Block #513,805

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/27/2014, 6:25:30 PM · Difficulty 10.8363 · 6,297,346 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4c1f00c17c8c997233537aa61d4684cfb11751addcf1ad915da3ee1857431f09

View on Chainz ↗

Height

#513,805

Difficulty

10.836345

Transactions

Size

400 B

Version

Bits

0ad61aba

Nonce

101,766,247

Timestamp

4/27/2014, 6:25:30 PM

Confirmations

6,297,346

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

e102af16a41233805f5429f10dc66646c5e2f147f52e8877c570a38f4a17fc3b

Transactions (2)

Coinbase23967242298d01…0e979748e2ba4e

1 in → 1 out8.5100 XPM116 B

AbwWkWZt…kawDhufa

e1d3db07768454…969fdeda7f31b5

1 in → 1 out2.9906 XPM192 B

AJoFY9Fp…DcoMyCAi

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.

9.174 × 10⁹⁹(100-digit number)

91748865731686391114…83421972063580211199

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

9.174 × 10⁹⁹(100-digit number)

91748865731686391114…83421972063580211199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.174 × 10⁹⁹(100-digit number)

91748865731686391114…83421972063580211201

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

1.834 × 10¹⁰⁰(101-digit number)

18349773146337278222…66843944127160422399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.834 × 10¹⁰⁰(101-digit number)

18349773146337278222…66843944127160422401

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

3.669 × 10¹⁰⁰(101-digit number)

36699546292674556445…33687888254320844799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.669 × 10¹⁰⁰(101-digit number)

36699546292674556445…33687888254320844801

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

7.339 × 10¹⁰⁰(101-digit number)

73399092585349112891…67375776508641689599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.339 × 10¹⁰⁰(101-digit number)

73399092585349112891…67375776508641689601

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

1.467 × 10¹⁰¹(102-digit number)

14679818517069822578…34751553017283379199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.467 × 10¹⁰¹(102-digit number)

14679818517069822578…34751553017283379201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #513,805

Cookie Preferences