Block #1,063,020

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/17/2015, 7:06:28 AM · Difficulty 10.7298 · 5,780,982 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

88bfdfcc7122d349b3665afdcbda23934dba54fc2f97a8e773dbf1d2a3544d6c

View on Chainz ↗

Height

#1,063,020

Difficulty

10.729845

Transactions

Size

1.15 KB

Version

Bits

0abad71c

Nonce

62,103,483

Timestamp

5/17/2015, 7:06:28 AM

Confirmations

5,780,982

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

afd98121850c800e05b3a5ef4a241b2848add84bc0ebbb6d87adec5ddf4d1dbb

Transactions (2)

Coinbase2457fc4934ed0f…177365b6ee6842

1 in → 1 out8.6800 XPM116 B

ANSXnLY2…Sd25TjkD

ca10f837d56601…2fcfb395ea98e0

6 in → 2 out49.4660 XPM967 B

ANXrRvan…qynWhSZg Aa84P6FQ…dLBxLJTC

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.

1.914 × 10¹⁰⁰(101-digit number)

19143215660896503498…10501979786878975999

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

1.914 × 10¹⁰⁰(101-digit number)

19143215660896503498…10501979786878975999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.914 × 10¹⁰⁰(101-digit number)

19143215660896503498…10501979786878976001

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

3.828 × 10¹⁰⁰(101-digit number)

38286431321793006996…21003959573757951999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.828 × 10¹⁰⁰(101-digit number)

38286431321793006996…21003959573757952001

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

7.657 × 10¹⁰⁰(101-digit number)

76572862643586013992…42007919147515903999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.657 × 10¹⁰⁰(101-digit number)

76572862643586013992…42007919147515904001

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

1.531 × 10¹⁰¹(102-digit number)

15314572528717202798…84015838295031807999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.531 × 10¹⁰¹(102-digit number)

15314572528717202798…84015838295031808001

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

3.062 × 10¹⁰¹(102-digit number)

30629145057434405597…68031676590063615999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.062 × 10¹⁰¹(102-digit number)

30629145057434405597…68031676590063616001

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 #1,063,020

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