Block #206,895

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/13/2013, 2:41:33 AM · Difficulty 9.9017 · 6,604,045 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f5b559ad92010df0a09e6111f3f807687a58b5ea7839360159448c3f0baefdf1

View on Chainz ↗

Height

#206,895

Difficulty

9.901665

Transactions

Size

800 B

Version

Bits

09e6d388

Nonce

23,270

Timestamp

10/13/2013, 2:41:33 AM

Confirmations

6,604,045

Mined by

⛏️ P2SHAGD4ELPmV9VxECkLLRQiFxvMNQsYtybN6f

Merkle Root

8983b5bf83b45f5222aba363b6f6d7aa51bcacc2ca7c2deedb76fdc4ed798058

Transactions (3)

Coinbase5d2174613c19b6…26014dd464e6e6

1 in → 1 out10.2000 XPM109 B

AGD4ELPm…sYtybN6f

deab9726c71da7…6a990220f5bc9a

2 in → 2 out10.3426 XPM374 B

AHyHEeYQ…XuELsExj ATPAEpy9…j6Hmjf6B

fcf9e9dede6356…19f29464ba12af

1 in → 2 out4.3139 XPM226 B

ANsZYAZy…wSk4mkms ANjN1xi2…z1Bd1aof

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.

2.088 × 10⁹⁶(97-digit number)

20883246179622595841…94379571616950775999

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

2.088 × 10⁹⁶(97-digit number)

20883246179622595841…94379571616950775999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.088 × 10⁹⁶(97-digit number)

20883246179622595841…94379571616950776001

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

4.176 × 10⁹⁶(97-digit number)

41766492359245191682…88759143233901551999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.176 × 10⁹⁶(97-digit number)

41766492359245191682…88759143233901552001

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

8.353 × 10⁹⁶(97-digit number)

83532984718490383365…77518286467803103999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.353 × 10⁹⁶(97-digit number)

83532984718490383365…77518286467803104001

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

1.670 × 10⁹⁷(98-digit number)

16706596943698076673…55036572935606207999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.670 × 10⁹⁷(98-digit number)

16706596943698076673…55036572935606208001

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

3.341 × 10⁹⁷(98-digit number)

33413193887396153346…10073145871212415999

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

Block #206,895

Cookie Preferences