Block #417,846

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/24/2014, 11:02:56 AM · Difficulty 10.3921 · 6,407,050 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2d78ca3803e426f7b96480d0b147772f485455d13b0e66977233ee0d0f8054c5

View on Chainz ↗

Height

#417,846

Difficulty

10.392125

Transactions

Size

435 B

Version

Bits

0a64624a

Nonce

Timestamp

2/24/2014, 11:02:56 AM

Confirmations

6,407,050

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

6bf2c8fa0b3aa0cf038fbf42ddd9c741a61902a0672a8c6169e4e0bb114435a0

Transactions (2)

Coinbase5755a6ef66f25e…edda16d5d3542c

1 in → 1 out9.2600 XPM116 B

AbwWkWZt…kawDhufa

d6ce86174893c5…9c777634b1de98

1 in → 2 out2.9941 XPM226 B

AK4K3ciG…VfGxrHiT APmeTCs6…JsEigXFK

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.

5.265 × 10¹⁰²(103-digit number)

52657512329639600572…34736641632496517119

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

5.265 × 10¹⁰²(103-digit number)

52657512329639600572…34736641632496517119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.265 × 10¹⁰²(103-digit number)

52657512329639600572…34736641632496517121

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

1.053 × 10¹⁰³(104-digit number)

10531502465927920114…69473283264993034239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.053 × 10¹⁰³(104-digit number)

10531502465927920114…69473283264993034241

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

2.106 × 10¹⁰³(104-digit number)

21063004931855840229…38946566529986068479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.106 × 10¹⁰³(104-digit number)

21063004931855840229…38946566529986068481

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

4.212 × 10¹⁰³(104-digit number)

42126009863711680458…77893133059972136959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.212 × 10¹⁰³(104-digit number)

42126009863711680458…77893133059972136961

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

8.425 × 10¹⁰³(104-digit number)

84252019727423360916…55786266119944273919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.425 × 10¹⁰³(104-digit number)

84252019727423360916…55786266119944273921

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 #417,846

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