Block #512,920

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/27/2014, 4:46:58 AM · Difficulty 10.8342 · 6,299,451 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ec9da17664d6d9c7067b8694871304b6972c88b06558d682eb7fb0edd32f4168

View on Chainz ↗

Height

#512,920

Difficulty

10.834180

Transactions

Size

1.08 KB

Version

Bits

0ad58cd1

Nonce

1,526,826

Timestamp

4/27/2014, 4:46:58 AM

Confirmations

6,299,451

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

a2d86a0362a8faa41c6d44f980d165056b7e2c7f8684ffc76d9f9266a42fef05

Transactions (4)

Coinbasef7a8db3160c127…6d700fd6bf93a8

1 in → 1 out8.5400 XPM116 B

AbwWkWZt…kawDhufa

6da2fdbe8a8430…aa48a75305eb60

2 in → 6 out17.2440 XPM443 B

Adv3q9qm…6e2LbBNU AWWeSvQW…Vm84TjJn ALG6Kwki…JVRCDqef AP6XU4Ao…mq8mf6N9 AHXJ1dhk…mhL46N6m

8395e4bd57c6ef…45a12bb2271c79

1 in → 2 out3.5093 XPM225 B

AN8T94pb…XpmKbTbK AL16EwgG…R5ntLopf

369bdcc57ef733…ffae028311fe2f

1 in → 2 out2.1148 XPM226 B

AHK1Apea…URE5hnSJ AcTo4ZmQ…33axAV7E

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.

3.421 × 10¹⁰⁰(101-digit number)

34212565493541740969…07932952833204610559

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

3.421 × 10¹⁰⁰(101-digit number)

34212565493541740969…07932952833204610559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.421 × 10¹⁰⁰(101-digit number)

34212565493541740969…07932952833204610561

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

6.842 × 10¹⁰⁰(101-digit number)

68425130987083481939…15865905666409221119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.842 × 10¹⁰⁰(101-digit number)

68425130987083481939…15865905666409221121

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

1.368 × 10¹⁰¹(102-digit number)

13685026197416696387…31731811332818442239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.368 × 10¹⁰¹(102-digit number)

13685026197416696387…31731811332818442241

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

2.737 × 10¹⁰¹(102-digit number)

27370052394833392775…63463622665636884479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.737 × 10¹⁰¹(102-digit number)

27370052394833392775…63463622665636884481

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

5.474 × 10¹⁰¹(102-digit number)

54740104789666785551…26927245331273768959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.474 × 10¹⁰¹(102-digit number)

54740104789666785551…26927245331273768961

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 #512,920

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