Block #287,649

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 10:05:47 AM · Difficulty 9.9869 · 6,514,804 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f5900355669e9c3a233b63751d01f4ac708dcc86a9d514b28d264baf25d5286f

View on Chainz ↗

Height

#287,649

Difficulty

9.986889

Transactions

Size

1.58 KB

Version

Bits

09fca4ca

Nonce

5,372

Timestamp

12/1/2013, 10:05:47 AM

Confirmations

6,514,804

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

513942a4a313ac51971ddd2997569b4a0fc64aecd58ac09e4190acee8d5238a5

Transactions (4)

Coinbase46effd7c948307…448901494333ae

1 in → 1 out10.0400 XPM110 B

AeKNrjNj…1NEq95Ta

82e7990fd35304…744a0f24f8688e

5 in → 2 out226.2481 XPM820 B

AP2EjXJB…e5gio4Pi AQvftpUz…fw8JQAtz

08218696066a7c…1d4457a42b293a

2 in → 2 out11.7552 XPM375 B

AXDHFc1M…uJRhNTrk Aboy8y2w…7vLqRDrD

7e1e7be4be0dfc…a75457ee34b0bc

1 in → 2 out0.2200 XPM226 B

AJHpMbht…cXiJkUMB AGvnyV3B…g1QNDZpo

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.

1.188 × 10⁹⁶(97-digit number)

11881127966712658650…74626703705619694079

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

1.188 × 10⁹⁶(97-digit number)

11881127966712658650…74626703705619694079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.188 × 10⁹⁶(97-digit number)

11881127966712658650…74626703705619694081

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

2.376 × 10⁹⁶(97-digit number)

23762255933425317301…49253407411239388159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.376 × 10⁹⁶(97-digit number)

23762255933425317301…49253407411239388161

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

4.752 × 10⁹⁶(97-digit number)

47524511866850634603…98506814822478776319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.752 × 10⁹⁶(97-digit number)

47524511866850634603…98506814822478776321

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

9.504 × 10⁹⁶(97-digit number)

95049023733701269206…97013629644957552639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.504 × 10⁹⁶(97-digit number)

95049023733701269206…97013629644957552641

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

1.900 × 10⁹⁷(98-digit number)

19009804746740253841…94027259289915105279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.900 × 10⁹⁷(98-digit number)

19009804746740253841…94027259289915105281

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