Block #419,651

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/25/2014, 7:52:27 PM · Difficulty 10.3728 · 6,396,977 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c0237765235b6e475120907b6d36f0464be650c1038e66223aa977b05ec1df89

View on Chainz ↗

Height

#419,651

Difficulty

10.372810

Transactions

Size

880 B

Version

Bits

0a5f707b

Nonce

108,923

Timestamp

2/25/2014, 7:52:27 PM

Confirmations

6,396,977

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

127302ff48be44c439f03d2b57fb8a1db9ff473b5dabfee6d071cea115d95f59

Transactions (4)

Coinbase7f8c8879d36717…335984f3c31668

1 in → 1 out9.3100 XPM110 B

AeKNrjNj…1NEq95Ta

b771a74c38b543…a867d7c89bbe6a

1 in → 2 out6.1278 XPM226 B

AJurNXaN…7gYMJQFu AZ3Juh27…ry7Gn84F

042fb991e67e66…268cba8f255d1d

1 in → 2 out5.1101 XPM226 B

AW4pidNv…cvKsHDkA AUUWNjzD…LWiX6g5j

4e894fff7c58cb…c959606b5fde4f

1 in → 2 out3.0752 XPM227 B

AaVFHFSq…bCnX1Bpw AS8R7dfc…nbotzNrj

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.

7.595 × 10⁹⁵(96-digit number)

75952313873101701106…39218138472678353919

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

7.595 × 10⁹⁵(96-digit number)

75952313873101701106…39218138472678353919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.595 × 10⁹⁵(96-digit number)

75952313873101701106…39218138472678353921

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

1.519 × 10⁹⁶(97-digit number)

15190462774620340221…78436276945356707839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.519 × 10⁹⁶(97-digit number)

15190462774620340221…78436276945356707841

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

3.038 × 10⁹⁶(97-digit number)

30380925549240680442…56872553890713415679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.038 × 10⁹⁶(97-digit number)

30380925549240680442…56872553890713415681

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

6.076 × 10⁹⁶(97-digit number)

60761851098481360885…13745107781426831359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.076 × 10⁹⁶(97-digit number)

60761851098481360885…13745107781426831361

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

1.215 × 10⁹⁷(98-digit number)

12152370219696272177…27490215562853662719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.215 × 10⁹⁷(98-digit number)

12152370219696272177…27490215562853662721

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 #419,651

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