Block #476,952

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/6/2014, 4:16:45 AM · Difficulty 10.4757 · 6,326,590 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3e718b03dccca0041b8f7497cc6c68373a00b602f733a9b44ad8c483228440ef

View on Chainz ↗

Height

#476,952

Difficulty

10.475659

Transactions

Size

2.01 KB

Version

Bits

0a79c4c7

Nonce

193,702

Timestamp

4/6/2014, 4:16:45 AM

Confirmations

6,326,590

Mined by

⛏️ G8{AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

da0cf444bcc818550b9fe79abd96025e33957616d8dacd7ecf34e3bfb01eeb10

Transactions (2)

Coinbase53ec0e01d1cb3e…49b955895c30a1

1 in → 24 out9.1200 XPM879 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw APtc8nU2…tp6qFHwW ASgUri65…C7NLcyBg AUFKXvnz…342ApNcm

1d15ea879c4180…3b4360cbbad607

5 in → 15 out45.8100 XPM1.06 KB

AYVBTwtR…mYqWBFRt AeKNrjNj…1NEq95Ta ATnofWiZ…EmYpDvjZ AeXJa6Wa…nc2thavR AYUpBNN7…qWKrtrsV

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.

3.497 × 10⁹⁴(95-digit number)

34974432250824360854…87491430606343566939

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

3.497 × 10⁹⁴(95-digit number)

34974432250824360854…87491430606343566939

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.497 × 10⁹⁴(95-digit number)

34974432250824360854…87491430606343566941

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

6.994 × 10⁹⁴(95-digit number)

69948864501648721708…74982861212687133879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.994 × 10⁹⁴(95-digit number)

69948864501648721708…74982861212687133881

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

1.398 × 10⁹⁵(96-digit number)

13989772900329744341…49965722425374267759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.398 × 10⁹⁵(96-digit number)

13989772900329744341…49965722425374267761

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

2.797 × 10⁹⁵(96-digit number)

27979545800659488683…99931444850748535519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.797 × 10⁹⁵(96-digit number)

27979545800659488683…99931444850748535521

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

5.595 × 10⁹⁵(96-digit number)

55959091601318977366…99862889701497071039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.595 × 10⁹⁵(96-digit number)

55959091601318977366…99862889701497071041

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