Block #967,511

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/10/2015, 7:59:00 AM · Difficulty 10.8282 · 5,841,554 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8902f939e1c8197af6942b2519fcba98671216f55bffc81dd4859d6be5bb868e

View on Chainz ↗

Height

#967,511

Difficulty

10.828210

Transactions

Size

1.14 KB

Version

Bits

0ad4058c

Nonce

1,777,293,918

Timestamp

3/10/2015, 7:59:00 AM

Confirmations

5,841,554

Mined by

⛏️ P2SHAa3qNa8pULNiwzuWxHuvCUDhfvAoEsGsH1

Merkle Root

326990c52afb1811f6657b83dd68cbe071bf527182f10211b17efaf91dae5b4b

Transactions (2)

Coinbase020b7580f4189e…0344e0f67e9ae6

1 in → 1 out8.5400 XPM109 B

Aa3qNa8p…AoEsGsH1

73dc587e50e363…e5eadc56521159

6 in → 2 out1888.0000 XPM966 B

AUPKmYue…MmLyrZX1 AHNccZy4…RwZSfQd3

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.

8.393 × 10⁹⁸(99-digit number)

83932491651186425421…37512986439057407999

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

8.393 × 10⁹⁸(99-digit number)

83932491651186425421…37512986439057407999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.393 × 10⁹⁸(99-digit number)

83932491651186425421…37512986439057408001

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

1.678 × 10⁹⁹(100-digit number)

16786498330237285084…75025972878114815999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.678 × 10⁹⁹(100-digit number)

16786498330237285084…75025972878114816001

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

3.357 × 10⁹⁹(100-digit number)

33572996660474570168…50051945756229631999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.357 × 10⁹⁹(100-digit number)

33572996660474570168…50051945756229632001

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

6.714 × 10⁹⁹(100-digit number)

67145993320949140337…00103891512459263999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.714 × 10⁹⁹(100-digit number)

67145993320949140337…00103891512459264001

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

1.342 × 10¹⁰⁰(101-digit number)

13429198664189828067…00207783024918527999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.342 × 10¹⁰⁰(101-digit number)

13429198664189828067…00207783024918528001

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 #967,511

Cookie Preferences