Block #586,193

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/12/2014, 8:23:11 PM · Difficulty 10.9529 · 6,223,971 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7b02aeca2f2f3e518088c7cd60a96b1b27292f4fa679e1e376b6a7cd1d611b2c

View on Chainz ↗

Height

#586,193

Difficulty

10.952947

Transactions

Size

7.22 KB

Version

Bits

0af3f45c

Nonce

70,160

Timestamp

6/12/2014, 8:23:11 PM

Confirmations

6,223,971

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

092106514bdd6b4494ffb2f64a1636ba683af281f1a243e1950d5a942985976f

Transactions (4)

Coinbase8295e9a1ec5334…04b853b01d7367

1 in → 1 out8.4100 XPM110 B

AeKNrjNj…1NEq95Ta

fdeb61839c51b0…acb5f17b072ccf

44 in → 2 out363.5664 XPM6.43 KB

AKBQKQ1u…CKKLJCCJ ATrZdpw2…4DB7ANgL

df3873c5e6a09f…6f7dd77d582d60

2 in → 2 out15.0760 XPM376 B

AUh8H8xt…HiUD4SSg AeEznxXW…ek3FGY6H

c8b1a71ca2259b…2d7cde9cf7d8f4

1 in → 2 out6.3327 XPM226 B

AWeFTqSF…usRDA3NM ALCcLFK2…nMCeATTr

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.

3.887 × 10¹⁰²(103-digit number)

38879007172119521077…56176981666923379199

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

3.887 × 10¹⁰²(103-digit number)

38879007172119521077…56176981666923379199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.887 × 10¹⁰²(103-digit number)

38879007172119521077…56176981666923379201

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

7.775 × 10¹⁰²(103-digit number)

77758014344239042154…12353963333846758399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.775 × 10¹⁰²(103-digit number)

77758014344239042154…12353963333846758401

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

1.555 × 10¹⁰³(104-digit number)

15551602868847808430…24707926667693516799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.555 × 10¹⁰³(104-digit number)

15551602868847808430…24707926667693516801

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

3.110 × 10¹⁰³(104-digit number)

31103205737695616861…49415853335387033599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.110 × 10¹⁰³(104-digit number)

31103205737695616861…49415853335387033601

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

6.220 × 10¹⁰³(104-digit number)

62206411475391233723…98831706670774067199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.220 × 10¹⁰³(104-digit number)

62206411475391233723…98831706670774067201

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 #586,193

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