Block #486,557

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/11/2014, 4:07:28 PM · Difficulty 10.6276 · 6,324,116 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4a41ef8e59fd273a17077f5687fbd006595ce0f7c3400afd77cd60b76694bf3a

View on Chainz ↗

Height

#486,557

Difficulty

10.627562

Transactions

Size

56.73 KB

Version

Bits

0aa0a7eb

Nonce

182,566,618

Timestamp

4/11/2014, 4:07:28 PM

Confirmations

6,324,116

Mined by

⛏️ P2SHASzy4zwZFATFjeHSqxnb3hKwFnGsycsfnT

Merkle Root

5f4fec9e0bb940ebb189c1b308cd415a3d90c6085f3818b7dc37e7d44ab07777

Transactions (3)

Coinbasefc8c14a92704d1…078a9db8208ee3

1 in → 1 out9.5700 XPM110 B

ASzy4zwZ…GsycsfnT

4eeb1af1b015f1…9457ca70a52eac

386 in → 2 out10000.0100 XPM55.88 KB

AN2B2BB8…8w4X3wQL Ae5WFHbn…gBo7rvHr

2b5644f8ab8f64…4f831d97eb171e

4 in → 2 out14.0186 XPM671 B

AWmMRv7k…QpTMAKCs ARtq2GAm…AiKvHW9z

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.

1.095 × 10⁹⁸(99-digit number)

10958647723248293780…12833848182670325199

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

1.095 × 10⁹⁸(99-digit number)

10958647723248293780…12833848182670325199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.095 × 10⁹⁸(99-digit number)

10958647723248293780…12833848182670325201

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

2.191 × 10⁹⁸(99-digit number)

21917295446496587560…25667696365340650399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.191 × 10⁹⁸(99-digit number)

21917295446496587560…25667696365340650401

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

4.383 × 10⁹⁸(99-digit number)

43834590892993175120…51335392730681300799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.383 × 10⁹⁸(99-digit number)

43834590892993175120…51335392730681300801

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

8.766 × 10⁹⁸(99-digit number)

87669181785986350240…02670785461362601599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.766 × 10⁹⁸(99-digit number)

87669181785986350240…02670785461362601601

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

1.753 × 10⁹⁹(100-digit number)

17533836357197270048…05341570922725203199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.753 × 10⁹⁹(100-digit number)

17533836357197270048…05341570922725203201

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 #486,557

Cookie Preferences