Block #250,893

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/8/2013, 5:43:50 PM · Difficulty 9.9692 · 6,574,232 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

535f39043b5b5c265fc4e695d1f7ae256b080fe32f6d834ec4ba40c618adc927

View on Chainz ↗

Height

#250,893

Difficulty

9.969151

Transactions

Size

2.44 KB

Version

Bits

09f81a4c

Nonce

41,933

Timestamp

11/8/2013, 5:43:50 PM

Confirmations

6,574,232

Mined by

⛏️ aR}"AdL4ZZDRpVXrdizsRm6Y8VcTzG2eQtg1T9

Merkle Root

584da4632ebd2260e459d31b0ec876b6dc0263e66422572767787ff05b2ae6e1

Transactions (2)

Coinbasef93b42c21e5d93…e3c9070e471685

1 in → 58 out10.0200 XPM1.99 KB

AdL4ZZDR…2eQtg1T9 APw6W8tk…RgVVbThY ARpndEmc…Hg792kEk AKDTDDtx…iqvw9cdY AJzWx2VD…j4ZSMit5

64a81556db816e…0cb77081170d63

2 in → 2 out26.3810 XPM375 B

AQvftpUz…fw8JQAtz AZirQKtM…FXCEcM9w

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.

1.240 × 10⁹²(93-digit number)

12404502043297042022…52842602787883241599

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

1.240 × 10⁹²(93-digit number)

12404502043297042022…52842602787883241599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.240 × 10⁹²(93-digit number)

12404502043297042022…52842602787883241601

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

2.480 × 10⁹²(93-digit number)

24809004086594084044…05685205575766483199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.480 × 10⁹²(93-digit number)

24809004086594084044…05685205575766483201

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

4.961 × 10⁹²(93-digit number)

49618008173188168088…11370411151532966399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.961 × 10⁹²(93-digit number)

49618008173188168088…11370411151532966401

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

9.923 × 10⁹²(93-digit number)

99236016346376336177…22740822303065932799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.923 × 10⁹²(93-digit number)

99236016346376336177…22740822303065932801

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

1.984 × 10⁹³(94-digit number)

19847203269275267235…45481644606131865599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.984 × 10⁹³(94-digit number)

19847203269275267235…45481644606131865601

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

Block #250,893

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