Block #253,107

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 11:09:11 PM · Difficulty 9.9718 · 6,549,571 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f589f01af394b8d7a4a798f85873bd380c2ad9c7a26e55d628892c34bf18f19b

View on Chainz ↗

Height

#253,107

Difficulty

9.971832

Transactions

Size

607 B

Version

Bits

09f8c9f3

Nonce

Timestamp

11/9/2013, 11:09:11 PM

Confirmations

6,549,571

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

69ae0ad2363d7ea9f9a86be89a7e148f59de205c09a4efb40607b08849a36231

Transactions (2)

Coinbasec32d645f856b3c…994185ce8d0ddd

1 in → 2 out10.0500 XPM142 B

AKcbk49N…GJbKa7j1 AU6kq4CL…dQBLvxLp

f2178fd145a56a…9a5f26d0e8ae49

2 in → 2 out2.0200 XPM374 B

AVARycdy…m3wpbwqV AKTcMgGK…nyDf5doz

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.

4.634 × 10⁹⁶(97-digit number)

46347199466783486950…18972353641452119039

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

4.634 × 10⁹⁶(97-digit number)

46347199466783486950…18972353641452119039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.634 × 10⁹⁶(97-digit number)

46347199466783486950…18972353641452119041

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

9.269 × 10⁹⁶(97-digit number)

92694398933566973901…37944707282904238079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.269 × 10⁹⁶(97-digit number)

92694398933566973901…37944707282904238081

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

1.853 × 10⁹⁷(98-digit number)

18538879786713394780…75889414565808476159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.853 × 10⁹⁷(98-digit number)

18538879786713394780…75889414565808476161

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

3.707 × 10⁹⁷(98-digit number)

37077759573426789560…51778829131616952319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.707 × 10⁹⁷(98-digit number)

37077759573426789560…51778829131616952321

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

7.415 × 10⁹⁷(98-digit number)

74155519146853579121…03557658263233904639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.415 × 10⁹⁷(98-digit number)

74155519146853579121…03557658263233904641

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