Block #783,050

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/25/2014, 10:20:58 PM · Difficulty 10.9751 · 6,008,740 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e1489564652033cddd2e73807b4cb0cfc3fd880c4ee6c2c620aaebc661bde971

View on Chainz ↗

Height

#783,050

Difficulty

10.975076

Transactions

Size

13.96 KB

Version

Bits

0af99e95

Nonce

128,690,301

Timestamp

10/25/2014, 10:20:58 PM

Confirmations

6,008,740

Merkle Root

88532b57024d3152ffedc17d3d2336d13ae943f9ab63ae2239942c0e497b80af

Transactions (4)

Coinbase8b3cc1bd7b3343…e0f6183e8adf22

1 in → 1 out8.4500 XPM116 B

ANSXnLY2…Sd25TjkD

9bcbe7fae7e258…06248ee5e5a19a

1 in → 392 out1307.6040 XPM13.17 KB

AMQsjej9…hQw7GZgF AMzSJ1xi…oVABHZ6P AMg3aDEM…2msPQXCw AMvA5hFn…3bfgLZ8i AMQoQjpf…2yTSXoLQ

fecb388807ee2a…49a9b5b12706be

1 in → 2 out1.2405 XPM227 B

AHDLT2xq…ESjKqkpt AGdWVjRk…LFVsqCnK

9e8e0ef6349755…3823ec96efa6ae

2 in → 2 out0.7605 XPM373 B

AGXqJki6…YNiMZGMN AWviQpGy…SU5jLKH6

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.

5.795 × 10⁹⁴(95-digit number)

57950656557844106018…28088011834147076219

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

5.795 × 10⁹⁴(95-digit number)

57950656557844106018…28088011834147076219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.795 × 10⁹⁴(95-digit number)

57950656557844106018…28088011834147076221

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

1.159 × 10⁹⁵(96-digit number)

11590131311568821203…56176023668294152439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.159 × 10⁹⁵(96-digit number)

11590131311568821203…56176023668294152441

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

2.318 × 10⁹⁵(96-digit number)

23180262623137642407…12352047336588304879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.318 × 10⁹⁵(96-digit number)

23180262623137642407…12352047336588304881

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

4.636 × 10⁹⁵(96-digit number)

46360525246275284814…24704094673176609759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.636 × 10⁹⁵(96-digit number)

46360525246275284814…24704094673176609761

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

9.272 × 10⁹⁵(96-digit number)

92721050492550569629…49408189346353219519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.272 × 10⁹⁵(96-digit number)

92721050492550569629…49408189346353219521

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

1.854 × 10⁹⁶(97-digit number)

18544210098510113925…98816378692706439039

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