Block #532,639

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/9/2014, 5:16:52 AM · Difficulty 10.8980 · 6,294,199 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d40008c2e8fb1d025b6794b6ea9cf3c6c5132f27f57d580aa93bde1ac01664ab

View on Chainz ↗

Height

#532,639

Difficulty

10.897996

Transactions

Size

20.67 KB

Version

Bits

0ae5e310

Nonce

62,718,566

Timestamp

5/9/2014, 5:16:52 AM

Confirmations

6,294,199

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

df0215c36fa9d52141f8320a4e1b5729526efbc325c1d6d4f072a89389c2e840

Transactions (4)

Coinbase09a218b279f2a7…820c215e570289

1 in → 1 out8.6400 XPM116 B

ANSXnLY2…Sd25TjkD

d18765068f0bfc…5ae911a7615d8c

138 in → 2 out500.0101 XPM20.02 KB

AJjnK9uC…VreFquR4 Aaf4xgTj…EdKedx8D

bd48dbec7d0f79…4a70ae6f7a37bf

1 in → 2 out3.8188 XPM225 B

Aeibw7eB…DXww2mo2 APueLXkL…2VEJ4Wvd

9bb36fcb79b51f…914580eb49b283

1 in → 2 out2.2485 XPM226 B

ALcBy7MP…nzj2PRxt AYZGBcB7…fPZS3p1z

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.

8.893 × 10⁹⁹(100-digit number)

88931762599331195138…92827717680661398399

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

8.893 × 10⁹⁹(100-digit number)

88931762599331195138…92827717680661398399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.893 × 10⁹⁹(100-digit number)

88931762599331195138…92827717680661398401

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

1.778 × 10¹⁰⁰(101-digit number)

17786352519866239027…85655435361322796799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.778 × 10¹⁰⁰(101-digit number)

17786352519866239027…85655435361322796801

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

3.557 × 10¹⁰⁰(101-digit number)

35572705039732478055…71310870722645593599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.557 × 10¹⁰⁰(101-digit number)

35572705039732478055…71310870722645593601

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

7.114 × 10¹⁰⁰(101-digit number)

71145410079464956110…42621741445291187199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.114 × 10¹⁰⁰(101-digit number)

71145410079464956110…42621741445291187201

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

1.422 × 10¹⁰¹(102-digit number)

14229082015892991222…85243482890582374399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.422 × 10¹⁰¹(102-digit number)

14229082015892991222…85243482890582374401

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 #532,639

Cookie Preferences