Block #310,987

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/14/2013, 8:27:15 AM · Difficulty 9.9953 · 6,498,700 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c27a188d774f5c053985d2381282eb84f6e746bb25106be872eb9f968e81545c

View on Chainz ↗

Height

#310,987

Difficulty

9.995345

Transactions

Size

901 B

Version

Bits

09fecef4

Nonce

247,782

Timestamp

12/14/2013, 8:27:15 AM

Confirmations

6,498,700

Mined by

⛏️ aR+Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

606f85016d7591c79d282011725688362dbeb59b826206ba0f68f6a1ae70f70f

Transactions (1)

Coinbase606f85016d7591…68f6a1ae70f70f

1 in → 22 out9.9900 XPM811 B

Aac9Hjdg…P4ktypc3 AUVbYLCo…Ha3ep88n Ad9pSzHt…cpJ3y2zz APeshfYV…3PKcKMKH AG5YAjec…VhA4Aeh1

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.

4.876 × 10⁹³(94-digit number)

48768384517883134579…24264704329795085159

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

4.876 × 10⁹³(94-digit number)

48768384517883134579…24264704329795085159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.876 × 10⁹³(94-digit number)

48768384517883134579…24264704329795085161

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

9.753 × 10⁹³(94-digit number)

97536769035766269159…48529408659590170319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.753 × 10⁹³(94-digit number)

97536769035766269159…48529408659590170321

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

1.950 × 10⁹⁴(95-digit number)

19507353807153253831…97058817319180340639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.950 × 10⁹⁴(95-digit number)

19507353807153253831…97058817319180340641

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

3.901 × 10⁹⁴(95-digit number)

39014707614306507663…94117634638360681279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.901 × 10⁹⁴(95-digit number)

39014707614306507663…94117634638360681281

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

7.802 × 10⁹⁴(95-digit number)

78029415228613015327…88235269276721362559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.802 × 10⁹⁴(95-digit number)

78029415228613015327…88235269276721362561

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 #310,987

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