Block #206,240

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/12/2013, 4:32:37 PM · Difficulty 9.9007 · 6,599,804 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7184f897f76f53c01a528767b530e2cf4d592a3ccc518840541d85f62f528ed1

View on Chainz ↗

Height

#206,240

Difficulty

9.900735

Transactions

Size

2.15 KB

Version

Bits

09e6968d

Nonce

24,282

Timestamp

10/12/2013, 4:32:37 PM

Confirmations

6,599,804

Mined by

⛏️ P2SHAXbpyooSXrgsDVAsu6AkhX5vgBbup7bQTH

Merkle Root

a80db19644a6c7978d5d950e116359cb133314f3d9faabc0cc15478c612894f0

Transactions (5)

Coinbase8dfcf7374f70ac…c9c9de323e5ed0

1 in → 1 out10.2300 XPM109 B

AXbpyooS…bup7bQTH

aa7e27884681fa…abe4561e9e7ae7

6 in → 2 out61.1900 XPM964 B

ANP3mT5K…dkjrtVpK AbwfLcRh…c9QSxoFu

2300c7c8d928b3…64bf9f000be06a

1 in → 3 out10.1900 XPM227 B

AcMPa5Yh…j5yHgkwm ANvtpRa1…QjsraDJz AQXUSoBL…CzbjKp8b

39099c1db0eee9…f4648d028c7efb

2 in → 2 out20.3900 XPM374 B

APrMDaPg…bACQZ8yn AbQVuXmJ…qZjmTccE

d388a87bee3a42…320820acb391f1

2 in → 5 out17.1065 XPM440 B

ATxhwXQd…2i75kbKH ANvtpRa1…QjsraDJz AbnGPKWX…yfuXELRu AQXUSoBL…CzbjKp8b AVKfZvtY…sCa4NTcM

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.

1.221 × 10⁹⁴(95-digit number)

12216814385316646497…83237479953831784959

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

1.221 × 10⁹⁴(95-digit number)

12216814385316646497…83237479953831784959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.221 × 10⁹⁴(95-digit number)

12216814385316646497…83237479953831784961

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

2.443 × 10⁹⁴(95-digit number)

24433628770633292995…66474959907663569919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.443 × 10⁹⁴(95-digit number)

24433628770633292995…66474959907663569921

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

4.886 × 10⁹⁴(95-digit number)

48867257541266585991…32949919815327139839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.886 × 10⁹⁴(95-digit number)

48867257541266585991…32949919815327139841

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

9.773 × 10⁹⁴(95-digit number)

97734515082533171983…65899839630654279679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.773 × 10⁹⁴(95-digit number)

97734515082533171983…65899839630654279681

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

1.954 × 10⁹⁵(96-digit number)

19546903016506634396…31799679261308559359

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