Block #277,317

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 12:57:47 PM · Difficulty 9.9658 · 6,518,637 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e8c2e477c6c6f0cfd89227b224dfe9babf201ef9090a44e844ecae8c57c8bccc

View on Chainz ↗

Height

#277,317

Difficulty

9.965843

Transactions

Size

685 B

Version

Bits

09f74176

Nonce

3,912

Timestamp

11/27/2013, 12:57:47 PM

Confirmations

6,518,637

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

214d87aef8dd853c1e9393cb11baf6dffcfd970a871779223fa198b5835aca41

Transactions (3)

Coinbasefb82e4be4ae8d1…875142f8e51994

1 in → 2 out10.0700 XPM141 B

AKcbk49N…GJbKa7j1 ALfEGCwh…VawujfMm

21fafd97b05b16…40afbf206a02d8

1 in → 2 out17752.6597 XPM225 B

AXSFSLWS…ivo6FeWf AMWFLN8T…WnNEz2VW

0854f508a9384d…07ce22609e23ae

1 in → 2 out10.3209 XPM226 B

AcEUjB8T…7y8mLUDZ ATj8SHF1…pMft1E3C

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.

3.505 × 10¹⁰¹(102-digit number)

35052901422661835082…93188097806660596799

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

3.505 × 10¹⁰¹(102-digit number)

35052901422661835082…93188097806660596799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.505 × 10¹⁰¹(102-digit number)

35052901422661835082…93188097806660596801

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

7.010 × 10¹⁰¹(102-digit number)

70105802845323670164…86376195613321193599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.010 × 10¹⁰¹(102-digit number)

70105802845323670164…86376195613321193601

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

1.402 × 10¹⁰²(103-digit number)

14021160569064734032…72752391226642387199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.402 × 10¹⁰²(103-digit number)

14021160569064734032…72752391226642387201

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

2.804 × 10¹⁰²(103-digit number)

28042321138129468065…45504782453284774399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.804 × 10¹⁰²(103-digit number)

28042321138129468065…45504782453284774401

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

5.608 × 10¹⁰²(103-digit number)

56084642276258936131…91009564906569548799

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