Block #244,617

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 11:41:04 PM · Difficulty 9.9630 · 6,560,590 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a66207ab7c5405226246cfe03e13e1fcbe1c216557b2a4f811657df35dba7460

View on Chainz ↗

Height

#244,617

Difficulty

9.963022

Transactions

Size

2.08 KB

Version

Bits

09f6889d

Nonce

59,527

Timestamp

11/4/2013, 11:41:04 PM

Confirmations

6,560,590

Mined by

⛏️ Rx0ARjgNH4dwxswDeAzJBcxMUGck9BU7Drh7C

Merkle Root

04c01d600031aa0a8d4a6b27e7901312091bd8a41568008a87a61dda6e3be359

Transactions (1)

Coinbase04c01d600031aa…a61dda6e3be359

1 in → 58 out10.0300 XPM1.99 KB

ARjgNH4d…BU7Drh7C AeLaP1NX…SJ53Q2G7 AQtzUSwq…htAuF3yC ANsrD1P6…m3RxY4uj AMbCuLHZ…WSoStwkc

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.

1.920 × 10⁹⁶(97-digit number)

19205809650032568547…91003190272953123839

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

1.920 × 10⁹⁶(97-digit number)

19205809650032568547…91003190272953123839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.920 × 10⁹⁶(97-digit number)

19205809650032568547…91003190272953123841

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

3.841 × 10⁹⁶(97-digit number)

38411619300065137095…82006380545906247679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.841 × 10⁹⁶(97-digit number)

38411619300065137095…82006380545906247681

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

7.682 × 10⁹⁶(97-digit number)

76823238600130274190…64012761091812495359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.682 × 10⁹⁶(97-digit number)

76823238600130274190…64012761091812495361

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

1.536 × 10⁹⁷(98-digit number)

15364647720026054838…28025522183624990719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.536 × 10⁹⁷(98-digit number)

15364647720026054838…28025522183624990721

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

3.072 × 10⁹⁷(98-digit number)

30729295440052109676…56051044367249981439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.072 × 10⁹⁷(98-digit number)

30729295440052109676…56051044367249981441

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