Block #303,104

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/10/2013, 4:56:28 AM · Difficulty 9.9929 · 6,494,762 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fc5bfd1d9e17955a752abec148c3dad90a3da4c6c174273499d81f88618327e1

View on Chainz ↗

Height

#303,104

Difficulty

9.992899

Transactions

Size

1.01 KB

Version

Bits

09fe2ea2

Nonce

48,640

Timestamp

12/10/2013, 4:56:28 AM

Confirmations

6,494,762

Mined by

⛏️ aRAMdvB6BSeR5j7BaEUYaiSNxidBDPq9FYdA

Merkle Root

9cf574957f85c55f4fb5529f2ccdd326611c06327ac96fefe88941a44fa71a3c

Transactions (1)

Coinbase9cf574957f85c5…8941a44fa71a3c

1 in → 26 out10.0000 XPM947 B

AMdvB6BS…DPq9FYdA ATnxsphh…CUMWquPs AMAhFBm2…B1MTCAzU AN63YyQR…1tfe566A ARjgNH4d…BU7Drh7C

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.

8.866 × 10⁹⁴(95-digit number)

88663882267632228989…31921075141147973599

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

8.866 × 10⁹⁴(95-digit number)

88663882267632228989…31921075141147973599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.866 × 10⁹⁴(95-digit number)

88663882267632228989…31921075141147973601

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

1.773 × 10⁹⁵(96-digit number)

17732776453526445797…63842150282295947199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.773 × 10⁹⁵(96-digit number)

17732776453526445797…63842150282295947201

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

3.546 × 10⁹⁵(96-digit number)

35465552907052891595…27684300564591894399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.546 × 10⁹⁵(96-digit number)

35465552907052891595…27684300564591894401

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

7.093 × 10⁹⁵(96-digit number)

70931105814105783191…55368601129183788799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.093 × 10⁹⁵(96-digit number)

70931105814105783191…55368601129183788801

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

1.418 × 10⁹⁶(97-digit number)

14186221162821156638…10737202258367577599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.418 × 10⁹⁶(97-digit number)

14186221162821156638…10737202258367577601

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