Block #279,561

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 9:36:00 AM · Difficulty 9.9721 · 6,531,295 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

54d7d6d2316af7d2cf7c9feff037e33b6981ef82a907c53a926da92fb53a02a7

View on Chainz ↗

Height

#279,561

Difficulty

9.972100

Transactions

Size

1.65 KB

Version

Bits

09f8db87

Nonce

215,687

Timestamp

11/28/2013, 9:36:00 AM

Confirmations

6,531,295

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

813c6426cd93f84ff387085c1eb6e735f4ef8031ac8ecff2cce32429bbe3e77b

Transactions (3)

Coinbasec9113f5aa71f8a…d6a6b4a4784d41

1 in → 1 out10.0700 XPM110 B

AeKNrjNj…1NEq95Ta

63b4adad1c145e…d760f3a1aa9c1d

1 in → 2 out762.3560 XPM226 B

AWUCmNBn…iQHQv3SF ATmW4nzh…Qx8gxXh8

a5077969d8f655…9eb98055509fcc

8 in → 2 out73.8200 XPM1.24 KB

AceFNCRT…8Df4ynrJ AejPivki…saQy4kWx

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.

8.404 × 10⁹⁶(97-digit number)

84046804839436748224…29278793539552332799

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

8.404 × 10⁹⁶(97-digit number)

84046804839436748224…29278793539552332799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.404 × 10⁹⁶(97-digit number)

84046804839436748224…29278793539552332801

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

1.680 × 10⁹⁷(98-digit number)

16809360967887349644…58557587079104665599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.680 × 10⁹⁷(98-digit number)

16809360967887349644…58557587079104665601

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

3.361 × 10⁹⁷(98-digit number)

33618721935774699289…17115174158209331199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.361 × 10⁹⁷(98-digit number)

33618721935774699289…17115174158209331201

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

6.723 × 10⁹⁷(98-digit number)

67237443871549398579…34230348316418662399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.723 × 10⁹⁷(98-digit number)

67237443871549398579…34230348316418662401

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

1.344 × 10⁹⁸(99-digit number)

13447488774309879715…68460696632837324799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.344 × 10⁹⁸(99-digit number)

13447488774309879715…68460696632837324801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #279,561

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