Block #291,796

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 9:21:49 AM · Difficulty 9.9900 · 6,506,776 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

18bbea66816cfa8217b1160b4a7790fa30698db0677a010285accacc5bd11935

View on Chainz ↗

Height

#291,796

Difficulty

9.990014

Transactions

Size

1.37 KB

Version

Bits

09fd718d

Nonce

24,365

Timestamp

12/3/2013, 9:21:49 AM

Confirmations

6,506,776

Mined by

⛏️ saRAZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

481a480dce162a2ae794018d7047aae633f45b9bf9baadfb34d00c1ab63f3fdd

Transactions (2)

Coinbase59d44605b95b1f…de3f13dc07d95e

1 in → 30 out9.9800 XPM1.06 KB

AZninDSu…FvgDMwC4 AToTBTPr…X3DsBU1U AYcLTeXR…bscgPops AJHH6QuE…N3s6fxLC AWA5FEzr…x9RdPKTy

792b712840be68…0e2923dddbcc70

1 in → 2 out26208.6950 XPM227 B

AX7SWJvn…XwDvgS7p AcpzcMMp…ZfQE5nqD

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.

1.330 × 10⁹⁸(99-digit number)

13303073080334800788…32509727855457808639

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

1.330 × 10⁹⁸(99-digit number)

13303073080334800788…32509727855457808639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.330 × 10⁹⁸(99-digit number)

13303073080334800788…32509727855457808641

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

2.660 × 10⁹⁸(99-digit number)

26606146160669601576…65019455710915617279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.660 × 10⁹⁸(99-digit number)

26606146160669601576…65019455710915617281

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

5.321 × 10⁹⁸(99-digit number)

53212292321339203153…30038911421831234559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.321 × 10⁹⁸(99-digit number)

53212292321339203153…30038911421831234561

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

1.064 × 10⁹⁹(100-digit number)

10642458464267840630…60077822843662469119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.064 × 10⁹⁹(100-digit number)

10642458464267840630…60077822843662469121

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

2.128 × 10⁹⁹(100-digit number)

21284916928535681261…20155645687324938239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.128 × 10⁹⁹(100-digit number)

21284916928535681261…20155645687324938241

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