Block #240,242

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/2/2013, 1:03:23 PM · Difficulty 9.9560 · 6,577,567 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

476d96dc78259fa54e71e148117b5f271acebea7a1e20bbb35023dec4e90c75b

View on Chainz ↗

Height

#240,242

Difficulty

9.955960

Transactions

Size

1.81 KB

Version

Bits

09f4b9cc

Nonce

21,783

Timestamp

11/2/2013, 1:03:23 PM

Confirmations

6,577,567

Mined by

⛏️ rRtALdHh27brbEqnGMrZaaR18HaaAXNbqrvPf

Merkle Root

c688270e90ad226ab259a870824cb42636cb4ad06f1c8d73563986c27d1cee70

Transactions (1)

Coinbasec688270e90ad22…3986c27d1cee70

1 in → 50 out10.0500 XPM1.72 KB

ALdHh27b…XNbqrvPf AHkgKuuD…TkWqWiw1 ATKK7iFz…wZm46KN1 ANuKx9Ke…wm7nrBRq AWCfnjpk…hb1ovL8F

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.

2.566 × 10⁹²(93-digit number)

25664838551943881477…92685922715263346559

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

2.566 × 10⁹²(93-digit number)

25664838551943881477…92685922715263346559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.566 × 10⁹²(93-digit number)

25664838551943881477…92685922715263346561

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

5.132 × 10⁹²(93-digit number)

51329677103887762954…85371845430526693119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.132 × 10⁹²(93-digit number)

51329677103887762954…85371845430526693121

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

1.026 × 10⁹³(94-digit number)

10265935420777552590…70743690861053386239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.026 × 10⁹³(94-digit number)

10265935420777552590…70743690861053386241

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

2.053 × 10⁹³(94-digit number)

20531870841555105181…41487381722106772479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.053 × 10⁹³(94-digit number)

20531870841555105181…41487381722106772481

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

4.106 × 10⁹³(94-digit number)

41063741683110210363…82974763444213544959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.106 × 10⁹³(94-digit number)

41063741683110210363…82974763444213544961

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 #240,242

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