Block #476,664

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 11:17:24 PM · Difficulty 10.4763 · 6,349,834 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9e17e409e935ac830bfb6bf2ca602b480235232ba4bd98974d3f103604c6e3da

View on Chainz ↗

Height

#476,664

Difficulty

10.476314

Transactions

Size

1.29 KB

Version

Bits

0a79efb3

Nonce

53,159

Timestamp

4/5/2014, 11:17:24 PM

Confirmations

6,349,834

Mined by

⛏️ P2SHAcpj6r2aE3X4AYuJ5e27RaKqF9fc88nyyP

Merkle Root

cdd67dcd748d898baa1de65712ccb11e8412d05c7186d7b7aaff4cb5e633184c

Transactions (4)

Coinbaseb35178669a22dd…b48881e63adc07

1 in → 1 out9.1300 XPM109 B

Acpj6r2a…fc88nyyP

4bdd95218106da…172dbf7793325e

1 in → 2 out5.0830 XPM226 B

AUXyR27A…ZuHsNn6z AGAuDbuA…ed3nVPFw

84b74439eaf44e…e3dc76567939fb

1 in → 2 out1.0796 XPM226 B

AHHqC5uT…S3nv61MK APdWPtDa…d12vYHeJ

f78e8cb9d87502…a46bd465380c2a

4 in → 2 out0.5422 XPM670 B

AJkWwn39…iMuXDj1r AXY8EgiU…keGzENVf

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.

6.636 × 10⁹⁵(96-digit number)

66364904627443362506…29696772855524914139

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

6.636 × 10⁹⁵(96-digit number)

66364904627443362506…29696772855524914139

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.636 × 10⁹⁵(96-digit number)

66364904627443362506…29696772855524914141

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

1.327 × 10⁹⁶(97-digit number)

13272980925488672501…59393545711049828279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.327 × 10⁹⁶(97-digit number)

13272980925488672501…59393545711049828281

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

2.654 × 10⁹⁶(97-digit number)

26545961850977345002…18787091422099656559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.654 × 10⁹⁶(97-digit number)

26545961850977345002…18787091422099656561

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

5.309 × 10⁹⁶(97-digit number)

53091923701954690005…37574182844199313119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.309 × 10⁹⁶(97-digit number)

53091923701954690005…37574182844199313121

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

1.061 × 10⁹⁷(98-digit number)

10618384740390938001…75148365688398626239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.061 × 10⁹⁷(98-digit number)

10618384740390938001…75148365688398626241

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 #476,664

Cookie Preferences