Block #2,801,989

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/20/2018, 9:47:52 AM · Difficulty 11.6712 · 4,040,738 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

157c8d6b41404ec2edafbc33e50336ecf47dc01ae7386be27f2a84acc2e2f74a

View on Chainz ↗

Height

#2,801,989

Difficulty

11.671226

Transactions

Size

1.72 KB

Version

Bits

0babd57d

Nonce

315,832,205

Timestamp

8/20/2018, 9:47:52 AM

Confirmations

4,040,738

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

5a3cc2646a2fb6428bf6b6642477ac5c07f36398331e75e82238db60b1e89bfc

Transactions (4)

Coinbasec63ec173a08f0c…f33af3c56f4a88

1 in → 1 out7.3600 XPM110 B

AZtxQr2F…7grUWrUz

3706a5111b7d2c…de027c3489ce1f

3 in → 2 out4.0400 XPM522 B

AZZ9SgYa…gb75k9v4 ARazkg1a…gNfgNwtK

88daf9447cc90b…6ed48ee2e76b0c

2 in → 2 out4.5200 XPM374 B

Ac46JApH…3bgULjJC AQHYSriJ…yYamv6o2

d7fbe959e828d3…4fa308366bf8a6

4 in → 2 out4.3300 XPM669 B

ASBfNz5M…SGi4McxW AZiXxXty…AFv43CYF

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.

5.538 × 10⁹⁷(98-digit number)

55385294834185411380…79268751219420159999

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

5.538 × 10⁹⁷(98-digit number)

55385294834185411380…79268751219420159999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.538 × 10⁹⁷(98-digit number)

55385294834185411380…79268751219420160001

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

1.107 × 10⁹⁸(99-digit number)

11077058966837082276…58537502438840319999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.107 × 10⁹⁸(99-digit number)

11077058966837082276…58537502438840320001

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

2.215 × 10⁹⁸(99-digit number)

22154117933674164552…17075004877680639999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.215 × 10⁹⁸(99-digit number)

22154117933674164552…17075004877680640001

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

4.430 × 10⁹⁸(99-digit number)

44308235867348329104…34150009755361279999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.430 × 10⁹⁸(99-digit number)

44308235867348329104…34150009755361280001

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

8.861 × 10⁹⁸(99-digit number)

88616471734696658208…68300019510722559999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.861 × 10⁹⁸(99-digit number)

88616471734696658208…68300019510722560001

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

1.772 × 10⁹⁹(100-digit number)

17723294346939331641…36600039021445119999

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 #2,801,989

Cookie Preferences