Block #3,489,727

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/26/2019, 6:38:39 AM · Difficulty 10.9651 · 3,352,474 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3cf2bb2a22a5b9ca3ce202342bd265372a2effe108b1431c0457f298b36f1650

View on Chainz ↗

Height

#3,489,727

Difficulty

10.965127

Transactions

Size

9.09 KB

Version

Bits

0af71292

Nonce

1,466,146,283

Timestamp

12/26/2019, 6:38:39 AM

Confirmations

3,352,474

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

ebe33c67325d466d56b89691a9e2cafaf742d7a80d5022988e0074fa4581e05e

Transactions (2)

Coinbase918c38aecb7189…4f06e8e6e70f4c

1 in → 1 out8.4000 XPM110 B

ASiq2qtK…VMhmk7yL

279d33e98db208…eb8fa277a95bdc

61 in → 2 out2365.3868 XPM8.89 KB

APm6jmiZ…ChwyddNY Aa5tsfcw…2KX6NT4z

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.

5.805 × 10⁹⁶(97-digit number)

58057633275707759069…21393222874869186559

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

5.805 × 10⁹⁶(97-digit number)

58057633275707759069…21393222874869186559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.805 × 10⁹⁶(97-digit number)

58057633275707759069…21393222874869186561

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

1.161 × 10⁹⁷(98-digit number)

11611526655141551813…42786445749738373119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.161 × 10⁹⁷(98-digit number)

11611526655141551813…42786445749738373121

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

2.322 × 10⁹⁷(98-digit number)

23223053310283103627…85572891499476746239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.322 × 10⁹⁷(98-digit number)

23223053310283103627…85572891499476746241

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

4.644 × 10⁹⁷(98-digit number)

46446106620566207255…71145782998953492479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.644 × 10⁹⁷(98-digit number)

46446106620566207255…71145782998953492481

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

9.289 × 10⁹⁷(98-digit number)

92892213241132414511…42291565997906984959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.289 × 10⁹⁷(98-digit number)

92892213241132414511…42291565997906984961

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

1.857 × 10⁹⁸(99-digit number)

18578442648226482902…84583131995813969919

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 #3,489,727

Cookie Preferences