Block #1,286,352

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/17/2015, 4:03:49 PM · Difficulty 10.8441 · 5,539,206 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6ea56c17b881f14f3d93e06ff72f4a8341fb870606ec4bb018bb9e590477f984

View on Chainz ↗

Height

#1,286,352

Difficulty

10.844062

Transactions

Size

1.29 KB

Version

Bits

0ad81472

Nonce

1,533,087,540

Timestamp

10/17/2015, 4:03:49 PM

Confirmations

5,539,206

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

3f27806c52bb34aec7cf7856a7cd93d4e718e02e05d8d2bf7435c80cd9bf44c4

Transactions (2)

Coinbaseda400115d04781…4995ca37d8c2be

1 in → 1 out8.5100 XPM116 B

AJCEY9yy…tg97E6zm

2da145a4ad9ec0…25738823b90e76

1 in → 28 out195.4434 XPM1.08 KB

ATuEdyaW…442tG6UG AdEb8Jj7…fYCYHo7M AYQUJ9DK…HZscnLdw ARAMeUBK…8vD868RT APr1Ufev…fgPhoT77

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.

1.364 × 10⁹⁶(97-digit number)

13642590744848147976…86382306519845375999

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

1.364 × 10⁹⁶(97-digit number)

13642590744848147976…86382306519845375999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.364 × 10⁹⁶(97-digit number)

13642590744848147976…86382306519845376001

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

2.728 × 10⁹⁶(97-digit number)

27285181489696295953…72764613039690751999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.728 × 10⁹⁶(97-digit number)

27285181489696295953…72764613039690752001

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

5.457 × 10⁹⁶(97-digit number)

54570362979392591907…45529226079381503999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.457 × 10⁹⁶(97-digit number)

54570362979392591907…45529226079381504001

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

1.091 × 10⁹⁷(98-digit number)

10914072595878518381…91058452158763007999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.091 × 10⁹⁷(98-digit number)

10914072595878518381…91058452158763008001

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

2.182 × 10⁹⁷(98-digit number)

21828145191757036763…82116904317526015999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.182 × 10⁹⁷(98-digit number)

21828145191757036763…82116904317526016001

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 #1,286,352

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