Block #277,552

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 3:07:49 PM · Difficulty 9.9666 · 6,532,996 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6a46111aa249ead386e0a1d84c09ac91e9ee98c720140feb92996060a2dc4052

View on Chainz ↗

Height

#277,552

Difficulty

9.966558

Transactions

Size

1.17 KB

Version

Bits

09f77060

Nonce

13,931

Timestamp

11/27/2013, 3:07:49 PM

Confirmations

6,532,996

Mined by

⛏️ 0<aRAScAzqGcxPcDWPrubeWQJ2B4ezBZ6tV1vJ

Merkle Root

53df1321c98c514e9d04b4002b40c815981549478992309f8f2a4b4d6f575157

Transactions (2)

Coinbase92e39f8c240d54…22bc254b3b1ac7

1 in → 24 out10.0500 XPM879 B

AScAzqGc…BZ6tV1vJ Acs9SHrk…QJSB8SFG AWGQhzDN…RDYvugUy AYrgZtF4…6oLCC7XK AJzWx2VD…j4ZSMit5

71bdd1c2255bb4…0445b87a6258f7

1 in → 2 out120.6480 XPM226 B

ARaKUszz…E5BYtrFM AYNboo8J…49HTiCLs

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.

7.764 × 10⁹⁵(96-digit number)

77644141649108204258…63444908566732693799

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

7.764 × 10⁹⁵(96-digit number)

77644141649108204258…63444908566732693799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.764 × 10⁹⁵(96-digit number)

77644141649108204258…63444908566732693801

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

1.552 × 10⁹⁶(97-digit number)

15528828329821640851…26889817133465387599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.552 × 10⁹⁶(97-digit number)

15528828329821640851…26889817133465387601

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

3.105 × 10⁹⁶(97-digit number)

31057656659643281703…53779634266930775199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.105 × 10⁹⁶(97-digit number)

31057656659643281703…53779634266930775201

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

6.211 × 10⁹⁶(97-digit number)

62115313319286563407…07559268533861550399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.211 × 10⁹⁶(97-digit number)

62115313319286563407…07559268533861550401

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

1.242 × 10⁹⁷(98-digit number)

12423062663857312681…15118537067723100799

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 #277,552

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