Block #178,629

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/24/2013, 1:04:17 PM · Difficulty 9.8630 · 6,612,311 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f95283c3e2250ef83ca1947ab7c084378086c73e2ca4c56ee08a489d227b50e0

View on Chainz ↗

Height

#178,629

Difficulty

9.862965

Transactions

Size

573 B

Version

Bits

09dceb4b

Nonce

29,862

Timestamp

9/24/2013, 1:04:17 PM

Confirmations

6,612,311

Merkle Root

bff35d0c6110e41bd2e0cbd026a37503647ce3584d96cb0c034cccf114266775

Transactions (2)

Coinbase684405138089b9…952c7c4e20560c

1 in → 1 out10.2700 XPM109 B

AHN4uRs7…CWWXD9E2

cee1a5d81aaedf…38b78415bf6756

2 in → 2 out221.8845 XPM374 B

AJjFSP52…2N1pwg4X AZ4Eh4pD…rnSjckYw

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.

7.893 × 10⁹³(94-digit number)

78930878766768549264…15920929501289756159

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

7.893 × 10⁹³(94-digit number)

78930878766768549264…15920929501289756159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.893 × 10⁹³(94-digit number)

78930878766768549264…15920929501289756161

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

1.578 × 10⁹⁴(95-digit number)

15786175753353709852…31841859002579512319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.578 × 10⁹⁴(95-digit number)

15786175753353709852…31841859002579512321

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

3.157 × 10⁹⁴(95-digit number)

31572351506707419705…63683718005159024639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.157 × 10⁹⁴(95-digit number)

31572351506707419705…63683718005159024641

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

6.314 × 10⁹⁴(95-digit number)

63144703013414839411…27367436010318049279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.314 × 10⁹⁴(95-digit number)

63144703013414839411…27367436010318049281

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

1.262 × 10⁹⁵(96-digit number)

12628940602682967882…54734872020636098559

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