Block #119,295

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/16/2013, 9:30:33 AM · Difficulty 9.7493 · 6,685,818 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2a6138d261b3120b125af18150c2a6586d0dffc0f1f6dde7ffdddbbc660d376b

View on Chainz ↗

Height

#119,295

Difficulty

9.749339

Transactions

Size

2.16 KB

Version

Bits

09bfd4a9

Nonce

292,685

Timestamp

8/16/2013, 9:30:33 AM

Confirmations

6,685,818

Mined by

⛏️ P2SHAbERMcutQDScg9DXkU4LAqx7CDQQKtkzeK

Merkle Root

88d01d6c77ad8215a574d5e4985dfefc37477df16136e52a559e0836eb89db01

Transactions (4)

Coinbasebdb29ee69b6f6b…cf2b696af05c64

1 in → 1 out10.5400 XPM109 B

AbERMcut…QQKtkzeK

77027528507311…26087b8e38a5c8

6 in → 2 out341.4489 XPM964 B

AcUdH9ys…k7Gqm7WE APUdBjGb…SXkyndBG

44a6b581e42ad1…878acd8cc6cd47

5 in → 2 out30.0110 XPM817 B

AYB73UfH…JsKJfL5E ANqNwUfL…YR8u7wDQ

d0740e274206ad…7f23ce6c334b1c

1 in → 2 out3.3047 XPM226 B

AJv5WoqT…tqCRQqFk Ab6tZpey…Hv1Dh677

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.

3.135 × 10⁹⁸(99-digit number)

31355379086523709428…57190265916157591819

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

3.135 × 10⁹⁸(99-digit number)

31355379086523709428…57190265916157591819

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.135 × 10⁹⁸(99-digit number)

31355379086523709428…57190265916157591821

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

6.271 × 10⁹⁸(99-digit number)

62710758173047418857…14380531832315183639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.271 × 10⁹⁸(99-digit number)

62710758173047418857…14380531832315183641

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

1.254 × 10⁹⁹(100-digit number)

12542151634609483771…28761063664630367279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.254 × 10⁹⁹(100-digit number)

12542151634609483771…28761063664630367281

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

2.508 × 10⁹⁹(100-digit number)

25084303269218967542…57522127329260734559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.508 × 10⁹⁹(100-digit number)

25084303269218967542…57522127329260734561

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

5.016 × 10⁹⁹(100-digit number)

50168606538437935085…15044254658521469119

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