Block #242,921

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 12:16:05 AM · Difficulty 9.9608 · 6,568,000 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ee5f6fbf12910164e0601b97ab6f14efd833b8f7a7f3a12f9a7c0997d99e2f78

View on Chainz ↗

Height

#242,921

Difficulty

9.960779

Transactions

Size

1.58 KB

Version

Bits

09f5f59f

Nonce

1,155,619

Timestamp

11/4/2013, 12:16:05 AM

Confirmations

6,568,000

Mined by

⛏️ Rv|ARXSrG7zDJaFCruTxsaP6YvsvPCRW69WR4

Merkle Root

0458d50d353f2f69b0773241eb47c09b3761b51dbe92cb01a3f2809ef81d3d1c

Transactions (1)

Coinbase0458d50d353f2f…f2809ef81d3d1c

1 in → 43 out10.0400 XPM1.49 KB

ARXSrG7z…CRW69WR4 AQtzUSwq…htAuF3yC Ab7ULbjQ…fuVABZZs AZWiC56x…NwextJca Ac5sZcdP…kzV4eckG

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.

6.876 × 10⁹³(94-digit number)

68767349111240969624…12092254043170740479

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

6.876 × 10⁹³(94-digit number)

68767349111240969624…12092254043170740479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.876 × 10⁹³(94-digit number)

68767349111240969624…12092254043170740481

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

1.375 × 10⁹⁴(95-digit number)

13753469822248193924…24184508086341480959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.375 × 10⁹⁴(95-digit number)

13753469822248193924…24184508086341480961

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

2.750 × 10⁹⁴(95-digit number)

27506939644496387849…48369016172682961919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.750 × 10⁹⁴(95-digit number)

27506939644496387849…48369016172682961921

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

5.501 × 10⁹⁴(95-digit number)

55013879288992775699…96738032345365923839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.501 × 10⁹⁴(95-digit number)

55013879288992775699…96738032345365923841

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

1.100 × 10⁹⁵(96-digit number)

11002775857798555139…93476064690731847679

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #242,921

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