Block #303,013

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/10/2013, 3:33:47 AM · Difficulty 9.9929 · 6,503,566 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8e611d557a65ecbec899de6a81bf7c30e9646379f5bcc6aa5e18b328c5ee1ce5

View on Chainz ↗

Height

#303,013

Difficulty

9.992884

Transactions

Size

2.12 KB

Version

Bits

09fe2daa

Nonce

154,839

Timestamp

12/10/2013, 3:33:47 AM

Confirmations

6,503,566

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

f8ea4e96b29fa9eedc388bbc1c30add0a1c60c74f1feb5d17c147c4b269afe0d

Transactions (4)

Coinbase7c39bb03897647…a941039d48d5bd

1 in → 1 out10.0310 XPM110 B

AeKNrjNj…1NEq95Ta

53c268d6405f29…76c6996a6f2c96

2 in → 2 out6.0175 XPM373 B

AaiGjyH2…RXFSRgFo Ab9dCnMQ…usp9ZTvC

dc47e46bb9c95e…32be30947054bc

4 in → 1 out0.9349 XPM634 B

AP3ojtPV…2kXNSjcE

4678348f2349dc…f33a36fc8216e3

6 in → 2 out6.0978 XPM965 B

AXrbrphP…49DT6Y8t AcbJ8wQu…ZcjKDhxX

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.

1.323 × 10⁹³(94-digit number)

13234909667300338336…65663555414348373919

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

1.323 × 10⁹³(94-digit number)

13234909667300338336…65663555414348373919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.323 × 10⁹³(94-digit number)

13234909667300338336…65663555414348373921

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

2.646 × 10⁹³(94-digit number)

26469819334600676672…31327110828696747839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.646 × 10⁹³(94-digit number)

26469819334600676672…31327110828696747841

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

5.293 × 10⁹³(94-digit number)

52939638669201353344…62654221657393495679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.293 × 10⁹³(94-digit number)

52939638669201353344…62654221657393495681

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

1.058 × 10⁹⁴(95-digit number)

10587927733840270668…25308443314786991359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.058 × 10⁹⁴(95-digit number)

10587927733840270668…25308443314786991361

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

2.117 × 10⁹⁴(95-digit number)

21175855467680541337…50616886629573982719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.117 × 10⁹⁴(95-digit number)

21175855467680541337…50616886629573982721

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 #303,013

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