Block #432,791

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/7/2014, 4:05:34 AM · Difficulty 10.3388 · 6,378,060 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1053783e196ad317166a77727295d3405fba9e3440a37bb9e369e2a32ab03e22

View on Chainz ↗

Height

#432,791

Difficulty

10.338821

Transactions

Size

832 B

Version

Bits

0a56bcfd

Nonce

6,289

Timestamp

3/7/2014, 4:05:34 AM

Confirmations

6,378,060

Mined by

⛏️ aSE*AGD4yZQwygGFSCiBcSnuDhf75LhGzM2XAx

Merkle Root

e55016a416e3bef638d487effbd1984be850493325af4cdc10ad55c0608f7f7f

Transactions (1)

Coinbasee55016a416e3be…ad55c0608f7f7f

1 in → 20 out9.3400 XPM743 B

AGD4yZQw…hGzM2XAx AScAzqGc…BZ6tV1vJ AXXTKghH…gPn9JQXc AGKhfQo2…h7fBXLX6 AFutDVqJ…TJTJj6UF

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.

9.276 × 10⁹²(93-digit number)

92766695304597092952…79036616605469983799

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

9.276 × 10⁹²(93-digit number)

92766695304597092952…79036616605469983799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.276 × 10⁹²(93-digit number)

92766695304597092952…79036616605469983801

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

1.855 × 10⁹³(94-digit number)

18553339060919418590…58073233210939967599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.855 × 10⁹³(94-digit number)

18553339060919418590…58073233210939967601

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

3.710 × 10⁹³(94-digit number)

37106678121838837180…16146466421879935199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.710 × 10⁹³(94-digit number)

37106678121838837180…16146466421879935201

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

7.421 × 10⁹³(94-digit number)

74213356243677674361…32292932843759870399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.421 × 10⁹³(94-digit number)

74213356243677674361…32292932843759870401

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

1.484 × 10⁹⁴(95-digit number)

14842671248735534872…64585865687519740799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.484 × 10⁹⁴(95-digit number)

14842671248735534872…64585865687519740801

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 #432,791

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