Block #453,667

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/21/2014, 11:10:46 AM · Difficulty 10.3879 · 6,360,341 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c04a2a941f897b1102f17ceb0308be37a0ea028137ef74b43f00704a2de6e24b

View on Chainz ↗

Height

#453,667

Difficulty

10.387918

Transactions

Size

1.43 KB

Version

Bits

0a634e95

Nonce

22,257,266

Timestamp

3/21/2014, 11:10:46 AM

Confirmations

6,360,341

Mined by

⛏️ P2SHAPTRFrULR4zwuihj1Vu9SPsvy1C8P1ALfQ

Merkle Root

64f2774ed319bd862527ad1a1094dc9f5551d00739a2675f75c349ccf48ec75e

Transactions (4)

Coinbase033ba2d3937562…9da6915c25500d

1 in → 1 out9.2800 XPM109 B

APTRFrUL…C8P1ALfQ

5baf7064972b8e…195205757724d2

4 in → 2 out200.6473 XPM667 B

AXYkqSwX…u7uhAorJ APbTM1iw…Y8vsDFxX

5cd15cd3dc011c…418804b2e7231e

1 in → 2 out1.1785 XPM226 B

ASq6p3Jn…uj6sGXHm AajzSvte…V7BMBiST

ffca221af0af5c…465615a95325f2

2 in → 2 out1.1049 XPM375 B

AK5eMZv7…7wDmjJxU AKbNDN9W…mzDJbc26

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.

1.651 × 10⁹⁷(98-digit number)

16519222709537514278…85336714806594406399

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

1.651 × 10⁹⁷(98-digit number)

16519222709537514278…85336714806594406399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.651 × 10⁹⁷(98-digit number)

16519222709537514278…85336714806594406401

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

3.303 × 10⁹⁷(98-digit number)

33038445419075028557…70673429613188812799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.303 × 10⁹⁷(98-digit number)

33038445419075028557…70673429613188812801

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

6.607 × 10⁹⁷(98-digit number)

66076890838150057114…41346859226377625599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.607 × 10⁹⁷(98-digit number)

66076890838150057114…41346859226377625601

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

1.321 × 10⁹⁸(99-digit number)

13215378167630011422…82693718452755251199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.321 × 10⁹⁸(99-digit number)

13215378167630011422…82693718452755251201

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

2.643 × 10⁹⁸(99-digit number)

26430756335260022845…65387436905510502399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.643 × 10⁹⁸(99-digit number)

26430756335260022845…65387436905510502401

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 #453,667

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