Block #489,907

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/13/2014, 1:50:51 PM · Difficulty 10.6702 · 6,313,511 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f79e90e69f17f35563d337e2d6389dc7647ad2195d7da2bb2d1c86ff58019319

View on Chainz ↗

Height

#489,907

Difficulty

10.670206

Transactions

Size

654 B

Version

Bits

0aab9298

Nonce

96,507

Timestamp

4/13/2014, 1:50:51 PM

Confirmations

6,313,511

Mined by

⛏️ P2SHAPASoLS4NEBmxx99MUxiDEGq67Pjt5nPCR

Merkle Root

273ff3ded6609d7357b7217dd948e3a23c34a668eaffb0586754d7f3a054162a

Transactions (3)

Coinbaseab5c144c3563f9…cc657dbd5e998f

1 in → 1 out8.7900 XPM111 B

APASoLS4…Pjt5nPCR

15cd1bb3c11c0f…a9a81e7b4eff3b

1 in → 2 out2.0726 XPM226 B

ARd47WCo…vXzjgLiX AMWoV2HZ…RHdpzsfB

490ed89e8f9ffe…fcd50185e09f4e

1 in → 2 out0.5555 XPM226 B

AaoSCozA…TCy2UANc AUEfgciq…JxYNG9Ty

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.

6.766 × 10⁹⁷(98-digit number)

67667641688172003613…75969782775723252959

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

6.766 × 10⁹⁷(98-digit number)

67667641688172003613…75969782775723252959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.766 × 10⁹⁷(98-digit number)

67667641688172003613…75969782775723252961

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

1.353 × 10⁹⁸(99-digit number)

13533528337634400722…51939565551446505919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.353 × 10⁹⁸(99-digit number)

13533528337634400722…51939565551446505921

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

2.706 × 10⁹⁸(99-digit number)

27067056675268801445…03879131102893011839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.706 × 10⁹⁸(99-digit number)

27067056675268801445…03879131102893011841

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

5.413 × 10⁹⁸(99-digit number)

54134113350537602891…07758262205786023679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.413 × 10⁹⁸(99-digit number)

54134113350537602891…07758262205786023681

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

1.082 × 10⁹⁹(100-digit number)

10826822670107520578…15516524411572047359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.082 × 10⁹⁹(100-digit number)

10826822670107520578…15516524411572047361

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