Block #449,092

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/18/2014, 9:22:49 AM · Difficulty 10.3671 · 6,356,574 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

358cc29c562ab8a6c9c60cc502b15f628926018d8dd86b1d0e27b22951c07372

View on Chainz ↗

Height

#449,092

Difficulty

10.367115

Transactions

Size

1.08 KB

Version

Bits

0a5dfb47

Nonce

179,599

Timestamp

3/18/2014, 9:22:49 AM

Confirmations

6,356,574

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

58055c04bbe4030875ed9fc307ca9e433c836154888f43baacabdf154ea005b6

Transactions (5)

Coinbasedf294b1558a22b…4250d5ae552e1c

1 in → 1 out9.3300 XPM116 B

AbwWkWZt…kawDhufa

ef7360b1bf3c99…3bbe40796dc25a

1 in → 2 out7.2592 XPM226 B

AZxcqZPk…vtbCNBMx AXq1kxLY…QU1dgktg

4614f7d7a92be0…a2a5c42150f0f0

1 in → 2 out3.6636 XPM225 B

ALHvf8iF…Kkqs2hBP AP24CAq5…gSiKC7Kd

8825f2b3c46d9c…f77bf828c7af14

1 in → 2 out1.4799 XPM225 B

APCza2xF…NYW1bK7F AX2a24Xa…jWVVLAJW

fd1948d095cc8f…aea1580c4f6887

1 in → 2 out6.2092 XPM226 B

AMGnU9kr…gZ9p5x4e AJ79bgac…XKCbN4WX

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.

1.663 × 10⁹⁹(100-digit number)

16638040555968694994…72933934771605831679

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

1.663 × 10⁹⁹(100-digit number)

16638040555968694994…72933934771605831679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.663 × 10⁹⁹(100-digit number)

16638040555968694994…72933934771605831681

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

3.327 × 10⁹⁹(100-digit number)

33276081111937389989…45867869543211663359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.327 × 10⁹⁹(100-digit number)

33276081111937389989…45867869543211663361

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

6.655 × 10⁹⁹(100-digit number)

66552162223874779978…91735739086423326719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.655 × 10⁹⁹(100-digit number)

66552162223874779978…91735739086423326721

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

1.331 × 10¹⁰⁰(101-digit number)

13310432444774955995…83471478172846653439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.331 × 10¹⁰⁰(101-digit number)

13310432444774955995…83471478172846653441

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

2.662 × 10¹⁰⁰(101-digit number)

26620864889549911991…66942956345693306879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.662 × 10¹⁰⁰(101-digit number)

26620864889549911991…66942956345693306881

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