Block #444,414

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/15/2014, 6:15:45 AM · Difficulty 10.3432 · 6,372,676 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

80270ed46cf5f1840f1834761c88b51b5dd56ec892ce18fad929372061ecbff7

View on Chainz ↗

Height

#444,414

Difficulty

10.343151

Transactions

Size

1.05 KB

Version

Bits

0a57d8be

Nonce

29,778

Timestamp

3/15/2014, 6:15:45 AM

Confirmations

6,372,676

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

87d32209468e99d2716ccf87956e70cf31ef4f6dafe886e6678d7ac417f5965f

Transactions (2)

Coinbasef4b3331c396635…99aeeb631d71eb

1 in → 1 out9.3400 XPM110 B

AeKNrjNj…1NEq95Ta

6761c076dcc65d…44c3f4ce29080d

4 in → 12 out37.3200 XPM877 B

AXB766PQ…1QeNDbxJ AeKNrjNj…1NEq95Ta AMByaWyW…KYi52kdE AJobi3ue…3WccitMD AMM3ziH3…kDbEwGup

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.

2.715 × 10¹⁰⁰(101-digit number)

27152758128100455103…77521923361802483799

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

2.715 × 10¹⁰⁰(101-digit number)

27152758128100455103…77521923361802483799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.715 × 10¹⁰⁰(101-digit number)

27152758128100455103…77521923361802483801

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

5.430 × 10¹⁰⁰(101-digit number)

54305516256200910207…55043846723604967599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.430 × 10¹⁰⁰(101-digit number)

54305516256200910207…55043846723604967601

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

1.086 × 10¹⁰¹(102-digit number)

10861103251240182041…10087693447209935199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.086 × 10¹⁰¹(102-digit number)

10861103251240182041…10087693447209935201

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

2.172 × 10¹⁰¹(102-digit number)

21722206502480364083…20175386894419870399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.172 × 10¹⁰¹(102-digit number)

21722206502480364083…20175386894419870401

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

4.344 × 10¹⁰¹(102-digit number)

43444413004960728166…40350773788839740799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.344 × 10¹⁰¹(102-digit number)

43444413004960728166…40350773788839740801

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 #444,414

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