Block #277,819

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 5:37:17 PM · Difficulty 9.9673 · 6,522,996 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

357926a6999f067db9f59015b9dc946d77c5e9c5a71718cff8d01105806f84d8

View on Chainz ↗

Height

#277,819

Difficulty

9.967340

Transactions

Size

1.04 KB

Version

Bits

09f7a391

Nonce

366,281

Timestamp

11/27/2013, 5:37:17 PM

Confirmations

6,522,996

Mined by

⛏️ ;=aR-AVzhvfTX6hcvuz5akKkM7Fnv6uZzNJYq61

Merkle Root

70522a0ec3ee0dd6763632cc159b672377c1df5b821e97108eb7282183a12585

Transactions (1)

Coinbase70522a0ec3ee0d…b7282183a12585

1 in → 27 out10.0500 XPM981 B

AVzhvfTX…ZzNJYq61 Ac5sZcdP…kzV4eckG ANo4YY1x…vnsPRDSU AGSJPspm…3nDdg1Xr AXWzmegk…XyxPXDLy

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.

1.279 × 10⁹¹(92-digit number)

12791033293198308100…66540696270587477199

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

1.279 × 10⁹¹(92-digit number)

12791033293198308100…66540696270587477199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.279 × 10⁹¹(92-digit number)

12791033293198308100…66540696270587477201

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

2.558 × 10⁹¹(92-digit number)

25582066586396616200…33081392541174954399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.558 × 10⁹¹(92-digit number)

25582066586396616200…33081392541174954401

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

5.116 × 10⁹¹(92-digit number)

51164133172793232401…66162785082349908799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.116 × 10⁹¹(92-digit number)

51164133172793232401…66162785082349908801

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

1.023 × 10⁹²(93-digit number)

10232826634558646480…32325570164699817599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.023 × 10⁹²(93-digit number)

10232826634558646480…32325570164699817601

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

2.046 × 10⁹²(93-digit number)

20465653269117292960…64651140329399635199

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