Block #464,875

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/29/2014, 2:07:40 AM · Difficulty 10.4224 · 6,345,510 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a62f00b81c61aff2f96e1f74631ec679e4b4c570fb50c3bf797b150a66e65612

View on Chainz ↗

Height

#464,875

Difficulty

10.422359

Transactions

Size

968 B

Version

Bits

0a6c1fbb

Nonce

145,398

Timestamp

3/29/2014, 2:07:40 AM

Confirmations

6,345,510

Mined by

⛏️ aS6*^AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

032d7b74edc384995f81a5b311590f3c6f44a2e1e69325268e2da43ced7d6f3b

Transactions (1)

Coinbase032d7b74edc384…2da43ced7d6f3b

1 in → 24 out9.1900 XPM879 B

AQvZBsUo…hppgRZTJ Ac5JXwCr…tf5C9dQa ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn

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.

2.316 × 10⁹²(93-digit number)

23168601330748765381…79748116170457599999

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

2.316 × 10⁹²(93-digit number)

23168601330748765381…79748116170457599999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.316 × 10⁹²(93-digit number)

23168601330748765381…79748116170457600001

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

4.633 × 10⁹²(93-digit number)

46337202661497530762…59496232340915199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.633 × 10⁹²(93-digit number)

46337202661497530762…59496232340915200001

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

9.267 × 10⁹²(93-digit number)

92674405322995061524…18992464681830399999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.267 × 10⁹²(93-digit number)

92674405322995061524…18992464681830400001

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

1.853 × 10⁹³(94-digit number)

18534881064599012304…37984929363660799999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.853 × 10⁹³(94-digit number)

18534881064599012304…37984929363660800001

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

3.706 × 10⁹³(94-digit number)

37069762129198024609…75969858727321599999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.706 × 10⁹³(94-digit number)

37069762129198024609…75969858727321600001

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 #464,875

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