Block #244,746

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/5/2013, 1:41:20 AM · Difficulty 9.9631 · 6,563,602 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4f4e50a90a55a8fc0f3fdbade2b29e407222e1b267b7a148f4c7618d3f42110e

View on Chainz ↗

Height

#244,746

Difficulty

9.963101

Transactions

Size

1.04 KB

Version

Bits

09f68dcf

Nonce

323,289

Timestamp

11/5/2013, 1:41:20 AM

Confirmations

6,563,602

Mined by

⛏️ RxLWALFWpHxdgP5jRvrZYxZVvW8nMMzhX7LjhL

Merkle Root

8fff0430380db87b65c16fcc89ae40aad9aaeecbc1543a2aefe74d63aecc0ebb

Transactions (1)

Coinbase8fff0430380db8…e74d63aecc0ebb

1 in → 27 out10.0600 XPM980 B

ALFWpHxd…zhX7LjhL AWCfnjpk…hb1ovL8F Acs9SHrk…QJSB8SFG AMR89gp5…oZEXFX4Z AG4tmsTw…YFrtq2r9

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.

1.334 × 10⁹⁴(95-digit number)

13342401949126145858…25914470400208591519

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

1.334 × 10⁹⁴(95-digit number)

13342401949126145858…25914470400208591519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.334 × 10⁹⁴(95-digit number)

13342401949126145858…25914470400208591521

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

2.668 × 10⁹⁴(95-digit number)

26684803898252291717…51828940800417183039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.668 × 10⁹⁴(95-digit number)

26684803898252291717…51828940800417183041

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

5.336 × 10⁹⁴(95-digit number)

53369607796504583434…03657881600834366079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.336 × 10⁹⁴(95-digit number)

53369607796504583434…03657881600834366081

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

1.067 × 10⁹⁵(96-digit number)

10673921559300916686…07315763201668732159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.067 × 10⁹⁵(96-digit number)

10673921559300916686…07315763201668732161

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

2.134 × 10⁹⁵(96-digit number)

21347843118601833373…14631526403337464319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.134 × 10⁹⁵(96-digit number)

21347843118601833373…14631526403337464321

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 #244,746

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