Block #959,873

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/3/2015, 12:57:19 PM · Difficulty 10.8876 · 5,839,566 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e784284cb772fbfa6b1f5e9ba1368ce332a722abdc36bce57cab6e7641f194ff

View on Chainz ↗

Height

#959,873

Difficulty

10.887565

Transactions

Size

1.23 KB

Version

Bits

0ae3377c

Nonce

1,755,129,259

Timestamp

3/3/2015, 12:57:19 PM

Confirmations

5,839,566

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3320a6b7c4f30ef63400486936729bc161dc352586c19388a41c1217a3b71e4e

Transactions (5)

Coinbasedb14f1bd445b24…dd16a5d9b50edf

1 in → 1 out8.4600 XPM116 B

ANSXnLY2…Sd25TjkD

cb81d8d5e143a9…04d52a0e885617

1 in → 2 out8.3900 XPM226 B

AbZKP33D…9yoodMsa AbvPGdpW…nARb1BE3

7a64af0e2d4ce6…9a425aa77be6de

2 in → 2 out11.4193 XPM373 B

APEp3NDq…kXkRBmWA AKrdoKFZ…o7W7Aqkj

9d52e5911bb6df…1295dfc4c36f0c

1 in → 2 out7.8798 XPM225 B

AR5AuxAt…m9T7FDWU ANfmUrFA…kVSzdPqM

e6b79be9aa4d2f…c2298b23706df1

1 in → 2 out7.6597 XPM226 B

ARpjHv1k…4F9NvuWN AduHRerV…CXpgKLuJ

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.

2.721 × 10⁹⁷(98-digit number)

27215881107608734379…07242124436492144639

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

2.721 × 10⁹⁷(98-digit number)

27215881107608734379…07242124436492144639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.721 × 10⁹⁷(98-digit number)

27215881107608734379…07242124436492144641

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

5.443 × 10⁹⁷(98-digit number)

54431762215217468758…14484248872984289279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.443 × 10⁹⁷(98-digit number)

54431762215217468758…14484248872984289281

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

1.088 × 10⁹⁸(99-digit number)

10886352443043493751…28968497745968578559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.088 × 10⁹⁸(99-digit number)

10886352443043493751…28968497745968578561

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

2.177 × 10⁹⁸(99-digit number)

21772704886086987503…57936995491937157119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.177 × 10⁹⁸(99-digit number)

21772704886086987503…57936995491937157121

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

4.354 × 10⁹⁸(99-digit number)

43545409772173975007…15873990983874314239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.354 × 10⁹⁸(99-digit number)

43545409772173975007…15873990983874314241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

8.709 × 10⁹⁸(99-digit number)

87090819544347950014…31747981967748628479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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