Block #1,823,586

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/25/2016, 1:02:09 PM · Difficulty 10.8200 · 4,975,353 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f5bbd3a2ad6a1f6119d9581d0f9420ad5157333b3917472eb02d9d5a0db87b8e

View on Chainz ↗

Height

#1,823,586

Difficulty

10.819994

Transactions

Size

1.36 KB

Version

Bits

0ad1eb1e

Nonce

136,297,903

Timestamp

10/25/2016, 1:02:09 PM

Confirmations

4,975,353

Mined by

⛏️ P2SHALe48fV1izTBQ3uSHJC36S3e6FG9eiJMs8

Merkle Root

a10101047d77873d8ae609846e157e8eb6b81121511df04234e704b1d41b25e8

Transactions (3)

Coinbase58dfe4a51aa981…3ea81e33eede6d

1 in → 1 out8.5500 XPM110 B

ALe48fV1…G9eiJMs8

b7b46a3942ef8a…f34d569ca8731c

1 in → 2 out49999.9900 XPM226 B

ASQvCg4A…hQn3kS8p AdiJAKay…po3JCbmh

34a6036c3f85a0…c36226627e1239

6 in → 2 out2.0079 XPM966 B

AGwPLvC9…vkkNU6Db AYaCwd5d…AjPmGup8

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.

5.187 × 10⁹⁵(96-digit number)

51878260533039547385…15241493291467989919

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

5.187 × 10⁹⁵(96-digit number)

51878260533039547385…15241493291467989919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.187 × 10⁹⁵(96-digit number)

51878260533039547385…15241493291467989921

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

1.037 × 10⁹⁶(97-digit number)

10375652106607909477…30482986582935979839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.037 × 10⁹⁶(97-digit number)

10375652106607909477…30482986582935979841

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

2.075 × 10⁹⁶(97-digit number)

20751304213215818954…60965973165871959679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.075 × 10⁹⁶(97-digit number)

20751304213215818954…60965973165871959681

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

4.150 × 10⁹⁶(97-digit number)

41502608426431637908…21931946331743919359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.150 × 10⁹⁶(97-digit number)

41502608426431637908…21931946331743919361

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

8.300 × 10⁹⁶(97-digit number)

83005216852863275817…43863892663487838719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.300 × 10⁹⁶(97-digit number)

83005216852863275817…43863892663487838721

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