Block #65,939

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 2:50:33 PM · Difficulty 8.9852 · 6,728,248 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

504d32aba633027caaac3a88ee1981ff333eb38a98ce41ffeca57fb70f91fb21

View on Chainz ↗

Height

#65,939

Difficulty

8.985195

Transactions

Size

361 B

Version

Bits

08fc35c4

Nonce

602

Timestamp

7/19/2013, 2:50:33 PM

Confirmations

6,728,248

Merkle Root

070bb989045af28f1ecb045ba13a1fd5cd160ca745997533c255aa92210f5431

Transactions (2)

Coinbase6c8954c1025bd8…c76c52902fef99

1 in → 1 out12.3800 XPM110 B

AJVLsmYD…DBgrZCRH

cbf8bcf6526504…3a98ed2af47872

1 in → 1 out12.3900 XPM157 B

AVArYEfV…KwFb28Bd

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.

8.555 × 10¹⁰³(104-digit number)

85556322908665453115…34964663029550286029

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

8.555 × 10¹⁰³(104-digit number)

85556322908665453115…34964663029550286029

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.555 × 10¹⁰³(104-digit number)

85556322908665453115…34964663029550286031

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

1.711 × 10¹⁰⁴(105-digit number)

17111264581733090623…69929326059100572059

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.711 × 10¹⁰⁴(105-digit number)

17111264581733090623…69929326059100572061

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

3.422 × 10¹⁰⁴(105-digit number)

34222529163466181246…39858652118201144119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.422 × 10¹⁰⁴(105-digit number)

34222529163466181246…39858652118201144121

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

6.844 × 10¹⁰⁴(105-digit number)

68445058326932362492…79717304236402288239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.844 × 10¹⁰⁴(105-digit number)

68445058326932362492…79717304236402288241

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

1.368 × 10¹⁰⁵(106-digit number)

13689011665386472498…59434608472804576479

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