Block #426,975

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2014, 1:53:50 AM · Difficulty 10.3454 · 6,368,864 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2433a26544e2fd5f6284d8434bfe0a6796ca3baca634bc449db85b4da25a3b63

View on Chainz ↗

Height

#426,975

Difficulty

10.345372

Transactions

Size

1.00 KB

Version

Bits

0a586a4b

Nonce

174,861

Timestamp

3/3/2014, 1:53:50 AM

Confirmations

6,368,864

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

13364dae863b5c20deaf059614e96296c7f5bfbd41959f914dd7e7ed4d71447e

Transactions (4)

Coinbasec430f4ec1c75a6…92193de156071e

1 in → 1 out9.3600 XPM110 B

AeKNrjNj…1NEq95Ta

5737bafdfcbdf3…8d99e5b3af42ee

1 in → 2 out5.4470 XPM226 B

Af2zhzpV…ABbCdJRJ AaHkE3Vn…8rX6MxY5

e40171f27def66…380766b3e4cabd

1 in → 2 out2.3833 XPM225 B

AJocVAH1…nStt7PAV AUAfYcmQ…B3DywuZK

136d2888485d91…d6c326678dcdbf

2 in → 2 out5.2736 XPM374 B

AFv6FpGB…HKczmteY AGe4m3Ww…izpDGUNT

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.

5.934 × 10⁹⁶(97-digit number)

59347992156530720327…29535172457619857399

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

5.934 × 10⁹⁶(97-digit number)

59347992156530720327…29535172457619857399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.934 × 10⁹⁶(97-digit number)

59347992156530720327…29535172457619857401

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

1.186 × 10⁹⁷(98-digit number)

11869598431306144065…59070344915239714799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.186 × 10⁹⁷(98-digit number)

11869598431306144065…59070344915239714801

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

2.373 × 10⁹⁷(98-digit number)

23739196862612288131…18140689830479429599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.373 × 10⁹⁷(98-digit number)

23739196862612288131…18140689830479429601

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

4.747 × 10⁹⁷(98-digit number)

47478393725224576262…36281379660958859199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.747 × 10⁹⁷(98-digit number)

47478393725224576262…36281379660958859201

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

9.495 × 10⁹⁷(98-digit number)

94956787450449152524…72562759321917718399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.495 × 10⁹⁷(98-digit number)

94956787450449152524…72562759321917718401

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