Block #479,232

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/7/2014, 1:41:20 PM · Difficulty 10.5038 · 6,324,387 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

50162d8df005c025fdf7007e59af62f4adc9c8269bc7d11a34bfe94329dfd289

View on Chainz ↗

Height

#479,232

Difficulty

10.503784

Transactions

Size

1.15 KB

Version

Bits

0a80f7fc

Nonce

17,710

Timestamp

4/7/2014, 1:41:20 PM

Confirmations

6,324,387

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

a1bc7fc51ad29859e7a3c549b24ef700e5239d1082b60b0469031100b40a963b

Transactions (4)

Coinbase4fdac0b68c0dce…e0df260b5bf363

1 in → 1 out9.0800 XPM116 B

AbwWkWZt…kawDhufa

ee640c84359f6a…16d4d31abd5d17

1 in → 2 out9.1000 XPM226 B

AN3nya1T…UXi1ys96 AGmK8DBz…xEmFc4aW

ab1a256f0d3eb0…7b05d1ccc617ff

1 in → 2 out8.0993 XPM226 B

Ac3adS2S…va6hWeMv APPwEhT6…qEkaiWra

e6f0e77dce5923…e6da3171c473aa

3 in → 2 out0.5174 XPM521 B

ARENd3V6…66TeRsPd AGQQpCHD…4jHRpYRE

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.

1.293 × 10¹⁰⁰(101-digit number)

12939033023269643930…33690986157310815999

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

1.293 × 10¹⁰⁰(101-digit number)

12939033023269643930…33690986157310815999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.293 × 10¹⁰⁰(101-digit number)

12939033023269643930…33690986157310816001

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

2.587 × 10¹⁰⁰(101-digit number)

25878066046539287861…67381972314621631999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.587 × 10¹⁰⁰(101-digit number)

25878066046539287861…67381972314621632001

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

5.175 × 10¹⁰⁰(101-digit number)

51756132093078575723…34763944629243263999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.175 × 10¹⁰⁰(101-digit number)

51756132093078575723…34763944629243264001

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

1.035 × 10¹⁰¹(102-digit number)

10351226418615715144…69527889258486527999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.035 × 10¹⁰¹(102-digit number)

10351226418615715144…69527889258486528001

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

2.070 × 10¹⁰¹(102-digit number)

20702452837231430289…39055778516973055999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.070 × 10¹⁰¹(102-digit number)

20702452837231430289…39055778516973056001

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