Block #63,629

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 2:40:55 AM · Difficulty 8.9797 · 6,754,091 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f15fc0eb1d7e570d7b4a4b2cb170c7b5fca932f1058efc9d3cb5b69bd1eeccc2

View on Chainz ↗

Height

#63,629

Difficulty

8.979659

Transactions

Size

199 B

Version

Bits

08facaef

Nonce

301

Timestamp

7/19/2013, 2:40:55 AM

Confirmations

6,754,091

Mined by

⛏️ P2SHAJbz55M2Xd4eSVXFrry1sb6y1EmoHxsz79

Merkle Root

bc026fe1dd7661ac45070d8fe6733543330cd420bd4b296f25d6702032aff51c

Transactions (1)

Coinbasebc026fe1dd7661…d6702032aff51c

1 in → 1 out12.3800 XPM110 B

AJbz55M2…moHxsz79

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.

1.971 × 10⁹¹(92-digit number)

19717567186506777311…67479427804215537119

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

1.971 × 10⁹¹(92-digit number)

19717567186506777311…67479427804215537119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.971 × 10⁹¹(92-digit number)

19717567186506777311…67479427804215537121

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

3.943 × 10⁹¹(92-digit number)

39435134373013554623…34958855608431074239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.943 × 10⁹¹(92-digit number)

39435134373013554623…34958855608431074241

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

7.887 × 10⁹¹(92-digit number)

78870268746027109247…69917711216862148479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.887 × 10⁹¹(92-digit number)

78870268746027109247…69917711216862148481

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

1.577 × 10⁹²(93-digit number)

15774053749205421849…39835422433724296959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.577 × 10⁹²(93-digit number)

15774053749205421849…39835422433724296961

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

3.154 × 10⁹²(93-digit number)

31548107498410843699…79670844867448593919

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 #63,629

Cookie Preferences