Block #569,791

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/31/2014, 9:31:39 AM · Difficulty 10.9647 · 6,226,208 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6866d043f184d9392ef5a881d5f97080fa51dd1d9cabd4ecfc7d2055577c183b

View on Chainz ↗

Height

#569,791

Difficulty

10.964733

Transactions

Size

1.65 KB

Version

Bits

0af6f8b6

Nonce

164,630,687

Timestamp

5/31/2014, 9:31:39 AM

Confirmations

6,226,208

Mined by

⛏️ P2SHAPzrwuRffpQEeV7qSvnghZnGTV3pUWpyUV

Merkle Root

0ad62a061625742d5ae3eff122eeb1a7c9e965b7ffb40e3bff855866ff4b92a6

Transactions (3)

Coinbase943708a1928187…c327639a822f74

1 in → 1 out8.3300 XPM109 B

APzrwuRf…3pUWpyUV

959d4328a12d6a…32792b075666b9

8 in → 2 out50.2167 XPM1.23 KB

AYiZQoDZ…6FrUMoub AasxZbg6…314MLCt3

e46802e3acb460…8c8ce239a0fb6c

1 in → 2 out6.6890 XPM227 B

AcVexCzF…SY75pd2v AR2kKDJL…n12Uf4VZ

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.

3.350 × 10⁹⁷(98-digit number)

33508494207979352575…03870071844346521599

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

3.350 × 10⁹⁷(98-digit number)

33508494207979352575…03870071844346521599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.350 × 10⁹⁷(98-digit number)

33508494207979352575…03870071844346521601

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

6.701 × 10⁹⁷(98-digit number)

67016988415958705150…07740143688693043199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.701 × 10⁹⁷(98-digit number)

67016988415958705150…07740143688693043201

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

1.340 × 10⁹⁸(99-digit number)

13403397683191741030…15480287377386086399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.340 × 10⁹⁸(99-digit number)

13403397683191741030…15480287377386086401

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

2.680 × 10⁹⁸(99-digit number)

26806795366383482060…30960574754772172799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.680 × 10⁹⁸(99-digit number)

26806795366383482060…30960574754772172801

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

5.361 × 10⁹⁸(99-digit number)

53613590732766964120…61921149509544345599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.361 × 10⁹⁸(99-digit number)

53613590732766964120…61921149509544345601

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

1.072 × 10⁹⁹(100-digit number)

10722718146553392824…23842299019088691199

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