Block #305,043

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/11/2013, 6:36:58 AM · Difficulty 9.9935 · 6,498,879 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cdc9ae7d576b4a3aba0c8a62c0e031570b04df0d4bdb9281b740be2973f1e3d5

View on Chainz ↗

Height

#305,043

Difficulty

9.993497

Transactions

Size

1.63 KB

Version

Bits

09fe55d8

Nonce

29,010

Timestamp

12/11/2013, 6:36:58 AM

Confirmations

6,498,879

Mined by

⛏️ P2SHAGmThQGEqAssVZWB9aZtKwNsAasuJM8bK3

Merkle Root

bb8c825e05433d62c5b65b365a94a99afa6d5f2f63e51f9d02ed9fa0747920ae

Transactions (3)

Coinbasea53ac571c001e0…cf9fbaba5b343e

1 in → 1 out10.0300 XPM109 B

AGmThQGE…suJM8bK3

29f3ae2eb4b728…e73bbb807f2afd

7 in → 2 out21.5900 XPM1.09 KB

AJ71k9rR…b6CHEJas AXYvT4Ut…PaRqbcY2

082c517c766e85…3aeab008b93686

1 in → 6 out17.2216 XPM362 B

AVg5YGji…Aq7MMxRC AHjWEVmK…cugYsuN3 AHbGXzeD…A3SKohbN AVHcc9zb…JkngbvXL ALkuQqhf…MysHQcED

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.

1.544 × 10⁹⁵(96-digit number)

15443763199745515615…41225416858862899199

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

1.544 × 10⁹⁵(96-digit number)

15443763199745515615…41225416858862899199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.544 × 10⁹⁵(96-digit number)

15443763199745515615…41225416858862899201

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

3.088 × 10⁹⁵(96-digit number)

30887526399491031231…82450833717725798399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.088 × 10⁹⁵(96-digit number)

30887526399491031231…82450833717725798401

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

6.177 × 10⁹⁵(96-digit number)

61775052798982062462…64901667435451596799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.177 × 10⁹⁵(96-digit number)

61775052798982062462…64901667435451596801

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

1.235 × 10⁹⁶(97-digit number)

12355010559796412492…29803334870903193599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.235 × 10⁹⁶(97-digit number)

12355010559796412492…29803334870903193601

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

2.471 × 10⁹⁶(97-digit number)

24710021119592824985…59606669741806387199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.471 × 10⁹⁶(97-digit number)

24710021119592824985…59606669741806387201

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