Block #379,159

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/28/2014, 8:41:10 AM · Difficulty 10.4157 · 6,435,978 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b31020a857861699d109c2fa5f73c85482ad1354748d1a565fcb32c4e7e51c0a

View on Chainz ↗

Height

#379,159

Difficulty

10.415723

Transactions

Size

800 B

Version

Bits

0a6a6cd4

Nonce

145,967

Timestamp

1/28/2014, 8:41:10 AM

Confirmations

6,435,978

Mined by

⛏️ aRlAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

21429338fc4bf2bf7cbd2abd8eca4da0a6ddd140c7f0a48a68acd0e808091463

Transactions (1)

Coinbase21429338fc4bf2…acd0e808091463

1 in → 19 out9.2000 XPM709 B

AQvZBsUo…hppgRZTJ AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH AFutDVqJ…TJTJj6UF AP5UvYhU…vLTDwkdA

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.

2.955 × 10⁹⁷(98-digit number)

29555371204188421265…81531261295214750189

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

2.955 × 10⁹⁷(98-digit number)

29555371204188421265…81531261295214750189

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.955 × 10⁹⁷(98-digit number)

29555371204188421265…81531261295214750191

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

5.911 × 10⁹⁷(98-digit number)

59110742408376842530…63062522590429500379

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.911 × 10⁹⁷(98-digit number)

59110742408376842530…63062522590429500381

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

1.182 × 10⁹⁸(99-digit number)

11822148481675368506…26125045180859000759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.182 × 10⁹⁸(99-digit number)

11822148481675368506…26125045180859000761

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

2.364 × 10⁹⁸(99-digit number)

23644296963350737012…52250090361718001519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.364 × 10⁹⁸(99-digit number)

23644296963350737012…52250090361718001521

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

4.728 × 10⁹⁸(99-digit number)

47288593926701474024…04500180723436003039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.728 × 10⁹⁸(99-digit number)

47288593926701474024…04500180723436003041

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 #379,159

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