Block #204,998

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/11/2013, 9:05:03 PM · Difficulty 9.8991 · 6,590,466 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c1c554ed7a92c1dc910b9125665a201933f0dad7ab78a361485afa20538e3dc6

View on Chainz ↗

Height

#204,998

Difficulty

9.899142

Transactions

Size

618 B

Version

Bits

09e62e32

Nonce

3,227

Timestamp

10/11/2013, 9:05:03 PM

Confirmations

6,590,466

Mined by

⛏️ P2SHAXkwZGZQUV996sgzkcs2jbamXUaP3jC9dV

Merkle Root

b1dcc7bc258e833b45fa2f3951700add034399b1e63d0d302836c21101ee7051

Transactions (3)

Coinbase7a898d055163b4…c6e17e5e1177cc

1 in → 1 out10.2100 XPM109 B

AXkwZGZQ…aP3jC9dV

87bb836c68fcf3…316f2c4059bcad

1 in → 2 out20.1600 XPM192 B

AT1mPASu…8jW9MJe6 AeinuRRR…4PcLyYqe

5a3317d636b6cf…9c4b43f7f9ed6c

1 in → 2 out8.1727 XPM225 B

AUfQa8AJ…R28qfzUc ASboj5nL…5aQjkdwN

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.

3.371 × 10⁹⁹(100-digit number)

33716198856822856738…35619262862833049599

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

3.371 × 10⁹⁹(100-digit number)

33716198856822856738…35619262862833049599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.371 × 10⁹⁹(100-digit number)

33716198856822856738…35619262862833049601

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

6.743 × 10⁹⁹(100-digit number)

67432397713645713477…71238525725666099199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.743 × 10⁹⁹(100-digit number)

67432397713645713477…71238525725666099201

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

1.348 × 10¹⁰⁰(101-digit number)

13486479542729142695…42477051451332198399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.348 × 10¹⁰⁰(101-digit number)

13486479542729142695…42477051451332198401

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

2.697 × 10¹⁰⁰(101-digit number)

26972959085458285391…84954102902664396799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.697 × 10¹⁰⁰(101-digit number)

26972959085458285391…84954102902664396801

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

5.394 × 10¹⁰⁰(101-digit number)

53945918170916570782…69908205805328793599

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