Block #365,333

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/18/2014, 4:19:02 PM · Difficulty 10.4251 · 6,438,143 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

17b2277f72895dd5e9bd6485c90308e9711e3a601895727c2700bfd8cc962e4e

View on Chainz ↗

Height

#365,333

Difficulty

10.425053

Transactions

Size

1.08 KB

Version

Bits

0a6cd03e

Nonce

5,511

Timestamp

1/18/2014, 4:19:02 PM

Confirmations

6,438,143

Mined by

⛏️ P2SHALTcyMEk8T46qjyjfQDPksYyoStvu3gpwc

Merkle Root

cf10236a9ad04c7258910650fa326211b090ee3e7b747243f542650793685fb2

Transactions (5)

Coinbase7914448f684085…03c26dad885515

1 in → 1 out9.2300 XPM109 B

ALTcyMEk…tvu3gpwc

04988b1a30d3e9…a05215c13a29e3

1 in → 2 out4.1169 XPM226 B

APeTUiNy…wVmVnapC Af1Tf4BC…Lanmx9j7

a0f3b1eeb881b4…4fd56e78cff25c

1 in → 2 out3.9275 XPM225 B

AT9y4iDW…R5Z1Livi ASew72YL…JXqeHRQx

ddbad98874a54b…5b4b47106d4d73

1 in → 2 out2.0059 XPM225 B

AVrEkjps…Kocgb9vD AXuoQd1C…76b1hjiQ

1433663536dd1d…cde28a4aedf6ba

1 in → 2 out1.0324 XPM227 B

AP5DvyuR…Q7eyA6Yp AXxjqNLU…he4hSEm7

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.

3.500 × 10⁹⁸(99-digit number)

35002018098674102974…86283776114112670639

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

3.500 × 10⁹⁸(99-digit number)

35002018098674102974…86283776114112670639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.500 × 10⁹⁸(99-digit number)

35002018098674102974…86283776114112670641

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

7.000 × 10⁹⁸(99-digit number)

70004036197348205949…72567552228225341279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.000 × 10⁹⁸(99-digit number)

70004036197348205949…72567552228225341281

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

1.400 × 10⁹⁹(100-digit number)

14000807239469641189…45135104456450682559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.400 × 10⁹⁹(100-digit number)

14000807239469641189…45135104456450682561

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

2.800 × 10⁹⁹(100-digit number)

28001614478939282379…90270208912901365119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.800 × 10⁹⁹(100-digit number)

28001614478939282379…90270208912901365121

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

5.600 × 10⁹⁹(100-digit number)

56003228957878564759…80540417825802730239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.600 × 10⁹⁹(100-digit number)

56003228957878564759…80540417825802730241

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