Block #279,370

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 8:04:57 AM · Difficulty 9.9715 · 6,516,974 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8087d7ab98ff5832782355e1d5fe163df25dc89f0cab5ca7714e788e5de7fa47

View on Chainz ↗

Height

#279,370

Difficulty

9.971531

Transactions

Size

1.11 KB

Version

Bits

09f8b648

Nonce

469

Timestamp

11/28/2013, 8:04:57 AM

Confirmations

6,516,974

Mined by

⛏️ P2SHAWjBcpbTkenswTxQyBULrMwyDVxoBX2egW

Merkle Root

6f33a97a007204cb1215efba58061a308b31b1481c7e2badf5d2d2b9feb6d091

Transactions (4)

Coinbase0f2fab6b7d3ab8…d811857b037791

1 in → 1 out10.0720 XPM109 B

AWjBcpbT…xoBX2egW

840a64b62d2df3…a7becef67e01b6

2 in → 2 out140.9600 XPM373 B

AMSj35t4…12GtKPQA AQUC7Hue…LL2XMoNY

1e92f74f459788…145d8528ca3f1a

1 in → 2 out10.0500 XPM225 B

AJAhvGzJ…NWwaLTBa AYSi8YAE…WzANgkBX

0b59284a7ca4e8…d4314eadd088d1

2 in → 1 out0.7180 XPM339 B

ATSY4PGY…rRrtMJwE

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.

2.469 × 10⁹⁷(98-digit number)

24691464899414717402…72158885617769806399

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

2.469 × 10⁹⁷(98-digit number)

24691464899414717402…72158885617769806399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.469 × 10⁹⁷(98-digit number)

24691464899414717402…72158885617769806401

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

4.938 × 10⁹⁷(98-digit number)

49382929798829434805…44317771235539612799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.938 × 10⁹⁷(98-digit number)

49382929798829434805…44317771235539612801

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

9.876 × 10⁹⁷(98-digit number)

98765859597658869611…88635542471079225599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.876 × 10⁹⁷(98-digit number)

98765859597658869611…88635542471079225601

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

1.975 × 10⁹⁸(99-digit number)

19753171919531773922…77271084942158451199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.975 × 10⁹⁸(99-digit number)

19753171919531773922…77271084942158451201

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

3.950 × 10⁹⁸(99-digit number)

39506343839063547844…54542169884316902399

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