Block #465,611

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/29/2014, 2:02:05 PM · Difficulty 10.4255 · 6,360,785 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

593b1b42878c4770f40818fc60d757908ef362b30b78bc556c3d08b602ebd1c6

View on Chainz ↗

Height

#465,611

Difficulty

10.425487

Transactions

Size

1.32 KB

Version

Bits

0a6cecba

Nonce

24,986

Timestamp

3/29/2014, 2:02:05 PM

Confirmations

6,360,785

Mined by

⛏️ oAGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

39f90a8231b26c4df74611779b1f31fec78e324c66f6287c46eaa5bbad7907f5

Transactions (3)

Coinbasec3ab229d6a2d03…6c5dace3d02625

1 in → 22 out9.2100 XPM811 B

AGz9gyZW…bo8NYQpw AdFLJFhb…bsaVkAyh AbHY4iza…Yckt2J5W AMW1p9oT…2TzdaZxH AcCojwbm…CbHpmxp9

645d4f7798d6ce…ed212e13a949c0

1 in → 2 out12.1900 XPM225 B

ATVq3n4S…o6jiyAwY Ae8ZExg5…tAZdwMQE

ae61a2b31eba7b…e28b465040d1d4

1 in → 2 out9.9900 XPM226 B

AUdkjRz8…JYywGfgo Ae8ZExg5…tAZdwMQE

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.

2.741 × 10⁹⁸(99-digit number)

27413362653588280300…06480704013804815359

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

2.741 × 10⁹⁸(99-digit number)

27413362653588280300…06480704013804815359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.741 × 10⁹⁸(99-digit number)

27413362653588280300…06480704013804815361

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

5.482 × 10⁹⁸(99-digit number)

54826725307176560600…12961408027609630719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.482 × 10⁹⁸(99-digit number)

54826725307176560600…12961408027609630721

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

1.096 × 10⁹⁹(100-digit number)

10965345061435312120…25922816055219261439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.096 × 10⁹⁹(100-digit number)

10965345061435312120…25922816055219261441

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

2.193 × 10⁹⁹(100-digit number)

21930690122870624240…51845632110438522879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.193 × 10⁹⁹(100-digit number)

21930690122870624240…51845632110438522881

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

4.386 × 10⁹⁹(100-digit number)

43861380245741248480…03691264220877045759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.386 × 10⁹⁹(100-digit number)

43861380245741248480…03691264220877045761

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 #465,611

Cookie Preferences