2RcM2H AN8nUzff…YcDfRDQ2 APHngwz2…oXWG6CFr AbJY5neX…1Qu8eT6s ANkX1YyE…kHwVW1hd

8890178436ae8f…ece90108debcd0

6 in → 2 out84.3711 XPM965 B

AGZoU6gX…cUNChN7J Aao4yL6S…ftt4f7vV

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.

3.459 × 10¹⁰⁰(101-digit number)

34591179850964746425…71763553662020253199

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

3.459 × 10¹⁰⁰(101-digit number)

34591179850964746425…71763553662020253199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.459 × 10¹⁰⁰(101-digit number)

34591179850964746425…71763553662020253201

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

6.918 × 10¹⁰⁰(101-digit number)

69182359701929492851…43527107324040506399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.918 × 10¹⁰⁰(101-digit number)

69182359701929492851…43527107324040506401

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

1.383 × 10¹⁰¹(102-digit number)

13836471940385898570…87054214648081012799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.383 × 10¹⁰¹(102-digit number)

13836471940385898570…87054214648081012801

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

2.767 × 10¹⁰¹(102-digit number)

27672943880771797140…74108429296162025599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.767 × 10¹⁰¹(102-digit number)

27672943880771797140…74108429296162025601

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

5.534 × 10¹⁰¹(102-digit number)

55345887761543594281…48216858592324051199

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 #277,176

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