Block #959,887

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2015, 1:06:58 PM · Difficulty 10.8875 · 5,848,791 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c01de99cd1386ffdfb9d0be6f8c68633d06544e2ca0ae3e1816a3a7f5f0d08bd

View on Chainz ↗

Height

#959,887

Difficulty

10.887537

Transactions

Size

1.81 KB

Version

Bits

0ae335a2

Nonce

22,978,710

Timestamp

3/3/2015, 1:06:58 PM

Confirmations

5,848,791

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

09711843c343c214916d0a70223e7a3e2970b1356016be8a800611e8a4951040

Transactions (5)

Coinbase81dbbd5b9e650e…3efafd68c7183d

1 in → 1 out8.4600 XPM116 B

ANSXnLY2…Sd25TjkD

8363ba42829315…430a454df33068

1 in → 2 out8.3900 XPM226 B

AFv8jiXE…b4pgdkLW AKAuqE7A…pMX1wcYA

6de2f7a253daed…97da807e06834e

1 in → 2 out8.3900 XPM225 B

AGeZ8NJn…ZBREQjik AN2JdR4o…6nQq4KPj

4ed2e60bac9bd4…82ed2b50c94e46

1 in → 2 out5.6896 XPM227 B

AUuxuekw…g4ssSvLj ANfmUrFA…kVSzdPqM

639ec22a258412…d023e91615f419

6 in → 2 out0.6419 XPM967 B

AZaP8Jpw…37x6Ao45 AdGRtqEp…VQ66rj7a

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.

4.129 × 10⁹⁸(99-digit number)

41290233701099088794…32082955170941000319

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

4.129 × 10⁹⁸(99-digit number)

41290233701099088794…32082955170941000319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.129 × 10⁹⁸(99-digit number)

41290233701099088794…32082955170941000321

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

8.258 × 10⁹⁸(99-digit number)

82580467402198177588…64165910341882000639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.258 × 10⁹⁸(99-digit number)

82580467402198177588…64165910341882000641

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

1.651 × 10⁹⁹(100-digit number)

16516093480439635517…28331820683764001279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.651 × 10⁹⁹(100-digit number)

16516093480439635517…28331820683764001281

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

3.303 × 10⁹⁹(100-digit number)

33032186960879271035…56663641367528002559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.303 × 10⁹⁹(100-digit number)

33032186960879271035…56663641367528002561

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

6.606 × 10⁹⁹(100-digit number)

66064373921758542070…13327282735056005119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.606 × 10⁹⁹(100-digit number)

66064373921758542070…13327282735056005121

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 #959,887

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