Block #2,281,994

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/4/2017, 10:59:50 AM · Difficulty 10.9557 · 4,535,979 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e34c115a06df0953dbe801c7ff6ba96929107d8a4038f23abf86eded39fe41e1

View on Chainz ↗

Height

#2,281,994

Difficulty

10.955668

Transactions

Size

802 B

Version

Bits

0af4a6a5

Nonce

369,385,706

Timestamp

9/4/2017, 10:59:50 AM

Confirmations

4,535,979

Mined by

⛏️ P2SHAMns3fLPSKHTEj8oyTbC69Bs11pE9mi8jC

Merkle Root

489a79d0c9afc1e9f759a75bb5713aa597c7eae1383ae8b64cea86d9fc4aba03

Transactions (3)

Coinbased3dd1bdcfc44d8…fb9574f55d63ae

1 in → 1 out8.3400 XPM110 B

AMns3fLP…pE9mi8jC

ef1682d35615d2…b6450874728ff8

1 in → 2 out4643.0800 XPM226 B

AapyoeuL…CmpqheUJ AZxSv1qo…psGzapJg

609591c5ca8646…9e5753cb2ddbf6

2 in → 2 out3017.5790 XPM375 B

AaAVK9nr…MbZrFQMu Ac7abfJW…KmkwQerd

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.

1.656 × 10⁹⁸(99-digit number)

16562296575710552366…17928127446837985279

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

1.656 × 10⁹⁸(99-digit number)

16562296575710552366…17928127446837985279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.656 × 10⁹⁸(99-digit number)

16562296575710552366…17928127446837985281

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

3.312 × 10⁹⁸(99-digit number)

33124593151421104733…35856254893675970559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.312 × 10⁹⁸(99-digit number)

33124593151421104733…35856254893675970561

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

6.624 × 10⁹⁸(99-digit number)

66249186302842209467…71712509787351941119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.624 × 10⁹⁸(99-digit number)

66249186302842209467…71712509787351941121

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

1.324 × 10⁹⁹(100-digit number)

13249837260568441893…43425019574703882239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.324 × 10⁹⁹(100-digit number)

13249837260568441893…43425019574703882241

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

2.649 × 10⁹⁹(100-digit number)

26499674521136883787…86850039149407764479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.649 × 10⁹⁹(100-digit number)

26499674521136883787…86850039149407764481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.299 × 10⁹⁹(100-digit number)

52999349042273767574…73700078298815528959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,281,994

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