Block #465,022

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/29/2014, 4:32:56 AM · Difficulty 10.4233 · 6,342,835 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f60591c8f24f6e05ba5a3d3ac8321b5e4c3133f7c3ffd20adc86161106f9f08d

View on Chainz ↗

Height

#465,022

Difficulty

10.423331

Transactions

Size

1004 B

Version

Bits

0a6c5f73

Nonce

426,874

Timestamp

3/29/2014, 4:32:56 AM

Confirmations

6,342,835

Mined by

AGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

13c9e963ca1891862202dd8fd7712d32ce6cc7f50049f82529f80fe6b1bf7748

Transactions (1)

Coinbase13c9e963ca1891…f80fe6b1bf7748

1 in → 25 out9.1900 XPM913 B

AGz9gyZW…bo8NYQpw AdFLJFhb…bsaVkAyh APtc8nU2…tp6qFHwW AUFKXvnz…342ApNcm AUDD9tmA…gJPQLnsz

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.

1.015 × 10⁹⁷(98-digit number)

10153773137310479014…33060853822417689599

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

1.015 × 10⁹⁷(98-digit number)

10153773137310479014…33060853822417689599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.015 × 10⁹⁷(98-digit number)

10153773137310479014…33060853822417689601

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

2.030 × 10⁹⁷(98-digit number)

20307546274620958028…66121707644835379199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.030 × 10⁹⁷(98-digit number)

20307546274620958028…66121707644835379201

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

4.061 × 10⁹⁷(98-digit number)

40615092549241916057…32243415289670758399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.061 × 10⁹⁷(98-digit number)

40615092549241916057…32243415289670758401

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

8.123 × 10⁹⁷(98-digit number)

81230185098483832114…64486830579341516799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.123 × 10⁹⁷(98-digit number)

81230185098483832114…64486830579341516801

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

1.624 × 10⁹⁸(99-digit number)

16246037019696766422…28973661158683033599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.624 × 10⁹⁸(99-digit number)

16246037019696766422…28973661158683033601

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 #465,022

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