Block #1,066,262

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/19/2015, 10:57:29 AM · Difficulty 10.7368 · 5,748,040 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

336f8d67fd0277acd15b8c1bb1f507bce7ee7dc552c98471871e77dca2e20ade

View on Chainz ↗

Height

#1,066,262

Difficulty

10.736796

Transactions

Size

198 B

Version

Bits

0abc9eab

Nonce

970,924,765

Timestamp

5/19/2015, 10:57:29 AM

Confirmations

5,748,040

Mined by

⛏️ P2SHARKZgmA3LCk36J1rb6vAQKxkeTS7FnTpBW

Merkle Root

16e3db8726b9294cd871b8007f5bc539bf231306fc55013764ea83e6969a08a2

Transactions (1)

Coinbase16e3db8726b929…ea83e6969a08a2

1 in → 1 out8.6600 XPM109 B

ARKZgmA3…S7FnTpBW

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.

2.417 × 10⁹³(94-digit number)

24179355754979664402…96448406643511986239

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

2.417 × 10⁹³(94-digit number)

24179355754979664402…96448406643511986239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.417 × 10⁹³(94-digit number)

24179355754979664402…96448406643511986241

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

4.835 × 10⁹³(94-digit number)

48358711509959328805…92896813287023972479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.835 × 10⁹³(94-digit number)

48358711509959328805…92896813287023972481

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

9.671 × 10⁹³(94-digit number)

96717423019918657610…85793626574047944959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.671 × 10⁹³(94-digit number)

96717423019918657610…85793626574047944961

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

1.934 × 10⁹⁴(95-digit number)

19343484603983731522…71587253148095889919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.934 × 10⁹⁴(95-digit number)

19343484603983731522…71587253148095889921

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

3.868 × 10⁹⁴(95-digit number)

38686969207967463044…43174506296191779839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.868 × 10⁹⁴(95-digit number)

38686969207967463044…43174506296191779841

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 #1,066,262

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