Block #248,199

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/7/2013, 5:58:13 AM · Difficulty 9.9655 · 6,543,704 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

476e91cc1c14ec424b967d156d1054bb05c6fe89bc15f2fdefed0a30d1c42b2b

View on Chainz ↗

Height

#248,199

Difficulty

9.965482

Transactions

Size

206 B

Version

Bits

09f729cc

Nonce

20,540

Timestamp

11/7/2013, 5:58:13 AM

Confirmations

6,543,704

Merkle Root

80be8d161ed3cda9b69cd6d303fec24b7244b3d2b81bed2cd089ec4982ee4bb2

Transactions (1)

Coinbase80be8d161ed3cd…89ec4982ee4bb2

1 in → 1 out10.0500 XPM116 B

AcLBm5Z9…S683d7c3

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.

2.667 × 10⁹⁴(95-digit number)

26675981195932708811…09645786227043500799

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

2.667 × 10⁹⁴(95-digit number)

26675981195932708811…09645786227043500799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.667 × 10⁹⁴(95-digit number)

26675981195932708811…09645786227043500801

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

5.335 × 10⁹⁴(95-digit number)

53351962391865417622…19291572454087001599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.335 × 10⁹⁴(95-digit number)

53351962391865417622…19291572454087001601

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

1.067 × 10⁹⁵(96-digit number)

10670392478373083524…38583144908174003199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.067 × 10⁹⁵(96-digit number)

10670392478373083524…38583144908174003201

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

2.134 × 10⁹⁵(96-digit number)

21340784956746167048…77166289816348006399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.134 × 10⁹⁵(96-digit number)

21340784956746167048…77166289816348006401

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

4.268 × 10⁹⁵(96-digit number)

42681569913492334097…54332579632696012799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.268 × 10⁹⁵(96-digit number)

42681569913492334097…54332579632696012801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

8.536 × 10⁹⁵(96-digit number)

85363139826984668195…08665159265392025599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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