Block #494,281

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/16/2014, 2:30:39 AM · Difficulty 10.7158 · 6,305,065 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

093213f81bf6fb1369d9023607be18d7a8f10ac5a2e0d5e1ddf738949e18375a

View on Chainz ↗

Height

#494,281

Difficulty

10.715820

Transactions

Size

398 B

Version

Bits

0ab73ff3

Nonce

39,624,085

Timestamp

4/16/2014, 2:30:39 AM

Confirmations

6,305,065

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

7abdbc122d852e482387966b7659005c748c24acc010a487e348e837e0aaa96f

Transactions (2)

Coinbaseb4908fcc692747…bc7fadd9f12e91

1 in → 1 out8.7000 XPM116 B

AbwWkWZt…kawDhufa

7c62832712666b…d65864478c29c4

1 in → 1 out10.7400 XPM191 B

AQUC7Hue…LL2XMoNY

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.

2.247 × 10⁹⁸(99-digit number)

22475811441502316958…01764511365747302399

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

2.247 × 10⁹⁸(99-digit number)

22475811441502316958…01764511365747302399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.247 × 10⁹⁸(99-digit number)

22475811441502316958…01764511365747302401

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

4.495 × 10⁹⁸(99-digit number)

44951622883004633917…03529022731494604799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.495 × 10⁹⁸(99-digit number)

44951622883004633917…03529022731494604801

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

8.990 × 10⁹⁸(99-digit number)

89903245766009267834…07058045462989209599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.990 × 10⁹⁸(99-digit number)

89903245766009267834…07058045462989209601

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

1.798 × 10⁹⁹(100-digit number)

17980649153201853566…14116090925978419199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.798 × 10⁹⁹(100-digit number)

17980649153201853566…14116090925978419201

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

3.596 × 10⁹⁹(100-digit number)

35961298306403707133…28232181851956838399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.596 × 10⁹⁹(100-digit number)

35961298306403707133…28232181851956838401

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

7.192 × 10⁹⁹(100-digit number)

71922596612807414267…56464363703913676799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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