Block #142,249

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/30/2013, 8:34:52 PM · Difficulty 9.8364 · 6,685,050 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

670968ea641b0cd2577c2a20b491a68ed38e88013ca0fe23bfa870dfe200e699

View on Chainz ↗

Height

#142,249

Difficulty

9.836380

Transactions

Size

1.21 KB

Version

Bits

09d61cf8

Nonce

93,372

Timestamp

8/30/2013, 8:34:52 PM

Confirmations

6,685,050

Mined by

⛏️ P2SHAZVbBbt3ksoqjxYUuNvNpqh252D8XoJT8s

Merkle Root

4415a896db86c82c78eff596debae1fb2b452d0a98c276f21313cd45c54347fa

Transactions (3)

Coinbase38a7ab8914017e…79ebaf944e92ac

1 in → 1 out10.3400 XPM109 B

AZVbBbt3…D8XoJT8s

8f9294588b34d8…f9db0edc2bfa65

4 in → 2 out1000.0174 XPM669 B

AboJSsvN…PFBhh2j6 AX5NDjSH…WRYQ9Yax

0fd2acdcd01857…1f1977a56b417b

2 in → 2 out10.1667 XPM373 B

AUobm2L1…smDmxw7h APs8K5WQ…wiuKvacz

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.

3.721 × 10⁹³(94-digit number)

37217882770754195702…24608535418408603519

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

3.721 × 10⁹³(94-digit number)

37217882770754195702…24608535418408603519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.721 × 10⁹³(94-digit number)

37217882770754195702…24608535418408603521

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

7.443 × 10⁹³(94-digit number)

74435765541508391405…49217070836817207039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.443 × 10⁹³(94-digit number)

74435765541508391405…49217070836817207041

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

1.488 × 10⁹⁴(95-digit number)

14887153108301678281…98434141673634414079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.488 × 10⁹⁴(95-digit number)

14887153108301678281…98434141673634414081

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

2.977 × 10⁹⁴(95-digit number)

29774306216603356562…96868283347268828159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.977 × 10⁹⁴(95-digit number)

29774306216603356562…96868283347268828161

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

5.954 × 10⁹⁴(95-digit number)

59548612433206713124…93736566694537656319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #142,249

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