Block #300,433

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/8/2013, 2:21:45 PM · Difficulty 9.9923 · 6,492,417 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e6411f83595e6b9de36cba35ae7a7a5e0411454504b4be8cb8375b95c01341e1

View on Chainz ↗

Height

#300,433

Difficulty

9.992291

Transactions

Size

1.33 KB

Version

Bits

09fe06cc

Nonce

62,228

Timestamp

12/8/2013, 2:21:45 PM

Confirmations

6,492,417

Merkle Root

f6d5a4e7b096b106599851dc24f97902c7e9f2e065c8b5f1afb42fa34ce46488

Transactions (5)

Coinbase128c50c66e9d26…ef656771933791

1 in → 1 out10.0400 XPM110 B

AeKNrjNj…1NEq95Ta

034f588f188c96…db0a21c5b7b841

2 in → 2 out6.0351 XPM374 B

ALnvBBgM…z9pgTdbQ ASSTZeg5…sJz2brYp

ddf693db07bb65…45786d8d56b05f

2 in → 1 out11.1000 XPM340 B

AZrhGz1v…yrh9Kkvx

0c88cf05b93a95…a24ee20f1a8fca

1 in → 2 out2781.4823 XPM226 B

AHx1UBSB…C2Nd7Rtd ANsppCNx…AmdHsrL3

abff5e57430277…453a9debef2b1f

1 in → 2 out2780.4717 XPM227 B

Af4g8Zy1…4mSxAiXa AUsrH6eZ…kmkE1u6v

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.

1.333 × 10⁹⁵(96-digit number)

13331584252310690680…06649194384776007679

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

1.333 × 10⁹⁵(96-digit number)

13331584252310690680…06649194384776007679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.333 × 10⁹⁵(96-digit number)

13331584252310690680…06649194384776007681

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

2.666 × 10⁹⁵(96-digit number)

26663168504621381361…13298388769552015359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.666 × 10⁹⁵(96-digit number)

26663168504621381361…13298388769552015361

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

5.332 × 10⁹⁵(96-digit number)

53326337009242762723…26596777539104030719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.332 × 10⁹⁵(96-digit number)

53326337009242762723…26596777539104030721

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

1.066 × 10⁹⁶(97-digit number)

10665267401848552544…53193555078208061439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.066 × 10⁹⁶(97-digit number)

10665267401848552544…53193555078208061441

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

2.133 × 10⁹⁶(97-digit number)

21330534803697105089…06387110156416122879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.133 × 10⁹⁶(97-digit number)

21330534803697105089…06387110156416122881

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