Block #461,272

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/26/2014, 2:48:34 PM · Difficulty 10.4157 · 6,334,057 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eff4fe452831f6cd0f13c7048be11e4573eefcc675e91b906dd2687f6d0fe310

View on Chainz ↗

Height

#461,272

Difficulty

10.415708

Transactions

Size

2.54 KB

Version

Bits

0a6a6bd0

Nonce

522,534

Timestamp

3/26/2014, 2:48:34 PM

Confirmations

6,334,057

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

2842980504dd21c0d056066fc84b5b85906bb1a8a1df91a5916c3b47da49ed74

Transactions (5)

Coinbase224dbd62095f53…68e29a811bd035

1 in → 22 out9.2400 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ATp4jJhs…TbSgR8Qb APtc8nU2…tp6qFHwW AUDD9tmA…gJPQLnsz

9b98afe7c7014b…e05f5aff3fab60

2 in → 2 out17.9976 XPM376 B

AJHSiJiY…D3CFhysG AdjnVxys…cw3ByVS5

f4de902e26e3df…cd7e02f5c9ae48

1 in → 2 out9.1900 XPM226 B

ASaSgZGu…ahEKVugG ALN33pZU…GyXnBcKg

f02c43f2eb1bac…c4f4d623d5ca1d

4 in → 12 out36.8113 XPM873 B

AeKNrjNj…1NEq95Ta ASQ5px2q…GkUPqKq4 AbfD3fnh…RMZ2Hw5f AMXQrWx5…XSxNgyAS AZH3aBJB…T7FVgZ83

ed66c02358d3c9…7fe3edbb17d008

1 in → 2 out8.6799 XPM226 B

AK5eMZv7…7wDmjJxU AKvfK1bP…1NdDqSj6

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.

5.579 × 10¹⁰²(103-digit number)

55798802054142790060…05222085933286727679

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

5.579 × 10¹⁰²(103-digit number)

55798802054142790060…05222085933286727679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.579 × 10¹⁰²(103-digit number)

55798802054142790060…05222085933286727681

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

1.115 × 10¹⁰³(104-digit number)

11159760410828558012…10444171866573455359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.115 × 10¹⁰³(104-digit number)

11159760410828558012…10444171866573455361

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

2.231 × 10¹⁰³(104-digit number)

22319520821657116024…20888343733146910719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.231 × 10¹⁰³(104-digit number)

22319520821657116024…20888343733146910721

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

4.463 × 10¹⁰³(104-digit number)

44639041643314232048…41776687466293821439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.463 × 10¹⁰³(104-digit number)

44639041643314232048…41776687466293821441

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

8.927 × 10¹⁰³(104-digit number)

89278083286628464097…83553374932587642879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.927 × 10¹⁰³(104-digit number)

89278083286628464097…83553374932587642881

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