Block #539,615

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/12/2014, 7:22:36 PM · Difficulty 10.9289 · 6,253,957 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8f562d503b88dfb61e883ef9e9feeea3b8c6e7d7d7294cd46a6de10132222350

View on Chainz ↗

Height

#539,615

Difficulty

10.928948

Transactions

Size

885 B

Version

Bits

0aedcf83

Nonce

26,547,922

Timestamp

5/12/2014, 7:22:36 PM

Confirmations

6,253,957

Merkle Root

302407271aff4a1eb8d640a56e4e2451bffa482b9e0caf2332a1e4d732cc5434

Transactions (4)

Coinbase13a82d1f6c5264…b594d81d633749

1 in → 1 out8.3900 XPM116 B

ANSXnLY2…Sd25TjkD

b5635e58820667…9768cc39162c9f

1 in → 2 out6.2240 XPM225 B

ANp2ubYF…Gqg6i2SB ASWygVYZ…Lp1jD6S1

e6bb458adedde4…b469c6b83934db

1 in → 2 out5.1137 XPM225 B

Aeibw7eB…DXww2mo2 AbH7DfYu…KGbtGnPj

b08456fc7d2e3c…2f2b0ceb3e1be3

1 in → 2 out2.2057 XPM226 B

ARDhgPZw…M2dQB4CT AMfpBx29…Cxz69rez

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.

1.445 × 10¹⁰¹(102-digit number)

14458485407294482129…74301247387036200959

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

1.445 × 10¹⁰¹(102-digit number)

14458485407294482129…74301247387036200959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.445 × 10¹⁰¹(102-digit number)

14458485407294482129…74301247387036200961

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

2.891 × 10¹⁰¹(102-digit number)

28916970814588964258…48602494774072401919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.891 × 10¹⁰¹(102-digit number)

28916970814588964258…48602494774072401921

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

5.783 × 10¹⁰¹(102-digit number)

57833941629177928516…97204989548144803839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.783 × 10¹⁰¹(102-digit number)

57833941629177928516…97204989548144803841

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

1.156 × 10¹⁰²(103-digit number)

11566788325835585703…94409979096289607679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.156 × 10¹⁰²(103-digit number)

11566788325835585703…94409979096289607681

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

2.313 × 10¹⁰²(103-digit number)

23133576651671171406…88819958192579215359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.313 × 10¹⁰²(103-digit number)

23133576651671171406…88819958192579215361

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

4.626 × 10¹⁰²(103-digit number)

46267153303342342813…77639916385158430719

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