Block #149,101

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/4/2013, 3:51:32 AM · Difficulty 9.8567 · 6,640,624 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7f9e3240171454cad7ad4607ba265837fab0e4385cf474bd026aef1c051574c1

View on Chainz ↗

Height

#149,101

Difficulty

9.856671

Transactions

Size

1.53 KB

Version

Bits

09db4ed0

Nonce

19,540

Timestamp

9/4/2013, 3:51:32 AM

Confirmations

6,640,624

Merkle Root

23e21e1a39f5ba9841e7ca1483a9e8ee50426a166c5b5eebff22c138a9f3aef4

Transactions (4)

Coinbase2fa9dd818eaf96…cae8cf02194851

1 in → 1 out10.3100 XPM109 B

AKASd69y…9DeLNPDd

09835137145b70…362b47f3ed1918

7 in → 1 out72.3800 XPM841 B

AX9US9BG…VNQafoJ4

fc5f0cba803839…7b65d61c4b995e

1 in → 1 out10.2900 XPM158 B

AZW5MnkK…BxHUwWD3

932d1c0813d831…de730dd14c975b

2 in → 2 out2.0103 XPM373 B

AYy6jDKp…aS5b1Ft6 APcvoFYG…8ftdPTZK

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.

8.876 × 10⁹¹(92-digit number)

88765046606754985321…04728405136306496279

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

8.876 × 10⁹¹(92-digit number)

88765046606754985321…04728405136306496279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.876 × 10⁹¹(92-digit number)

88765046606754985321…04728405136306496281

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

1.775 × 10⁹²(93-digit number)

17753009321350997064…09456810272612992559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.775 × 10⁹²(93-digit number)

17753009321350997064…09456810272612992561

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

3.550 × 10⁹²(93-digit number)

35506018642701994128…18913620545225985119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.550 × 10⁹²(93-digit number)

35506018642701994128…18913620545225985121

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

7.101 × 10⁹²(93-digit number)

71012037285403988257…37827241090451970239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.101 × 10⁹²(93-digit number)

71012037285403988257…37827241090451970241

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

1.420 × 10⁹³(94-digit number)

14202407457080797651…75654482180903940479

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