Block #303,870

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/10/2013, 2:57:10 PM · Difficulty 9.9932 · 6,491,970 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9bb62e21bc7511b75eb6a43a559e614432076d0f932ce7335bfcf1e07229d1b1

View on Chainz ↗

Height

#303,870

Difficulty

9.993152

Transactions

Size

1.14 KB

Version

Bits

09fe3f3d

Nonce

283,137

Timestamp

12/10/2013, 2:57:10 PM

Confirmations

6,491,970

Mined by

⛏️ aR+APeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

527fac382088172ac028571c60ded4a0fe9aba3c02abbee9d9972d9c01818af1

Transactions (1)

Coinbase527fac38208817…972d9c01818af1

1 in → 30 out9.9800 XPM1.06 KB

APeshfYV…3PKcKMKH AHuJ9wYh…BGmgHrKZ AZ2pPuKg…95SN2Yr7 AG5YAjec…VhA4Aeh1 AKwqFUdz…D4jGNKFN

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.

9.932 × 10⁹²(93-digit number)

99320857490749599938…74421057560054394019

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

9.932 × 10⁹²(93-digit number)

99320857490749599938…74421057560054394019

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.932 × 10⁹²(93-digit number)

99320857490749599938…74421057560054394021

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

1.986 × 10⁹³(94-digit number)

19864171498149919987…48842115120108788039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.986 × 10⁹³(94-digit number)

19864171498149919987…48842115120108788041

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

3.972 × 10⁹³(94-digit number)

39728342996299839975…97684230240217576079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.972 × 10⁹³(94-digit number)

39728342996299839975…97684230240217576081

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

7.945 × 10⁹³(94-digit number)

79456685992599679950…95368460480435152159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.945 × 10⁹³(94-digit number)

79456685992599679950…95368460480435152161

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

1.589 × 10⁹⁴(95-digit number)

15891337198519935990…90736920960870304319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.589 × 10⁹⁴(95-digit number)

15891337198519935990…90736920960870304321

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