Block #291,532

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 5:47:16 AM · Difficulty 9.9899 · 6,517,405 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

30531492f046eb07210d321c9f9921942eb1e90f2d81d947a93ae4652f682c8b

View on Chainz ↗

Height

#291,532

Difficulty

9.989891

Transactions

Size

1.08 KB

Version

Bits

09fd6978

Nonce

205,148

Timestamp

12/3/2013, 5:47:16 AM

Confirmations

6,517,405

Mined by

⛏️ raRr_AYckRkCFgTH4MEfpDbaimvV5cSTgDe5VSp

Merkle Root

1ef9f294637c2268b763105fd1adccf38199a7c48f8b70835c166dba1d0f124d

Transactions (1)

Coinbase1ef9f294637c22…166dba1d0f124d

1 in → 28 out9.9900 XPM1015 B

AYckRkCF…TgDe5VSp AZninDSu…FvgDMwC4 AeAvCqzy…VAJ6Bwj8 AVss9H5F…zXhyMijY AYcLTeXR…bscgPops

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.

1.951 × 10⁹²(93-digit number)

19514204748367641706…69450228310288407599

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

1.951 × 10⁹²(93-digit number)

19514204748367641706…69450228310288407599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.951 × 10⁹²(93-digit number)

19514204748367641706…69450228310288407601

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

3.902 × 10⁹²(93-digit number)

39028409496735283412…38900456620576815199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.902 × 10⁹²(93-digit number)

39028409496735283412…38900456620576815201

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

7.805 × 10⁹²(93-digit number)

78056818993470566824…77800913241153630399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.805 × 10⁹²(93-digit number)

78056818993470566824…77800913241153630401

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

1.561 × 10⁹³(94-digit number)

15611363798694113364…55601826482307260799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.561 × 10⁹³(94-digit number)

15611363798694113364…55601826482307260801

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

3.122 × 10⁹³(94-digit number)

31222727597388226729…11203652964614521599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.122 × 10⁹³(94-digit number)

31222727597388226729…11203652964614521601

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 #291,532

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