Block #439,465

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/11/2014, 5:16:01 PM · Difficulty 10.3590 · 6,368,511 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8de70ed8d89a97513d9d9702a904443f73995406e663f7135b8ec58bd4496cf4

View on Chainz ↗

Height

#439,465

Difficulty

10.358992

Transactions

Size

1006 B

Version

Bits

0a5be6e9

Nonce

33,667

Timestamp

3/11/2014, 5:16:01 PM

Confirmations

6,368,511

Mined by

⛏️ aSDAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

3800a1fa9c65134ebfcc499f093082330af99de90ee5a08dba92fa98a3a7839d

Transactions (1)

Coinbase3800a1fa9c6513…92fa98a3a7839d

1 in → 25 out9.3000 XPM913 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGD4yZQw…hGzM2XAx AScAzqGc…BZ6tV1vJ AJLB8H7s…MRD4s5wA

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.

4.481 × 10¹⁰⁰(101-digit number)

44818966391687623234…53510974778824401919

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

4.481 × 10¹⁰⁰(101-digit number)

44818966391687623234…53510974778824401919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.481 × 10¹⁰⁰(101-digit number)

44818966391687623234…53510974778824401921

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

8.963 × 10¹⁰⁰(101-digit number)

89637932783375246469…07021949557648803839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.963 × 10¹⁰⁰(101-digit number)

89637932783375246469…07021949557648803841

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

1.792 × 10¹⁰¹(102-digit number)

17927586556675049293…14043899115297607679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.792 × 10¹⁰¹(102-digit number)

17927586556675049293…14043899115297607681

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

3.585 × 10¹⁰¹(102-digit number)

35855173113350098587…28087798230595215359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.585 × 10¹⁰¹(102-digit number)

35855173113350098587…28087798230595215361

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

7.171 × 10¹⁰¹(102-digit number)

71710346226700197175…56175596461190430719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.171 × 10¹⁰¹(102-digit number)

71710346226700197175…56175596461190430721

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 #439,465

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