Block #2,596,057

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/1/2018, 11:10:44 PM · Difficulty 11.3025 · 4,246,758 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

06a5584a3a9bccfaaf3f7b8b69dd04ba3930adacd954cacfa43190e793cf8d89

View on Chainz ↗

Height

#2,596,057

Difficulty

11.302516

Transactions

Size

1.57 KB

Version

Bits

0b4d71ae

Nonce

1,150,123,173

Timestamp

4/1/2018, 11:10:44 PM

Confirmations

4,246,758

Mined by

⛏️ P2SHALjdoR9LmEKkJw8G2KdgiyNnjRe9AAicuv

Merkle Root

5c2d341ae666a7f797945045dd8e69e544dc28ec145f99034a22511a608adac2

Transactions (2)

Coinbase09550f59bedccd…00adc0b5946eb5

1 in → 1 out7.8400 XPM110 B

ALjdoR9L…e9AAicuv

7d9b9d17d73d41…2a621407890aa4

9 in → 2 out80.6500 XPM1.38 KB

AWJbjFzy…6j3zUWLU ASrXvKkC…LXAYuKos

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.

3.343 × 10⁹⁵(96-digit number)

33439926979794121741…40148104871241896959

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

3.343 × 10⁹⁵(96-digit number)

33439926979794121741…40148104871241896959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.343 × 10⁹⁵(96-digit number)

33439926979794121741…40148104871241896961

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

6.687 × 10⁹⁵(96-digit number)

66879853959588243482…80296209742483793919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.687 × 10⁹⁵(96-digit number)

66879853959588243482…80296209742483793921

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

1.337 × 10⁹⁶(97-digit number)

13375970791917648696…60592419484967587839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.337 × 10⁹⁶(97-digit number)

13375970791917648696…60592419484967587841

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

2.675 × 10⁹⁶(97-digit number)

26751941583835297392…21184838969935175679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.675 × 10⁹⁶(97-digit number)

26751941583835297392…21184838969935175681

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

5.350 × 10⁹⁶(97-digit number)

53503883167670594785…42369677939870351359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.350 × 10⁹⁶(97-digit number)

53503883167670594785…42369677939870351361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.070 × 10⁹⁷(98-digit number)

10700776633534118957…84739355879740702719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,596,057

Cookie Preferences