Block #291,648

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 7:21:45 AM · Difficulty 9.9900 · 6,551,566 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

15f1366bfab9b0bb3dc8d93faba8ae17c75ea27687b71c311e7cbd49228150bb

View on Chainz ↗

Height

#291,648

Difficulty

9.989953

Transactions

Size

1.11 KB

Version

Bits

09fd6d92

Nonce

48,326

Timestamp

12/3/2013, 7:21:45 AM

Confirmations

6,551,566

Mined by

⛏️ @saRAZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

ccb76fba186f663ce192a010d9e52b17bebf494fb809d9f2066260fc6890c8ed

Transactions (1)

Coinbaseccb76fba186f66…6260fc6890c8ed

1 in → 29 out9.9900 XPM1.02 KB

AZninDSu…FvgDMwC4 AWXYBWKP…qQAoisBJ Ac5sZcdP…kzV4eckG AUzqCwbh…i87C1Lrr ASXEwJrb…E3MLWChF

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.

6.305 × 10⁹²(93-digit number)

63058787078533853304…16841609346795027679

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

6.305 × 10⁹²(93-digit number)

63058787078533853304…16841609346795027679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.305 × 10⁹²(93-digit number)

63058787078533853304…16841609346795027681

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

1.261 × 10⁹³(94-digit number)

12611757415706770660…33683218693590055359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.261 × 10⁹³(94-digit number)

12611757415706770660…33683218693590055361

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

2.522 × 10⁹³(94-digit number)

25223514831413541321…67366437387180110719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.522 × 10⁹³(94-digit number)

25223514831413541321…67366437387180110721

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

5.044 × 10⁹³(94-digit number)

50447029662827082643…34732874774360221439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.044 × 10⁹³(94-digit number)

50447029662827082643…34732874774360221441

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

1.008 × 10⁹⁴(95-digit number)

10089405932565416528…69465749548720442879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.008 × 10⁹⁴(95-digit number)

10089405932565416528…69465749548720442881

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 #291,648

Cookie Preferences