Block #147,522

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/3/2013, 4:04:40 AM · Difficulty 9.8521 · 6,646,671 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ab5a548dd407875d4ca1982539a9801e55a6fc21a0f95f233f93b3994bd86bc4

View on Chainz ↗

Height

#147,522

Difficulty

9.852108

Transactions

Size

1.16 KB

Version

Bits

09da23be

Nonce

34,426

Timestamp

9/3/2013, 4:04:40 AM

Confirmations

6,646,671

Merkle Root

52556675d7cb18718277fc0529e5a41ab71c324bbb722ff10016d6502f9a77b8

Transactions (2)

Coinbasee9a1222d817436…e8af01674d0ca7

1 in → 1 out10.3000 XPM109 B

AZaviS5n…oHuQufdR

58b1bcb07e30b2…55b4a17fcf02ee

8 in → 2 out82.5900 XPM993 B

AdktB7K3…uWFqnnCf Acd1BgN5…bE5c9NoN

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.

2.275 × 10⁹⁴(95-digit number)

22753359431299269073…37043665274043261359

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

2.275 × 10⁹⁴(95-digit number)

22753359431299269073…37043665274043261359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.275 × 10⁹⁴(95-digit number)

22753359431299269073…37043665274043261361

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

4.550 × 10⁹⁴(95-digit number)

45506718862598538147…74087330548086522719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.550 × 10⁹⁴(95-digit number)

45506718862598538147…74087330548086522721

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

9.101 × 10⁹⁴(95-digit number)

91013437725197076294…48174661096173045439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.101 × 10⁹⁴(95-digit number)

91013437725197076294…48174661096173045441

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

1.820 × 10⁹⁵(96-digit number)

18202687545039415258…96349322192346090879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.820 × 10⁹⁵(96-digit number)

18202687545039415258…96349322192346090881

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

3.640 × 10⁹⁵(96-digit number)

36405375090078830517…92698644384692181759

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