Block #41,488

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 4:44:31 PM · Difficulty 8.5287 · 6,748,184 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

31e491df87a7d1877242870c5a476cda561c52d72de19a743e3ecc80f5d57394

View on Chainz ↗

Height

#41,488

Difficulty

8.528748

Transactions

Size

200 B

Version

Bits

08875c02

Nonce

168

Timestamp

7/14/2013, 4:44:31 PM

Confirmations

6,748,184

Merkle Root

5ae528d0da40b4a1118b6f2e73d3eacf5aa366372e12e7ebc3b31f209658cfaf

Transactions (1)

Coinbase5ae528d0da40b4…b31f209658cfaf

1 in → 1 out13.7300 XPM110 B

AUBa4jPW…r2keVjVD

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.

1.390 × 10⁹⁴(95-digit number)

13905028701264980393…37263080843091145459

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

1.390 × 10⁹⁴(95-digit number)

13905028701264980393…37263080843091145459

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.390 × 10⁹⁴(95-digit number)

13905028701264980393…37263080843091145461

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

2.781 × 10⁹⁴(95-digit number)

27810057402529960787…74526161686182290919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.781 × 10⁹⁴(95-digit number)

27810057402529960787…74526161686182290921

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

5.562 × 10⁹⁴(95-digit number)

55620114805059921575…49052323372364581839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.562 × 10⁹⁴(95-digit number)

55620114805059921575…49052323372364581841

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

1.112 × 10⁹⁵(96-digit number)

11124022961011984315…98104646744729163679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.112 × 10⁹⁵(96-digit number)

11124022961011984315…98104646744729163681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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