Block #487,035

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/11/2014, 10:04:56 PM · Difficulty 10.6362 · 6,339,928 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d7ce77cc6723b66a6ef50f1e9e15486ba718ef138091a403bbab8900e823f3e6

View on Chainz ↗

Height

#487,035

Difficulty

10.636215

Transactions

Size

798 B

Version

Bits

0aa2defb

Nonce

224,789,789

Timestamp

4/11/2014, 10:04:56 PM

Confirmations

6,339,928

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

59f810b366b9303cdabfbceafe5b95b1d4216775e477ffe17b6bb455910c6aef

Transactions (2)

Coinbase51104d87f2e259…e8ef96a70a797c

1 in → 1 out8.8400 XPM116 B

AbwWkWZt…kawDhufa

2553910468cadc…916deef608d6cd

3 in → 7 out26.8400 XPM590 B

AefjmuCW…iLY7neu2 AeRBaJVT…ZmU87Dc5 AMXQrWx5…XSxNgyAS ASzYyYoj…ZaU2GP4b AP6XU4Ao…mq8mf6N9

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.

5.819 × 10⁹⁹(100-digit number)

58190002809083330977…98659572343644799999

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

5.819 × 10⁹⁹(100-digit number)

58190002809083330977…98659572343644799999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.819 × 10⁹⁹(100-digit number)

58190002809083330977…98659572343644800001

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

1.163 × 10¹⁰⁰(101-digit number)

11638000561816666195…97319144687289599999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.163 × 10¹⁰⁰(101-digit number)

11638000561816666195…97319144687289600001

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

2.327 × 10¹⁰⁰(101-digit number)

23276001123633332391…94638289374579199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.327 × 10¹⁰⁰(101-digit number)

23276001123633332391…94638289374579200001

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

4.655 × 10¹⁰⁰(101-digit number)

46552002247266664782…89276578749158399999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.655 × 10¹⁰⁰(101-digit number)

46552002247266664782…89276578749158400001

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

9.310 × 10¹⁰⁰(101-digit number)

93104004494533329564…78553157498316799999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.310 × 10¹⁰⁰(101-digit number)

93104004494533329564…78553157498316800001

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 #487,035

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