Block #34,919

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 7:14:58 AM · Difficulty 7.9939 · 6,758,651 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e8b2f14f54ee655192e4e739d425f3d739e69ca97f7b694f01c95e5e7d4c469a

View on Chainz ↗

Height

#34,919

Difficulty

7.993856

Transactions

Size

197 B

Version

Bits

07fe6d5d

Nonce

226

Timestamp

7/14/2013, 7:14:58 AM

Confirmations

6,758,651

Merkle Root

8a080e7bbd78b61ac39a455dc27f759394328f0e3532d27c22d1e26d7c8910b8

Transactions (1)

Coinbase8a080e7bbd78b6…d1e26d7c8910b8

1 in → 1 out15.6300 XPM109 B

AV5orpg7…1a8XXi2s

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.

1.687 × 10⁹⁰(91-digit number)

16871986589843053419…32355532908434166579

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

1.687 × 10⁹⁰(91-digit number)

16871986589843053419…32355532908434166579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.687 × 10⁹⁰(91-digit number)

16871986589843053419…32355532908434166581

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

3.374 × 10⁹⁰(91-digit number)

33743973179686106839…64711065816868333159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.374 × 10⁹⁰(91-digit number)

33743973179686106839…64711065816868333161

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

6.748 × 10⁹⁰(91-digit number)

67487946359372213679…29422131633736666319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.748 × 10⁹⁰(91-digit number)

67487946359372213679…29422131633736666321

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

1.349 × 10⁹¹(92-digit number)

13497589271874442735…58844263267473332639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.349 × 10⁹¹(92-digit number)

13497589271874442735…58844263267473332641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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