Block #506,046

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/22/2014, 8:23:19 PM · Difficulty 10.8124 · 6,305,029 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e241c46a2beebdf9f0de119072e063451c2aa1002694e9a30877d3eb338bfdb1

View on Chainz ↗

Height

#506,046

Difficulty

10.812424

Transactions

Size

433 B

Version

Bits

0acffb0b

Nonce

14,162,411

Timestamp

4/22/2014, 8:23:19 PM

Confirmations

6,305,029

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

0602a5cd75af561a6c9f8bd4dd1a02dda6c71f96370c2856ea1f1a5b91e2b742

Transactions (2)

Coinbase5d1206e187584d…67721d53bd2bd3

1 in → 1 out8.5500 XPM116 B

AbwWkWZt…kawDhufa

2e561812bb4535…5b210052cf1be2

1 in → 2 out1.9003 XPM225 B

APFtzZbN…aDBn6MMt AGRtt4qy…B7rzXbGu

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.

1.346 × 10⁹⁹(100-digit number)

13462402077310751857…16180240631386722799

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

1.346 × 10⁹⁹(100-digit number)

13462402077310751857…16180240631386722799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.346 × 10⁹⁹(100-digit number)

13462402077310751857…16180240631386722801

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

2.692 × 10⁹⁹(100-digit number)

26924804154621503715…32360481262773445599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.692 × 10⁹⁹(100-digit number)

26924804154621503715…32360481262773445601

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

5.384 × 10⁹⁹(100-digit number)

53849608309243007431…64720962525546891199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.384 × 10⁹⁹(100-digit number)

53849608309243007431…64720962525546891201

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

1.076 × 10¹⁰⁰(101-digit number)

10769921661848601486…29441925051093782399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.076 × 10¹⁰⁰(101-digit number)

10769921661848601486…29441925051093782401

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

2.153 × 10¹⁰⁰(101-digit number)

21539843323697202972…58883850102187564799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.153 × 10¹⁰⁰(101-digit number)

21539843323697202972…58883850102187564801

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 #506,046

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