Block #1,410,423

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2016, 5:07:37 PM · Difficulty 10.8045 · 5,414,358 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cf03153dc2a2579f4ad102be755d3c5d6d228ed067ae0fd22940c6a84ad20e03

View on Chainz ↗

Height

#1,410,423

Difficulty

10.804528

Transactions

Size

1.01 KB

Version

Bits

0acdf58b

Nonce

1,024,468,621

Timestamp

1/12/2016, 5:07:37 PM

Confirmations

5,414,358

Mined by

⛏️ P2SHAQKQGiRjpACHWEEsiCmaRoJHW8iuqoTfpE

Merkle Root

c91040512dea2d5ae45c307f514624b60b24931fdcd8580b3553134d75554d84

Transactions (2)

Coinbase67fb5ca90e4d73…7ca0d047f143ae

1 in → 1 out8.5600 XPM109 B

AQKQGiRj…iuqoTfpE

9ce38e4702e6e7…95c795e9113ed0

1 in → 20 out45.4633 XPM838 B

AcPE5uxb…DWsxDifC AX9xnpbA…3aGRUYJc AGfTDXLr…hSfQKKfi AGskjDpg…pYnEzeYR AVEYJtbR…Zqkssptv

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.

2.822 × 10⁹⁸(99-digit number)

28223376446055015066…44884096316913418239

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

2.822 × 10⁹⁸(99-digit number)

28223376446055015066…44884096316913418239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.822 × 10⁹⁸(99-digit number)

28223376446055015066…44884096316913418241

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

5.644 × 10⁹⁸(99-digit number)

56446752892110030133…89768192633826836479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.644 × 10⁹⁸(99-digit number)

56446752892110030133…89768192633826836481

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

1.128 × 10⁹⁹(100-digit number)

11289350578422006026…79536385267653672959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.128 × 10⁹⁹(100-digit number)

11289350578422006026…79536385267653672961

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

2.257 × 10⁹⁹(100-digit number)

22578701156844012053…59072770535307345919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.257 × 10⁹⁹(100-digit number)

22578701156844012053…59072770535307345921

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

4.515 × 10⁹⁹(100-digit number)

45157402313688024106…18145541070614691839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.515 × 10⁹⁹(100-digit number)

45157402313688024106…18145541070614691841

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 #1,410,423

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