Block #748,645

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/1/2014, 11:04:18 AM · Difficulty 10.9779 · 6,046,832 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9c2b068ad131cb04747c7b6032d899806c0ebea9217112821c5dc0af78b26c45

View on Chainz ↗

Height

#748,645

Difficulty

10.977896

Transactions

Size

1.87 KB

Version

Bits

0afa575d

Nonce

140,826,773

Timestamp

10/1/2014, 11:04:18 AM

Confirmations

6,046,832

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f10a61cb63e5bf183d429d13920bd05197abf0a0fcbe72fadd3f99da7276b772

Transactions (4)

Coinbase7cdd0cc59224dc…f6b902e4249285

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

4a22a46266ba04…459632669222b8

5 in → 2 out898.1100 XPM816 B

AJJBaUbb…jGfry5Dy AGuisewS…kixoacNm

279efe5cbb6529…bc0ef1a572d8e1

4 in → 2 out20.0219 XPM670 B

AdMb8XQA…PmCvgqDb AePF5HW1…VNA6s7WF

17ac9609e2111e…3880b705572829

1 in → 2 out1.0392 XPM226 B

AaCgQmyk…ANXFLQft AccQkurr…fiJjt7wZ

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.

1.924 × 10⁹⁴(95-digit number)

19245229331851604146…48040205523581940059

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

1.924 × 10⁹⁴(95-digit number)

19245229331851604146…48040205523581940059

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.924 × 10⁹⁴(95-digit number)

19245229331851604146…48040205523581940061

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

3.849 × 10⁹⁴(95-digit number)

38490458663703208293…96080411047163880119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.849 × 10⁹⁴(95-digit number)

38490458663703208293…96080411047163880121

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

7.698 × 10⁹⁴(95-digit number)

76980917327406416587…92160822094327760239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.698 × 10⁹⁴(95-digit number)

76980917327406416587…92160822094327760241

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

1.539 × 10⁹⁵(96-digit number)

15396183465481283317…84321644188655520479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.539 × 10⁹⁵(96-digit number)

15396183465481283317…84321644188655520481

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

3.079 × 10⁹⁵(96-digit number)

30792366930962566635…68643288377311040959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.079 × 10⁹⁵(96-digit number)

30792366930962566635…68643288377311040961

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

6.158 × 10⁹⁵(96-digit number)

61584733861925133270…37286576754622081919

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