Block #203,737

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/11/2013, 1:22:55 AM · Difficulty 9.8975 · 6,605,973 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3b8e1c60fe90665325ddcf02a3c545941250eb62f38b17546903a9f6bd9302a1

View on Chainz ↗

Height

#203,737

Difficulty

9.897516

Transactions

Size

425 B

Version

Bits

09e5c39d

Nonce

21,892

Timestamp

10/11/2013, 1:22:55 AM

Confirmations

6,605,973

Mined by

⛏️ P2SHANr2BTuR2dZQ7zj1p5e7reb7UNcvZLCKVf

Merkle Root

6d4d2e6149ccb5aec0d57c3f19fcc871dec92fe9c621976eeb31519d63e6ec10

Transactions (2)

Coinbasef04e06637b8c36…d64e6440c9b342

1 in → 1 out10.2000 XPM109 B

ANr2BTuR…cvZLCKVf

00711d7cb325d8…318dbb1cb71554

1 in → 2 out8.1627 XPM226 B

ATC9nney…J3LRZ8XP AP4fYrWf…QKVzAUtY

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.

4.106 × 10⁹⁴(95-digit number)

41064900934437970475…71305149796536550399

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

4.106 × 10⁹⁴(95-digit number)

41064900934437970475…71305149796536550399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.106 × 10⁹⁴(95-digit number)

41064900934437970475…71305149796536550401

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

8.212 × 10⁹⁴(95-digit number)

82129801868875940950…42610299593073100799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.212 × 10⁹⁴(95-digit number)

82129801868875940950…42610299593073100801

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

1.642 × 10⁹⁵(96-digit number)

16425960373775188190…85220599186146201599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.642 × 10⁹⁵(96-digit number)

16425960373775188190…85220599186146201601

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

3.285 × 10⁹⁵(96-digit number)

32851920747550376380…70441198372292403199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.285 × 10⁹⁵(96-digit number)

32851920747550376380…70441198372292403201

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

6.570 × 10⁹⁵(96-digit number)

65703841495100752760…40882396744584806399

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

Block #203,737

Cookie Preferences