Block #1,442,837

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2016, 11:03:03 PM · Difficulty 10.7600 · 5,391,057 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4a702591b0d9ecd0ee1e47542a31459ffba697ad4860c65663fb0bb35078a4ab

View on Chainz ↗

Height

#1,442,837

Difficulty

10.759950

Transactions

Size

832 B

Version

Bits

0ac28c16

Nonce

1,839,059,038

Timestamp

2/4/2016, 11:03:03 PM

Confirmations

5,391,057

Mined by

⛏️ P2SHAdPrJ4sPTn3bEqbLt9o7ENQqZq2CchBLSV

Merkle Root

fe8750e1ffffa44b794c87ae6a03af2ead40b2c3d8408fedbb96e034cd423e9f

Transactions (2)

Coinbase91724ad46d97d1…5676961f02714b

1 in → 1 out8.6300 XPM109 B

AdPrJ4sP…2CchBLSV

4e7102e3605a13…01b48559c8da6f

1 in → 14 out48.0408 XPM633 B

APXgoiYr…DPoJr5zt AFqPR7E5…vqB4Fc6t Ac3qDtW5…8bYZSGfW AR948gVq…y7uqPqsK AGfTDXLr…hSfQKKfi

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.

2.500 × 10⁹⁵(96-digit number)

25008519335616017364…03505013138661883519

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

2.500 × 10⁹⁵(96-digit number)

25008519335616017364…03505013138661883519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.500 × 10⁹⁵(96-digit number)

25008519335616017364…03505013138661883521

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

5.001 × 10⁹⁵(96-digit number)

50017038671232034729…07010026277323767039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.001 × 10⁹⁵(96-digit number)

50017038671232034729…07010026277323767041

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

1.000 × 10⁹⁶(97-digit number)

10003407734246406945…14020052554647534079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.000 × 10⁹⁶(97-digit number)

10003407734246406945…14020052554647534081

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

2.000 × 10⁹⁶(97-digit number)

20006815468492813891…28040105109295068159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.000 × 10⁹⁶(97-digit number)

20006815468492813891…28040105109295068161

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

4.001 × 10⁹⁶(97-digit number)

40013630936985627783…56080210218590136319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.001 × 10⁹⁶(97-digit number)

40013630936985627783…56080210218590136321

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

Block #1,442,837

Cookie Preferences