Block #279,322

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 7:39:15 AM · Difficulty 9.9714 · 6,524,565 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f64a9516d8ba93b0cf5b282215f895184d14e61438d1cd56651d6fb5c01834e7

View on Chainz ↗

Height

#279,322

Difficulty

9.971399

Transactions

Size

915 B

Version

Bits

09f8ad9a

Nonce

989

Timestamp

11/28/2013, 7:39:15 AM

Confirmations

6,524,565

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

b529831dc7d4cbe5e4ee120a52001e01d1aa774f647b3d4e0155d28007a7f629

Transactions (4)

Coinbaseb0a5105f663ac6…3b4eeccac5d5b3

1 in → 2 out10.0700 XPM142 B

AKcbk49N…GJbKa7j1 ASNt3cJa…L5zCqAYM

40dfbe5ca363c4…458c8a5b5dc173

1 in → 2 out9.0354 XPM226 B

AVPZM1Yv…WrZr24yP AYrTSh94…LiYQqq2k

081cdc56b1fb1b…0ae31ae05d9be8

1 in → 2 out3.5693 XPM226 B

AMRrU8B3…eXUkXEBH ATqDht7F…xHD53DYv

012ed20ddc8e98…15d40eabc30d56

1 in → 2 out6.9926 XPM227 B

APgWdEs2…H4TxEN83 AT8nCzoD…zXk6iamh

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.

5.480 × 10¹⁰⁴(105-digit number)

54804935195122014297…96644227926801532159

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

5.480 × 10¹⁰⁴(105-digit number)

54804935195122014297…96644227926801532159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.480 × 10¹⁰⁴(105-digit number)

54804935195122014297…96644227926801532161

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

1.096 × 10¹⁰⁵(106-digit number)

10960987039024402859…93288455853603064319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.096 × 10¹⁰⁵(106-digit number)

10960987039024402859…93288455853603064321

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

2.192 × 10¹⁰⁵(106-digit number)

21921974078048805718…86576911707206128639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.192 × 10¹⁰⁵(106-digit number)

21921974078048805718…86576911707206128641

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

4.384 × 10¹⁰⁵(106-digit number)

43843948156097611437…73153823414412257279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.384 × 10¹⁰⁵(106-digit number)

43843948156097611437…73153823414412257281

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

8.768 × 10¹⁰⁵(106-digit number)

87687896312195222875…46307646828824514559

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