Block #1,040,983

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/1/2015, 11:52:01 PM · Difficulty 10.7289 · 5,753,290 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40d776bf5b87564c46648c5a55151c2306d392d79634988eca35a9ab1d1f513b

View on Chainz ↗

Height

#1,040,983

Difficulty

10.728866

Transactions

Size

581 B

Version

Bits

0aba96ef

Nonce

1,273,071,346

Timestamp

5/1/2015, 11:52:01 PM

Confirmations

5,753,290

Merkle Root

352e05ea364f2df1755680b0f80f473d32b704f72b7c30f317e47886c080b27a

Transactions (2)

Coinbased1f10ecbc6ed97…5df427676c6350

1 in → 1 out8.6800 XPM116 B

ANSXnLY2…Sd25TjkD

0cf41733ae8bbe…99b2dc66e5d6f6

2 in → 2 out10.7133 XPM374 B

Ae9drWdk…FnLTm9Pn ASCEeHfj…ktphAaSV

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.

3.354 × 10⁹⁷(98-digit number)

33546616048054902189…35149724525881514239

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

3.354 × 10⁹⁷(98-digit number)

33546616048054902189…35149724525881514239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.354 × 10⁹⁷(98-digit number)

33546616048054902189…35149724525881514241

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

6.709 × 10⁹⁷(98-digit number)

67093232096109804378…70299449051763028479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.709 × 10⁹⁷(98-digit number)

67093232096109804378…70299449051763028481

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

1.341 × 10⁹⁸(99-digit number)

13418646419221960875…40598898103526056959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.341 × 10⁹⁸(99-digit number)

13418646419221960875…40598898103526056961

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

2.683 × 10⁹⁸(99-digit number)

26837292838443921751…81197796207052113919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.683 × 10⁹⁸(99-digit number)

26837292838443921751…81197796207052113921

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

5.367 × 10⁹⁸(99-digit number)

53674585676887843502…62395592414104227839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.367 × 10⁹⁸(99-digit number)

53674585676887843502…62395592414104227841

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