Block #98,205

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/5/2013, 3:09:31 AM · Difficulty 9.3339 · 6,700,844 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bb84a6c3f4c3094ad9c1ab43f43c756009a93dded2df7840c68c4017e7ab3834

View on Chainz ↗

Height

#98,205

Difficulty

9.333941

Transactions

Size

7.39 KB

Version

Bits

09557d29

Nonce

234,049

Timestamp

8/5/2013, 3:09:31 AM

Confirmations

6,700,844

Mined by

⛏️ P2SHAQ9AxwTmeeKHBwrGPaJDsnWBnk9TNaDEUY

Merkle Root

c4ca9b6bc3b39578b6be7ea851a8f6891771e9d5c5e9aae5afa07362f4c5d9da

Transactions (2)

Coinbasefd8feaa76b2e98…807b7ac980c9a7

1 in → 1 out11.5400 XPM109 B

AQ9AxwTm…9TNaDEUY

412ee908d6fc91…4ec2c544a22fce

64 in → 2 out749.0100 XPM7.19 KB

AMkDPURg…qPW9rfen AdD9gugr…dxcSMAJi

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.

1.263 × 10⁹⁸(99-digit number)

12639889750189897402…05539445242961898399

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

1.263 × 10⁹⁸(99-digit number)

12639889750189897402…05539445242961898399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.263 × 10⁹⁸(99-digit number)

12639889750189897402…05539445242961898401

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

2.527 × 10⁹⁸(99-digit number)

25279779500379794804…11078890485923796799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.527 × 10⁹⁸(99-digit number)

25279779500379794804…11078890485923796801

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

5.055 × 10⁹⁸(99-digit number)

50559559000759589608…22157780971847593599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.055 × 10⁹⁸(99-digit number)

50559559000759589608…22157780971847593601

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

1.011 × 10⁹⁹(100-digit number)

10111911800151917921…44315561943695187199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.011 × 10⁹⁹(100-digit number)

10111911800151917921…44315561943695187201

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

2.022 × 10⁹⁹(100-digit number)

20223823600303835843…88631123887390374399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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