Block #596,414

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/21/2014, 2:34:33 AM · Difficulty 10.9348 · 6,197,996 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

312efc967939e265175f498fb1fc20dbf51b010f282bac6bb4262c214eb0f9de

View on Chainz ↗

Height

#596,414

Difficulty

10.934833

Transactions

Size

583 B

Version

Bits

0aef5132

Nonce

16,642,635

Timestamp

6/21/2014, 2:34:33 AM

Confirmations

6,197,996

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

948620a4de8d3da6b1b588a8951a20852ea30869f43c3e655116b399e3df23d1

Transactions (2)

Coinbase552ff30af4fc4f…1cea625a267874

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

a13de25f40801a…985bc53feb7611

2 in → 2 out469.9254 XPM375 B

AGuisewS…kixoacNm ALjA7Gng…FgQeF66r

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.

3.116 × 10⁹⁸(99-digit number)

31165175425403357037…49035855901614028799

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

3.116 × 10⁹⁸(99-digit number)

31165175425403357037…49035855901614028799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.116 × 10⁹⁸(99-digit number)

31165175425403357037…49035855901614028801

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

6.233 × 10⁹⁸(99-digit number)

62330350850806714074…98071711803228057599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.233 × 10⁹⁸(99-digit number)

62330350850806714074…98071711803228057601

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

1.246 × 10⁹⁹(100-digit number)

12466070170161342814…96143423606456115199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.246 × 10⁹⁹(100-digit number)

12466070170161342814…96143423606456115201

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

2.493 × 10⁹⁹(100-digit number)

24932140340322685629…92286847212912230399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.493 × 10⁹⁹(100-digit number)

24932140340322685629…92286847212912230401

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

4.986 × 10⁹⁹(100-digit number)

49864280680645371259…84573694425824460799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.986 × 10⁹⁹(100-digit number)

49864280680645371259…84573694425824460801

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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