Block #494,202

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/16/2014, 1:39:32 AM · Difficulty 10.7143 · 6,330,613 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2581f0f9c45ae8b5dc5b4d6f8b0975809d7833724604a6dd160f04fcab988035

View on Chainz ↗

Height

#494,202

Difficulty

10.714294

Transactions

Size

886 B

Version

Bits

0ab6dbfd

Nonce

6,890

Timestamp

4/16/2014, 1:39:32 AM

Confirmations

6,330,613

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

87ad485f72e75f9b53ee62fd54fd4fd54c5062b0aa165e418c249701ef8d0360

Transactions (4)

Coinbase17654676fca00d…3019483323be8d

1 in → 1 out8.7300 XPM116 B

AbwWkWZt…kawDhufa

95f3680a82660d…7ace03c1f5cc8f

1 in → 2 out5.1763 XPM226 B

AQQ4QXJG…5oSH58gp AL43arzT…GrscpU5h

c4afb860a7df96…4a5706433e8c8b

1 in → 2 out3.6626 XPM226 B

AQfr3SHk…ZT3KVc3T AQYfM6tR…wtD7VsKo

ab4c82585022d6…a02dca4f0c643f

1 in → 2 out5.5845 XPM226 B

ATdtomYD…mXhzxvF9 AJLZQYiD…C283CfoH

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.

3.864 × 10⁹⁹(100-digit number)

38647472593400357731…60043405780310732799

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

3.864 × 10⁹⁹(100-digit number)

38647472593400357731…60043405780310732799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.864 × 10⁹⁹(100-digit number)

38647472593400357731…60043405780310732801

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

7.729 × 10⁹⁹(100-digit number)

77294945186800715462…20086811560621465599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.729 × 10⁹⁹(100-digit number)

77294945186800715462…20086811560621465601

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

1.545 × 10¹⁰⁰(101-digit number)

15458989037360143092…40173623121242931199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.545 × 10¹⁰⁰(101-digit number)

15458989037360143092…40173623121242931201

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

3.091 × 10¹⁰⁰(101-digit number)

30917978074720286184…80347246242485862399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.091 × 10¹⁰⁰(101-digit number)

30917978074720286184…80347246242485862401

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

6.183 × 10¹⁰⁰(101-digit number)

61835956149440572369…60694492484971724799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.183 × 10¹⁰⁰(101-digit number)

61835956149440572369…60694492484971724801

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 #494,202

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