Block #332,987

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/28/2013, 11:14:31 AM · Difficulty 10.1658 · 6,498,107 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ee55bb13cac3dc5c58ba426a1873e860b127937b855acc0746b3a914b31c9ef8

View on Chainz ↗

Height

#332,987

Difficulty

10.165804

Transactions

Size

2.92 KB

Version

Bits

0a2a7223

Nonce

199,334

Timestamp

12/28/2013, 11:14:31 AM

Confirmations

6,498,107

Mined by

⛏️ P2SHAUrHttwXxVZBKw28HWMYx9yGcGTP1uPoyR

Merkle Root

814599d891d25af038d6ad50a2e198af8dbc871e62139fd1950ff0aa980063f3

Transactions (3)

Coinbase92aee61b01247a…f1da51fd580ed1

1 in → 1 out9.7072 XPM109 B

AUrHttwX…TP1uPoyR

abaff9fe79e394…e98df1124fa6db

16 in → 1 out5.6700 XPM2.36 KB

ARjzzjSp…V1sSS15g

46e7cf1cc8cd42…0f15170664062c

2 in → 2 out6.0292 XPM374 B

AWJPWw1S…fEuT21SL ALzgu8Xw…ytvjsBEK

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.

5.821 × 10¹⁰¹(102-digit number)

58219951144026050268…70884444813139132799

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

5.821 × 10¹⁰¹(102-digit number)

58219951144026050268…70884444813139132799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.821 × 10¹⁰¹(102-digit number)

58219951144026050268…70884444813139132801

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

1.164 × 10¹⁰²(103-digit number)

11643990228805210053…41768889626278265599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.164 × 10¹⁰²(103-digit number)

11643990228805210053…41768889626278265601

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

2.328 × 10¹⁰²(103-digit number)

23287980457610420107…83537779252556531199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.328 × 10¹⁰²(103-digit number)

23287980457610420107…83537779252556531201

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

4.657 × 10¹⁰²(103-digit number)

46575960915220840214…67075558505113062399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.657 × 10¹⁰²(103-digit number)

46575960915220840214…67075558505113062401

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

9.315 × 10¹⁰²(103-digit number)

93151921830441680429…34151117010226124799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.315 × 10¹⁰²(103-digit number)

93151921830441680429…34151117010226124801

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 #332,987

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