Block #260,949

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/15/2013, 1:06:12 AM · Difficulty 9.9749 · 6,549,006 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

24d30789664f92b6287a680dd3f521fd95d70c5fde88102e20c6978601df4ec2

View on Chainz ↗

Height

#260,949

Difficulty

9.974887

Transactions

Size

1.91 KB

Version

Bits

09f99232

Nonce

1,237,838

Timestamp

11/15/2013, 1:06:12 AM

Confirmations

6,549,006

Mined by

⛏️ UaRrgAXv9vYQFMoy1kdHJMsnhFe6DFzhtr3KHVQ

Merkle Root

596ee65329227ce3e35bd5db562835bc13e034d76dea1b9aa798bf270d8dddb2

Transactions (1)

Coinbase596ee65329227c…98bf270d8dddb2

1 in → 53 out10.0200 XPM1.82 KB

AXv9vYQF…htr3KHVQ AbeUZSvK…ijGzuyjz AR6Lnfrd…BmHL7S76 AQtzUSwq…htAuF3yC APZy8y6E…QZaGQjfp

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.

1.063 × 10⁹³(94-digit number)

10633098337190055844…80262216756565729279

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

1.063 × 10⁹³(94-digit number)

10633098337190055844…80262216756565729279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.063 × 10⁹³(94-digit number)

10633098337190055844…80262216756565729281

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

2.126 × 10⁹³(94-digit number)

21266196674380111689…60524433513131458559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.126 × 10⁹³(94-digit number)

21266196674380111689…60524433513131458561

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

4.253 × 10⁹³(94-digit number)

42532393348760223379…21048867026262917119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.253 × 10⁹³(94-digit number)

42532393348760223379…21048867026262917121

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

8.506 × 10⁹³(94-digit number)

85064786697520446758…42097734052525834239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.506 × 10⁹³(94-digit number)

85064786697520446758…42097734052525834241

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

1.701 × 10⁹⁴(95-digit number)

17012957339504089351…84195468105051668479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.701 × 10⁹⁴(95-digit number)

17012957339504089351…84195468105051668481

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 #260,949

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