Block #260,806

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/14/2013, 7:58:35 PM · Difficulty 9.9757 · 6,545,367 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40c43b27325dc4d11b4ca9aff6941d58dd14c6e4eb1642f998bdebdb75e2d605

View on Chainz ↗

Height

#260,806

Difficulty

9.975691

Transactions

Size

2.07 KB

Version

Bits

09f9c6e7

Nonce

507,273

Timestamp

11/14/2013, 7:58:35 PM

Confirmations

6,545,367

Mined by

⛏️ aR*ARanXFdqZu3gw2gscjananFaiq2FNquU2w

Merkle Root

6c7f157c9c9f253feb2118062b531fa2d922851252f84d0445bf69f39411581a

Transactions (1)

Coinbase6c7f157c9c9f25…bf69f39411581a

1 in → 58 out10.0000 XPM1.99 KB

ARanXFdq…2FNquU2w AJzWx2VD…j4ZSMit5 AbeUZSvK…ijGzuyjz 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.

2.277 × 10⁹³(94-digit number)

22770274297699093763…53666629393644669599

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

2.277 × 10⁹³(94-digit number)

22770274297699093763…53666629393644669599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.277 × 10⁹³(94-digit number)

22770274297699093763…53666629393644669601

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

4.554 × 10⁹³(94-digit number)

45540548595398187526…07333258787289339199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.554 × 10⁹³(94-digit number)

45540548595398187526…07333258787289339201

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

9.108 × 10⁹³(94-digit number)

91081097190796375052…14666517574578678399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.108 × 10⁹³(94-digit number)

91081097190796375052…14666517574578678401

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

1.821 × 10⁹⁴(95-digit number)

18216219438159275010…29333035149157356799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.821 × 10⁹⁴(95-digit number)

18216219438159275010…29333035149157356801

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

3.643 × 10⁹⁴(95-digit number)

36432438876318550020…58666070298314713599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.643 × 10⁹⁴(95-digit number)

36432438876318550020…58666070298314713601

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