Block #75,909

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 7:58:56 PM · Difficulty 9.0526 · 6,717,555 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

86cc18c34dc51478e15dd7d475e1e3b02a5ba13bc94cf14ecd2b981faa5b336d

View on Chainz ↗

Height

#75,909

Difficulty

9.052572

Transactions

Size

361 B

Version

Bits

090d755c

Nonce

Timestamp

7/21/2013, 7:58:56 PM

Confirmations

6,717,555

Merkle Root

bec1e62212ae65cd10b6bbb5dde91463f502f3298ea289813f5ad61f7287f830

Transactions (2)

Coinbaseba119150b77773…ad8f5be6a1a7fb

1 in → 1 out12.2000 XPM110 B

AGCUbq6M…QSxWg1oL

d4959087f5eda4…b8bfa6f30cac83

1 in → 1 out12.3300 XPM157 B

AaGrdg3x…FpKQ8mir

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.

1.617 × 10¹⁰³(104-digit number)

16173075901310427299…35044958863155079399

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

1.617 × 10¹⁰³(104-digit number)

16173075901310427299…35044958863155079399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.617 × 10¹⁰³(104-digit number)

16173075901310427299…35044958863155079401

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

3.234 × 10¹⁰³(104-digit number)

32346151802620854598…70089917726310158799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.234 × 10¹⁰³(104-digit number)

32346151802620854598…70089917726310158801

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

6.469 × 10¹⁰³(104-digit number)

64692303605241709197…40179835452620317599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.469 × 10¹⁰³(104-digit number)

64692303605241709197…40179835452620317601

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

1.293 × 10¹⁰⁴(105-digit number)

12938460721048341839…80359670905240635199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.293 × 10¹⁰⁴(105-digit number)

12938460721048341839…80359670905240635201

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

2.587 × 10¹⁰⁴(105-digit number)

25876921442096683679…60719341810481270399

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