Block #503,299

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/21/2014, 12:19:28 AM · Difficulty 10.8082 · 6,304,615 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

31c7f8a8a40f7abec70e43b439bb632e2ef55eee8ceb0f69eeb0eaca42d00c23

View on Chainz ↗

Height

#503,299

Difficulty

10.808159

Transactions

Size

400 B

Version

Bits

0acee380

Nonce

150,548,026

Timestamp

4/21/2014, 12:19:28 AM

Confirmations

6,304,615

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

5b13eaa7ba48b3095d953d8537fe8d8c4deb593d79aaa749eeaae4b5a91eae6e

Transactions (2)

Coinbase078fb3a839040d…8af6ac28524cf6

1 in → 1 out8.5600 XPM116 B

AbwWkWZt…kawDhufa

e2f1a099c1d628…dbce3adcc360a5

1 in → 1 out2.9919 XPM192 B

AXCNJAvq…qsPtg17V

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.

6.567 × 10⁹⁸(99-digit number)

65678493213160205101…26373163181033111679

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

6.567 × 10⁹⁸(99-digit number)

65678493213160205101…26373163181033111679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.567 × 10⁹⁸(99-digit number)

65678493213160205101…26373163181033111681

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

1.313 × 10⁹⁹(100-digit number)

13135698642632041020…52746326362066223359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.313 × 10⁹⁹(100-digit number)

13135698642632041020…52746326362066223361

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

2.627 × 10⁹⁹(100-digit number)

26271397285264082040…05492652724132446719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.627 × 10⁹⁹(100-digit number)

26271397285264082040…05492652724132446721

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

5.254 × 10⁹⁹(100-digit number)

52542794570528164081…10985305448264893439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.254 × 10⁹⁹(100-digit number)

52542794570528164081…10985305448264893441

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

1.050 × 10¹⁰⁰(101-digit number)

10508558914105632816…21970610896529786879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.050 × 10¹⁰⁰(101-digit number)

10508558914105632816…21970610896529786881

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 #503,299

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