Block #407,890

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/17/2014, 7:12:28 AM · Difficulty 10.4283 · 6,398,267 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

efb5f628e6e1998037099bb72ceffb6d0080b4fe64c043123a0312496a19c567

View on Chainz ↗

Height

#407,890

Difficulty

10.428295

Transactions

Size

936 B

Version

Bits

0a6da4be

Nonce

101,574

Timestamp

2/17/2014, 7:12:28 AM

Confirmations

6,398,267

Mined by

⛏️ R9aSSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

78da4eef0b97cf3023ad4227b1b257f817a8f220aab7af437682b8cb83d8a052

Transactions (1)

Coinbase78da4eef0b97cf…82b8cb83d8a052

1 in → 23 out9.1800 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ATKK7iFz…wZm46KN1 AQmbMrbE…rVBzHMyY

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.

1.103 × 10⁹⁷(98-digit number)

11030734917898165591…84778888985269269999

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

1.103 × 10⁹⁷(98-digit number)

11030734917898165591…84778888985269269999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.103 × 10⁹⁷(98-digit number)

11030734917898165591…84778888985269270001

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

2.206 × 10⁹⁷(98-digit number)

22061469835796331182…69557777970538539999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.206 × 10⁹⁷(98-digit number)

22061469835796331182…69557777970538540001

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

4.412 × 10⁹⁷(98-digit number)

44122939671592662365…39115555941077079999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.412 × 10⁹⁷(98-digit number)

44122939671592662365…39115555941077080001

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

8.824 × 10⁹⁷(98-digit number)

88245879343185324731…78231111882154159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.824 × 10⁹⁷(98-digit number)

88245879343185324731…78231111882154160001

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

1.764 × 10⁹⁸(99-digit number)

17649175868637064946…56462223764308319999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.764 × 10⁹⁸(99-digit number)

17649175868637064946…56462223764308320001

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