Block #945,446

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/21/2015, 3:26:13 AM · Difficulty 10.8986 · 5,879,379 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c1efcdd79166fd773908f27698708c2fa26dcd64295fcf37148544442463d566

View on Chainz ↗

Height

#945,446

Difficulty

10.898553

Transactions

Size

1.66 KB

Version

Bits

0ae60795

Nonce

535,111,975

Timestamp

2/21/2015, 3:26:13 AM

Confirmations

5,879,379

Mined by

⛏️ P2SHAZtzmiWQkVQgRK8x1CCz57f6F51uu4Qjtv

Merkle Root

3cd93a5c1315110886d5f811874f4971972abd064d1665512a6fdda7853c05d9

Transactions (5)

Coinbaseb6a4ac6cfa911a…b035a27a64b831

1 in → 1 out8.4500 XPM109 B

AZtzmiWQ…1uu4Qjtv

2251d5a430a775…660f6239ddf9a6

2 in → 2 out5.3127 XPM374 B

APkQt3xL…kUCpBGfP ANia7wgK…VR264iFL

8d91506f75e6a9…7bddadde4818e4

1 in → 2 out2.4309 XPM226 B

AHRoBSh4…BSVTQ36Q AeE7aKac…ndFrxKCa

a404aa29cacb93…3b74b554d82f15

1 in → 2 out1.0925 XPM227 B

AVZwze3C…1DNKwKx6 AVKcZ4L8…zbGt9txk

99c384a392248e…7abe7159e4c1c6

4 in → 2 out5.2557 XPM669 B

ARpjHv1k…4F9NvuWN APu9UkCG…M96TcczX

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.

5.892 × 10⁹⁴(95-digit number)

58927733375199289877…21888431283493437679

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

5.892 × 10⁹⁴(95-digit number)

58927733375199289877…21888431283493437679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.892 × 10⁹⁴(95-digit number)

58927733375199289877…21888431283493437681

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

1.178 × 10⁹⁵(96-digit number)

11785546675039857975…43776862566986875359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.178 × 10⁹⁵(96-digit number)

11785546675039857975…43776862566986875361

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

2.357 × 10⁹⁵(96-digit number)

23571093350079715951…87553725133973750719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.357 × 10⁹⁵(96-digit number)

23571093350079715951…87553725133973750721

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

4.714 × 10⁹⁵(96-digit number)

47142186700159431902…75107450267947501439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.714 × 10⁹⁵(96-digit number)

47142186700159431902…75107450267947501441

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

9.428 × 10⁹⁵(96-digit number)

94284373400318863804…50214900535895002879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.428 × 10⁹⁵(96-digit number)

94284373400318863804…50214900535895002881

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 #945,446

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