Block #567,989

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/30/2014, 2:11:18 AM · Difficulty 10.9652 · 6,248,230 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7e8d5db52b22b679cdacb098127ec377aed781382d159d91777f9c8f84e18173

View on Chainz ↗

Height

#567,989

Difficulty

10.965215

Transactions

Size

730 B

Version

Bits

0af7184f

Nonce

1,160,591,453

Timestamp

5/30/2014, 2:11:18 AM

Confirmations

6,248,230

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6d5049985492cb17647cfc9a39e7a4700e65cb5678aef73bb1243447c1b5c2f7

Transactions (2)

Coinbaseefc98b3d59580f…65c58a31573826

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

9fe2db287b117c…8f1ef46916d0b7

3 in → 2 out45.8196 XPM522 B

AUfwfN8t…VHZcxFYJ ARTM86Pv…bMaumYfr

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.

1.303 × 10¹⁰⁰(101-digit number)

13032378920275779285…48136725556774277119

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

1.303 × 10¹⁰⁰(101-digit number)

13032378920275779285…48136725556774277119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.303 × 10¹⁰⁰(101-digit number)

13032378920275779285…48136725556774277121

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

2.606 × 10¹⁰⁰(101-digit number)

26064757840551558571…96273451113548554239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.606 × 10¹⁰⁰(101-digit number)

26064757840551558571…96273451113548554241

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

5.212 × 10¹⁰⁰(101-digit number)

52129515681103117143…92546902227097108479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.212 × 10¹⁰⁰(101-digit number)

52129515681103117143…92546902227097108481

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

1.042 × 10¹⁰¹(102-digit number)

10425903136220623428…85093804454194216959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.042 × 10¹⁰¹(102-digit number)

10425903136220623428…85093804454194216961

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

2.085 × 10¹⁰¹(102-digit number)

20851806272441246857…70187608908388433919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.085 × 10¹⁰¹(102-digit number)

20851806272441246857…70187608908388433921

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 #567,989

Cookie Preferences