Block #489,680

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/13/2014, 10:38:09 AM · Difficulty 10.6678 · 6,320,060 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d58daff3371e2babd8851ca9bafd7f78e1fd755b6d3f1e16cfc2ae11d8f8f3c5

View on Chainz ↗

Height

#489,680

Difficulty

10.667831

Transactions

Size

853 B

Version

Bits

0aaaf6f6

Nonce

714,781,083

Timestamp

4/13/2014, 10:38:09 AM

Confirmations

6,320,060

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

d2e4dbf17ce3f5b5ebfe8c1c94b6095cea32dc9d6c0d2814ed670bf902be739f

Transactions (4)

Coinbase589dddfe9e0724…5a4b509a762fef

1 in → 1 out8.8032 XPM116 B

AbwWkWZt…kawDhufa

fbaebd6d986ce3…528906c02a7e10

1 in → 2 out8.8300 XPM227 B

AMcYamcU…TBcJQ9Cx AKTEP1Kj…WMNi2PX3

5d0a80c2839c40…670e78a59252c4

1 in → 1 out2.9900 XPM192 B

AKM55Mo9…bysT2sro

69cab65f8fa9fe…2dbe00e368001f

1 in → 2 out7.3078 XPM226 B

AXzpqNSy…k7EXAc7N AKfLMCY5…LdMKEvCN

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.

1.805 × 10¹⁰⁰(101-digit number)

18058101791299233618…56322439881383423999

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

1.805 × 10¹⁰⁰(101-digit number)

18058101791299233618…56322439881383423999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.805 × 10¹⁰⁰(101-digit number)

18058101791299233618…56322439881383424001

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

3.611 × 10¹⁰⁰(101-digit number)

36116203582598467237…12644879762766847999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.611 × 10¹⁰⁰(101-digit number)

36116203582598467237…12644879762766848001

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

7.223 × 10¹⁰⁰(101-digit number)

72232407165196934474…25289759525533695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.223 × 10¹⁰⁰(101-digit number)

72232407165196934474…25289759525533696001

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

1.444 × 10¹⁰¹(102-digit number)

14446481433039386894…50579519051067391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.444 × 10¹⁰¹(102-digit number)

14446481433039386894…50579519051067392001

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

2.889 × 10¹⁰¹(102-digit number)

28892962866078773789…01159038102134783999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.889 × 10¹⁰¹(102-digit number)

28892962866078773789…01159038102134784001

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 #489,680

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