Block #380,836

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/29/2014, 1:27:13 PM · Difficulty 10.4102 · 6,435,083 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ef8c6380983f518593bc730a25d446c3b6ec9e7ce3302a8d73261d934574fef7

View on Chainz ↗

Height

#380,836

Difficulty

10.410247

Transactions

Size

881 B

Version

Bits

0a6905ee

Nonce

6,287

Timestamp

1/29/2014, 1:27:13 PM

Confirmations

6,435,083

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

3d4f781708deacc3ecf458ed0fc0f74edccd34a31ded942440eb18f66d35bf75

Transactions (2)

Coinbase99f30398cca917…4eac15c0daba4d

1 in → 1 out9.2300 XPM116 B

AbwWkWZt…kawDhufa

8f164373738401…facf13871be286

4 in → 2 out150.0145 XPM672 B

AZxdfPJk…RRWdruyP AFqyFthm…oQ6uFBHe

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.

1.805 × 10¹⁰²(103-digit number)

18058331273237187277…61211962524387246079

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

1.805 × 10¹⁰²(103-digit number)

18058331273237187277…61211962524387246079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.805 × 10¹⁰²(103-digit number)

18058331273237187277…61211962524387246081

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

3.611 × 10¹⁰²(103-digit number)

36116662546474374554…22423925048774492159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.611 × 10¹⁰²(103-digit number)

36116662546474374554…22423925048774492161

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

7.223 × 10¹⁰²(103-digit number)

72233325092948749109…44847850097548984319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.223 × 10¹⁰²(103-digit number)

72233325092948749109…44847850097548984321

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

1.444 × 10¹⁰³(104-digit number)

14446665018589749821…89695700195097968639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.444 × 10¹⁰³(104-digit number)

14446665018589749821…89695700195097968641

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

2.889 × 10¹⁰³(104-digit number)

28893330037179499643…79391400390195937279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.889 × 10¹⁰³(104-digit number)

28893330037179499643…79391400390195937281

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 #380,836

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