Block #399,862

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/11/2014, 4:29:27 PM · Difficulty 10.4316 · 6,393,807 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9555cc0af19bf6f3545a735f53504edfd66a087ec377c844d60d678b3cb4d956

View on Chainz ↗

Height

#399,862

Difficulty

10.431634

Transactions

Size

584 B

Version

Bits

0a6e7f99

Nonce

363,535

Timestamp

2/11/2014, 4:29:27 PM

Confirmations

6,393,807

Merkle Root

2a562c11f6819bdca9ec58fab9ab2639bafe20ab2de3a86193fab4a80b2d9155

Transactions (3)

Coinbase97640ca21b56a2…e83af694053d43

1 in → 1 out9.2009 XPM109 B

AXFzYFTn…mB23xSqH

1275e98ef0cd35…9d038d31747595

1 in → 1 out2.9900 XPM192 B

ARBngPYP…LzCWc5RR

b06feb88ddfb74…ba045c332f4dd2

1 in → 1 out2.9900 XPM192 B

AFou2W6d…qRHGKK2u

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.

8.978 × 10⁹⁵(96-digit number)

89781727425551459361…40859717235133954879

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

8.978 × 10⁹⁵(96-digit number)

89781727425551459361…40859717235133954879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.978 × 10⁹⁵(96-digit number)

89781727425551459361…40859717235133954881

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

1.795 × 10⁹⁶(97-digit number)

17956345485110291872…81719434470267909759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.795 × 10⁹⁶(97-digit number)

17956345485110291872…81719434470267909761

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

3.591 × 10⁹⁶(97-digit number)

35912690970220583744…63438868940535819519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.591 × 10⁹⁶(97-digit number)

35912690970220583744…63438868940535819521

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

7.182 × 10⁹⁶(97-digit number)

71825381940441167489…26877737881071639039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.182 × 10⁹⁶(97-digit number)

71825381940441167489…26877737881071639041

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

1.436 × 10⁹⁷(98-digit number)

14365076388088233497…53755475762143278079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.436 × 10⁹⁷(98-digit number)

14365076388088233497…53755475762143278081

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