Block #3,288,886

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/31/2019, 5:09:33 AM · Difficulty 10.9947 · 3,554,267 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

33b0d616ff40c6847f082d9631a7ec185590dee9b99fedb38656d950aa56e584

View on Chainz ↗

Height

#3,288,886

Difficulty

10.994719

Transactions

Size

1.43 KB

Version

Bits

0afea5e7

Nonce

484,483,647

Timestamp

7/31/2019, 5:09:33 AM

Confirmations

3,554,267

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

6cb13dee61c40dc281ca1b428bf2a2ae9121f1245c636e34bc40b2b383a18080

Transactions (2)

Coinbased5766a0ea62b94…cc8d4c7ebfdc96

1 in → 1 out8.2800 XPM109 B

ASiq2qtK…VMhmk7yL

b24e889ff72e0a…a1f9f9c0b99c4b

8 in → 2 out123.8443 XPM1.23 KB

ALPhqDWq…8HHmYGkx AbTmPKJC…b8MHxnG9

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.

1.274 × 10⁹⁷(98-digit number)

12749454442732687519…95300468751586918399

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

1.274 × 10⁹⁷(98-digit number)

12749454442732687519…95300468751586918399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.274 × 10⁹⁷(98-digit number)

12749454442732687519…95300468751586918401

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

2.549 × 10⁹⁷(98-digit number)

25498908885465375039…90600937503173836799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.549 × 10⁹⁷(98-digit number)

25498908885465375039…90600937503173836801

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

5.099 × 10⁹⁷(98-digit number)

50997817770930750079…81201875006347673599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.099 × 10⁹⁷(98-digit number)

50997817770930750079…81201875006347673601

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

1.019 × 10⁹⁸(99-digit number)

10199563554186150015…62403750012695347199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.019 × 10⁹⁸(99-digit number)

10199563554186150015…62403750012695347201

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

2.039 × 10⁹⁸(99-digit number)

20399127108372300031…24807500025390694399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.039 × 10⁹⁸(99-digit number)

20399127108372300031…24807500025390694401

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

4.079 × 10⁹⁸(99-digit number)

40798254216744600063…49615000050781388799

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 #3,288,886

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