Block #399,726

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/11/2014, 2:29:56 PM · Difficulty 10.4298 · 6,427,384 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1f7f50e91576d416cc47476a34c937e1d4df94e90bb849105fb1891f2ddfc5b2

View on Chainz ↗

Height

#399,726

Difficulty

10.429842

Transactions

Size

4.20 KB

Version

Bits

0a6e0a1c

Nonce

59,412

Timestamp

2/11/2014, 2:29:56 PM

Confirmations

6,427,384

Mined by

⛏️ naR3Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

9cc2d12121a908966fa9cef0794d97d13718dbc8277d3fc67a6c1eb1735e75d4

Transactions (2)

Coinbase3ef514cb0cacdf…a32fa573202801

1 in → 24 out9.1800 XPM879 B

Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH Af76ewER…EzGhbQ6S AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

b748fc06d20d56…1a7cdc722d81b0

22 in → 2 out57.3840 XPM3.26 KB

Aa5jkS8Z…P8zPcdbk Ad2c7z6w…WvGjsCCw

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.

8.759 × 10⁹²(93-digit number)

87593985211829660641…97108801477509759999

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

8.759 × 10⁹²(93-digit number)

87593985211829660641…97108801477509759999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.759 × 10⁹²(93-digit number)

87593985211829660641…97108801477509760001

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

1.751 × 10⁹³(94-digit number)

17518797042365932128…94217602955019519999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.751 × 10⁹³(94-digit number)

17518797042365932128…94217602955019520001

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

3.503 × 10⁹³(94-digit number)

35037594084731864256…88435205910039039999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.503 × 10⁹³(94-digit number)

35037594084731864256…88435205910039040001

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

7.007 × 10⁹³(94-digit number)

70075188169463728513…76870411820078079999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.007 × 10⁹³(94-digit number)

70075188169463728513…76870411820078080001

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

1.401 × 10⁹⁴(95-digit number)

14015037633892745702…53740823640156159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.401 × 10⁹⁴(95-digit number)

14015037633892745702…53740823640156160001

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 #399,726

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