Block #29,290

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 3:02:37 PM · Difficulty 7.9843 · 6,780,365 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

89d8f3ed8e86a2dea7bbffbd87ca54fd625aac4eee4d572f2bc59a1278ef402d

View on Chainz ↗

Height

#29,290

Difficulty

7.984250

Transactions

Size

199 B

Version

Bits

07fbf7d3

Nonce

403

Timestamp

7/13/2013, 3:02:37 PM

Confirmations

6,780,365

Mined by

⛏️ P2SHAKSwr9eUsXtYAeGKZ6MmF96jvsdLNxuVyn

Merkle Root

691285bc89eacabcd9cc66ebc088e376765956fc68f7429f9dc5b45bbdcf89b1

Transactions (1)

Coinbase691285bc89eaca…c5b45bbdcf89b1

1 in → 1 out15.6700 XPM108 B

AKSwr9eU…dLNxuVyn

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.

2.022 × 10⁹⁸(99-digit number)

20223683464993385521…55263007944755549659

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

2.022 × 10⁹⁸(99-digit number)

20223683464993385521…55263007944755549659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.022 × 10⁹⁸(99-digit number)

20223683464993385521…55263007944755549661

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

4.044 × 10⁹⁸(99-digit number)

40447366929986771043…10526015889511099319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.044 × 10⁹⁸(99-digit number)

40447366929986771043…10526015889511099321

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

8.089 × 10⁹⁸(99-digit number)

80894733859973542087…21052031779022198639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.089 × 10⁹⁸(99-digit number)

80894733859973542087…21052031779022198641

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

1.617 × 10⁹⁹(100-digit number)

16178946771994708417…42104063558044397279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.617 × 10⁹⁹(100-digit number)

16178946771994708417…42104063558044397281

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

Block #29,290

Cookie Preferences