Block #293,962

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/4/2013, 2:53:40 PM · Difficulty 9.9908 · 6,532,243 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4016f13687880dd62f335b12432587c4e28fc565d22fa95464a0a59a3011f17d

View on Chainz ↗

Height

#293,962

Difficulty

9.990832

Transactions

Size

1.18 KB

Version

Bits

09fda723

Nonce

63,396

Timestamp

12/4/2013, 2:53:40 PM

Confirmations

6,532,243

Mined by

⛏️ J|aRAdAX2VaXupcbcUkrTifD2PFDzF51gXWCNRYT

Merkle Root

18897ffc560c0d29df35da72ac100fa6f09a17858a065632597990f6749e2d64

Transactions (1)

Coinbase18897ffc560c0d…7990f6749e2d64

1 in → 31 out9.9800 XPM1.09 KB

AX2VaXup…gXWCNRYT Ae58nAEb…GFUA15fv AdyKWr2A…7PSnFqeJ ASD5y7K3…PadKp2tW AJzWx2VD…j4ZSMit5

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.

2.569 × 10⁹²(93-digit number)

25695347369331917675…45394445395986509479

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

2.569 × 10⁹²(93-digit number)

25695347369331917675…45394445395986509479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.569 × 10⁹²(93-digit number)

25695347369331917675…45394445395986509481

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

5.139 × 10⁹²(93-digit number)

51390694738663835350…90788890791973018959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.139 × 10⁹²(93-digit number)

51390694738663835350…90788890791973018961

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

1.027 × 10⁹³(94-digit number)

10278138947732767070…81577781583946037919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.027 × 10⁹³(94-digit number)

10278138947732767070…81577781583946037921

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

2.055 × 10⁹³(94-digit number)

20556277895465534140…63155563167892075839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.055 × 10⁹³(94-digit number)

20556277895465534140…63155563167892075841

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

4.111 × 10⁹³(94-digit number)

41112555790931068280…26311126335784151679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.111 × 10⁹³(94-digit number)

41112555790931068280…26311126335784151681

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 #293,962

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