Block #247,023

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/6/2013, 12:33:53 PM · Difficulty 9.9645 · 6,549,073 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a0ad64f6256bb7a5094face9b214320a9d981e0b020c4aac51c87f0fe29c80c6

View on Chainz ↗

Height

#247,023

Difficulty

9.964513

Transactions

Size

1.31 KB

Version

Bits

09f6ea4c

Nonce

5,728

Timestamp

11/6/2013, 12:33:53 PM

Confirmations

6,549,073

Mined by

⛏️ Rz71AVHALRmpAPxZDqWxYpqoeMHbdFuGQgfcS9

Merkle Root

03376397b319f8e954e6a187cf9e4a2eee6a95b3ae6df06adbe1572fa90ac34f

Transactions (1)

Coinbase03376397b319f8…e1572fa90ac34f

1 in → 35 out10.0400 XPM1.22 KB

AVHALRmp…uGQgfcS9 APVGazMT…cDCk2nwA ANuKx9Ke…wm7nrBRq AddsiWZi…H6Q5LUPW AJaGRnaj…iCHGoy6E

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.

1.500 × 10⁹⁶(97-digit number)

15008035233485548428…32863099257302646079

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

1.500 × 10⁹⁶(97-digit number)

15008035233485548428…32863099257302646079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.500 × 10⁹⁶(97-digit number)

15008035233485548428…32863099257302646081

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

3.001 × 10⁹⁶(97-digit number)

30016070466971096856…65726198514605292159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.001 × 10⁹⁶(97-digit number)

30016070466971096856…65726198514605292161

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

6.003 × 10⁹⁶(97-digit number)

60032140933942193712…31452397029210584319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.003 × 10⁹⁶(97-digit number)

60032140933942193712…31452397029210584321

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

1.200 × 10⁹⁷(98-digit number)

12006428186788438742…62904794058421168639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.200 × 10⁹⁷(98-digit number)

12006428186788438742…62904794058421168641

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

2.401 × 10⁹⁷(98-digit number)

24012856373576877484…25809588116842337279

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