Block #305,629

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/11/2013, 2:48:46 PM · Difficulty 9.9936 · 6,489,804 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de5f77b52e70e89a39359db6d075e2816c3c538c484af71a020da04a94e65efc

View on Chainz ↗

Height

#305,629

Difficulty

9.993634

Transactions

Size

3.02 KB

Version

Bits

09fe5ed2

Nonce

52,220

Timestamp

12/11/2013, 2:48:46 PM

Confirmations

6,489,804

Mined by

⛏️ P2SHAGAZ2wz6EeAUJiVP8kFKgTNx8T84mNH2V3

Merkle Root

5706cb87784b97bf2031b1a5ef7f9d52c476ddb69fc32ed92b3d908533b68491

Transactions (4)

Coinbase5b3da4773704b9…fb3d85dabc9e1c

1 in → 1 out10.0500 XPM109 B

AGAZ2wz6…84mNH2V3

10bde3c7dc4246…8f2171b50371d1

15 in → 2 out6.0880 XPM2.24 KB

AdygwDHr…hCUyB95K AKeSCMf5…ReWxqRmu

ee0cbae5d89f74…3574557189fd47

1 in → 2 out2.8753 XPM227 B

ATCLL4gX…bmZsCdXw AJz987nj…X2bMmzq6

0ac7bc25258edd…08485cf124b383

2 in → 2 out1.3832 XPM373 B

AWMrD5hP…ZwsoxvZ3 ASkpYeJA…j9R2PVGv

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.

7.197 × 10⁹⁶(97-digit number)

71975374143018975053…89527018225391576959

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

7.197 × 10⁹⁶(97-digit number)

71975374143018975053…89527018225391576959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.197 × 10⁹⁶(97-digit number)

71975374143018975053…89527018225391576961

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

1.439 × 10⁹⁷(98-digit number)

14395074828603795010…79054036450783153919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.439 × 10⁹⁷(98-digit number)

14395074828603795010…79054036450783153921

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

2.879 × 10⁹⁷(98-digit number)

28790149657207590021…58108072901566307839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.879 × 10⁹⁷(98-digit number)

28790149657207590021…58108072901566307841

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

5.758 × 10⁹⁷(98-digit number)

57580299314415180042…16216145803132615679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.758 × 10⁹⁷(98-digit number)

57580299314415180042…16216145803132615681

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

1.151 × 10⁹⁸(99-digit number)

11516059862883036008…32432291606265231359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.151 × 10⁹⁸(99-digit number)

11516059862883036008…32432291606265231361

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