Block #65,636

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 1:16:28 PM · Difficulty 8.9846 · 6,727,104 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a4026778b26dbc017988bda530dd5c748d12a8f770277a81a6d5d2191c130c2d

View on Chainz ↗

Height

#65,636

Difficulty

8.984563

Transactions

Size

4.41 KB

Version

Bits

08fc0c51

Nonce

Timestamp

7/19/2013, 1:16:28 PM

Confirmations

6,727,104

Merkle Root

d3dd2bbf44c9deab7c583c34a6644bc6a124cc57d96e9e7b32786c88576a8b6a

Transactions (4)

Coinbase3c3ae4c698a814…0a6c8598cf945d

1 in → 1 out12.4300 XPM110 B

AcDVkhAL…1TcTFwYe

41e286258b7efc…ed5400ed503a1d

1 in → 2 out6999.9700 XPM227 B

AVGYbnAB…ZoyYY9J3 ASSFsrKb…mVrzz8rj

1c210f872c6556…675b0127d99a62

30 in → 2 out360.8600 XPM3.48 KB

ARsrDwcp…Fv5SKr8Y AbT67voR…xAkfubm5

3b9266210d3c47…22528e6192987b

3 in → 2 out73.3437 XPM522 B

AaMV4Fet…DTAjPuix ASJ95UBq…bWLnFrdg

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.

1.141 × 10¹⁰⁰(101-digit number)

11418991530077520527…80878602202164294479

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

1.141 × 10¹⁰⁰(101-digit number)

11418991530077520527…80878602202164294479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.141 × 10¹⁰⁰(101-digit number)

11418991530077520527…80878602202164294481

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

2.283 × 10¹⁰⁰(101-digit number)

22837983060155041054…61757204404328588959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.283 × 10¹⁰⁰(101-digit number)

22837983060155041054…61757204404328588961

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

4.567 × 10¹⁰⁰(101-digit number)

45675966120310082109…23514408808657177919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.567 × 10¹⁰⁰(101-digit number)

45675966120310082109…23514408808657177921

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

9.135 × 10¹⁰⁰(101-digit number)

91351932240620164219…47028817617314355839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.135 × 10¹⁰⁰(101-digit number)

91351932240620164219…47028817617314355841

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

1.827 × 10¹⁰¹(102-digit number)

18270386448124032843…94057635234628711679

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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