Block #170,519

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/18/2013, 7:58:40 PM · Difficulty 9.8656 · 6,620,794 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4699c2689efd5dc49e72075099f5df723219393ce062f0ae86218c9d794e88f6

View on Chainz ↗

Height

#170,519

Difficulty

9.865618

Transactions

Size

648 B

Version

Bits

09dd991e

Nonce

44,628

Timestamp

9/18/2013, 7:58:40 PM

Confirmations

6,620,794

Merkle Root

6e841d2799bacc4cd19ec0f91f6af4720c65b892c3e7da8d73ce13e477a9edba

Transactions (3)

Coinbase57cd6857ab357c…e6aae84deda93b

1 in → 1 out10.2800 XPM109 B

AHTCuref…ciGEetrY

2d5aa7c09a0162…367b4b042f30ea

1 in → 2 out10.2400 XPM225 B

AXwKKGcU…yK2w3TwR AQPVDAVn…Wpb9d33V

df00a9b6ce8003…0a2c5c2518f487

1 in → 2 out2.1897 XPM226 B

Adg3kpjQ…5PNg52z7 AeNo3RVm…WruQcTwE

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.

6.573 × 10⁸⁹(90-digit number)

65737612594812575459…17973661002294962249

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

6.573 × 10⁸⁹(90-digit number)

65737612594812575459…17973661002294962249

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.573 × 10⁸⁹(90-digit number)

65737612594812575459…17973661002294962251

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

1.314 × 10⁹⁰(91-digit number)

13147522518962515091…35947322004589924499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.314 × 10⁹⁰(91-digit number)

13147522518962515091…35947322004589924501

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

2.629 × 10⁹⁰(91-digit number)

26295045037925030183…71894644009179848999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.629 × 10⁹⁰(91-digit number)

26295045037925030183…71894644009179849001

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

5.259 × 10⁹⁰(91-digit number)

52590090075850060367…43789288018359697999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.259 × 10⁹⁰(91-digit number)

52590090075850060367…43789288018359698001

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

1.051 × 10⁹¹(92-digit number)

10518018015170012073…87578576036719395999

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