Block #424,764

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/1/2014, 10:36:40 AM · Difficulty 10.3629 · 6,374,721 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

84877c15595be57545791de84934f911a08be1ba2ea0126c62fd6cac2ab6c450

View on Chainz ↗

Height

#424,764

Difficulty

10.362898

Transactions

Size

1.37 KB

Version

Bits

0a5ce6db

Nonce

100,654

Timestamp

3/1/2014, 10:36:40 AM

Confirmations

6,374,721

Mined by

⛏️ P2SHAYJKoL3F6g1erSFJZSXrV8nXGxYbF1dKov

Merkle Root

5ed22419cdffb496dfa7f155c11366746e886adf89b2ccb0483c6bf8c1936ecc

Transactions (2)

Coinbase5d6732ad94eefe…0955f656916a27

1 in → 1 out9.3200 XPM109 B

AYJKoL3F…YbF1dKov

5a67dac8808c71…5a55b017709e9f

6 in → 14 out47.2889 XPM1.18 KB

ATQEEGRr…6Hta95NV AbpVB1nR…SWfdKu93 AazfaUAJ…WaQjuUwm ASvbnyvb…4CP8B7rG AHSx1yai…YVKKVMzF

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.

1.555 × 10⁹⁴(95-digit number)

15556639719966846525…51106196713171209999

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

1.555 × 10⁹⁴(95-digit number)

15556639719966846525…51106196713171209999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.555 × 10⁹⁴(95-digit number)

15556639719966846525…51106196713171210001

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

3.111 × 10⁹⁴(95-digit number)

31113279439933693051…02212393426342419999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.111 × 10⁹⁴(95-digit number)

31113279439933693051…02212393426342420001

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

6.222 × 10⁹⁴(95-digit number)

62226558879867386103…04424786852684839999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.222 × 10⁹⁴(95-digit number)

62226558879867386103…04424786852684840001

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

1.244 × 10⁹⁵(96-digit number)

12445311775973477220…08849573705369679999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.244 × 10⁹⁵(96-digit number)

12445311775973477220…08849573705369680001

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

2.489 × 10⁹⁵(96-digit number)

24890623551946954441…17699147410739359999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.489 × 10⁹⁵(96-digit number)

24890623551946954441…17699147410739360001

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