Block #380,738

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/29/2014, 11:46:50 AM · Difficulty 10.4112 · 6,428,640 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1e660790dcfa2d45a80a2a94672809abc480000b9552c112cd69fa2528d132e6

View on Chainz ↗

Height

#380,738

Difficulty

10.411187

Transactions

Size

1.23 KB

Version

Bits

0a694390

Nonce

97,463

Timestamp

1/29/2014, 11:46:50 AM

Confirmations

6,428,640

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

4b5b9ae9d27ffee12c9960aa308a884ee2cd6748fde7a86351dd5da7ec69a3bd

Transactions (5)

Coinbaseeeabfae52e2bdd…0d22c55139ad8e

1 in → 1 out9.2500 XPM110 B

AeKNrjNj…1NEq95Ta

08ef4b92c79e92…7eefdae97e68eb

2 in → 2 out11.5453 XPM375 B

ALaMXXem…wBfwP8XS ActCgm6j…4qH4GTxN

ec810a17fd2770…3164f71db493eb

1 in → 2 out4.1470 XPM227 B

AMf7wPnV…bUfe2A8A ALjsFYuS…AM5mnrdW

38493b716657c3…ec52738fc4dcb8

1 in → 2 out3.1460 XPM225 B

ARpzqnUm…DmQAk68w AQQc32Ef…BsVjXrh3

0f1e7dd9530cdf…5e599193504b1c

1 in → 2 out5.1240 XPM226 B

Ad2Gs3gt…2pUQhcbx AWtuVYFp…X17pfJ78

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.

1.653 × 10¹⁰⁰(101-digit number)

16534201762726917962…18134092722804838399

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

1.653 × 10¹⁰⁰(101-digit number)

16534201762726917962…18134092722804838399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.653 × 10¹⁰⁰(101-digit number)

16534201762726917962…18134092722804838401

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

3.306 × 10¹⁰⁰(101-digit number)

33068403525453835924…36268185445609676799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.306 × 10¹⁰⁰(101-digit number)

33068403525453835924…36268185445609676801

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

6.613 × 10¹⁰⁰(101-digit number)

66136807050907671848…72536370891219353599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.613 × 10¹⁰⁰(101-digit number)

66136807050907671848…72536370891219353601

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

1.322 × 10¹⁰¹(102-digit number)

13227361410181534369…45072741782438707199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.322 × 10¹⁰¹(102-digit number)

13227361410181534369…45072741782438707201

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

2.645 × 10¹⁰¹(102-digit number)

26454722820363068739…90145483564877414399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.645 × 10¹⁰¹(102-digit number)

26454722820363068739…90145483564877414401

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 #380,738

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