Block #605,993

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/28/2014, 10:42:33 PM · Difficulty 10.9090 · 6,202,268 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

34d1099a426fd8c7c7e751bcc8895daa0848ea966e764a63b8a742f604bb6f73

View on Chainz ↗

Height

#605,993

Difficulty

10.909009

Transactions

Size

1.50 KB

Version

Bits

0ae8b4d2

Nonce

101,808

Timestamp

6/28/2014, 10:42:33 PM

Confirmations

6,202,268

Mined by

AbPcCMg4L29d17fPXxDc6v13Qy719q6mAX

Merkle Root

d49942fbf1499fad01c34be1ad96e7c7115ce8f499fba3996b1ff74a88e706bd

Transactions (5)

Coinbase35ad265ac652fd…d2e8dd272c115f

1 in → 14 out8.4300 XPM539 B

AbPcCMg4…719q6mAX AXVLciVJ…uTVo9CdN AGz9gyZW…bo8NYQpw AWrWZJwt…V19G6gs3 ALkuF5Je…KBUB19wB

ed79c220f23a01…cf896e7957444e

1 in → 2 out6.2162 XPM225 B

AMx9mTdJ…UwM1tSSA AGjfrUuG…Wkiqkcni

e85193aea30795…3a2118058b0a03

1 in → 2 out4.9186 XPM226 B

AW7k2MZd…9b8YznyG AUtSvhpp…aCbL6TYU

b080612e09802d…b36b7d5032f4c4

1 in → 2 out4.1388 XPM226 B

AVbLxVJb…PRg27irr AJqBpjSZ…9eLc1yR4

277fc26ddf704c…c8fb6905c080a3

1 in → 2 out3.6668 XPM226 B

AVeEi4Sk…5sYwWC2A AS9ZCvju…bu3NEFwZ

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.

5.480 × 10¹⁰¹(102-digit number)

54808007010400563656…30531655496182399999

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

5.480 × 10¹⁰¹(102-digit number)

54808007010400563656…30531655496182399999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.480 × 10¹⁰¹(102-digit number)

54808007010400563656…30531655496182400001

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

1.096 × 10¹⁰²(103-digit number)

10961601402080112731…61063310992364799999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.096 × 10¹⁰²(103-digit number)

10961601402080112731…61063310992364800001

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

2.192 × 10¹⁰²(103-digit number)

21923202804160225462…22126621984729599999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.192 × 10¹⁰²(103-digit number)

21923202804160225462…22126621984729600001

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

4.384 × 10¹⁰²(103-digit number)

43846405608320450925…44253243969459199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.384 × 10¹⁰²(103-digit number)

43846405608320450925…44253243969459200001

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

8.769 × 10¹⁰²(103-digit number)

87692811216640901850…88506487938918399999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.769 × 10¹⁰²(103-digit number)

87692811216640901850…88506487938918400001

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 #605,993

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