Block #959,572

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2015, 7:33:04 AM · Difficulty 10.8880 · 5,845,449 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e65c979c37e286462f007ff899d6f536ab7cfa65c47afd8ef19cfefdc6c7a61c

View on Chainz ↗

Height

#959,572

Difficulty

10.887959

Transactions

Size

2.24 KB

Version

Bits

0ae35144

Nonce

253,639,782

Timestamp

3/3/2015, 7:33:04 AM

Confirmations

5,845,449

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

dddc0689a3feccbb86262996d72a512486cf282e4df9771150976cf1a6929195

Transactions (3)

Coinbase3207a6d0049035…7836c65c74c25d

1 in → 1 out8.4500 XPM116 B

ANSXnLY2…Sd25TjkD

21f8a797db015b…183f23249f5c20

12 in → 2 out100.1120 XPM1.81 KB

AcHPKkfc…Urxy9vZw AUcwu7yP…wtCnojds

6d74bb19271734…0a08d707ea3888

1 in → 2 out3.3795 XPM226 B

Ae7YXEyn…hnSYZsCr AFuAbYhM…VwBukyRz

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.

1.097 × 10⁹⁸(99-digit number)

10972117575422792320…31842595654515097599

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

1.097 × 10⁹⁸(99-digit number)

10972117575422792320…31842595654515097599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.097 × 10⁹⁸(99-digit number)

10972117575422792320…31842595654515097601

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

2.194 × 10⁹⁸(99-digit number)

21944235150845584641…63685191309030195199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.194 × 10⁹⁸(99-digit number)

21944235150845584641…63685191309030195201

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

4.388 × 10⁹⁸(99-digit number)

43888470301691169282…27370382618060390399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.388 × 10⁹⁸(99-digit number)

43888470301691169282…27370382618060390401

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

8.777 × 10⁹⁸(99-digit number)

87776940603382338565…54740765236120780799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.777 × 10⁹⁸(99-digit number)

87776940603382338565…54740765236120780801

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

1.755 × 10⁹⁹(100-digit number)

17555388120676467713…09481530472241561599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.755 × 10⁹⁹(100-digit number)

17555388120676467713…09481530472241561601

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