Block #63,932

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 4:39:00 AM · Difficulty 8.9804 · 6,742,770 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dcc0566b2cfc32982b87230628b76030a71e25796ea3be688b4c96fc3a08e4b8

View on Chainz ↗

Height

#63,932

Difficulty

8.980403

Transactions

Size

364 B

Version

Bits

08fafbb0

Nonce

210

Timestamp

7/19/2013, 4:39:00 AM

Confirmations

6,742,770

Mined by

⛏️ P2SHATkPCNiuYBqcNeSBc2y1E58R3MsUjt7RrN

Merkle Root

89844363eca41c74189705e070eba422446974cb4d501f7e467fc71b4a1695fe

Transactions (2)

Coinbase1b1ee0f6505390…213d8deb22f42e

1 in → 1 out12.3900 XPM110 B

ATkPCNiu…sUjt7RrN

25a36c432a36d2…b3d3cb78816452

1 in → 1 out12.4000 XPM159 B

AVjWiv4g…PKJ7FE2n

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.

4.951 × 10¹⁰⁵(106-digit number)

49516496496849696894…19430434472920319069

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

4.951 × 10¹⁰⁵(106-digit number)

49516496496849696894…19430434472920319069

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.951 × 10¹⁰⁵(106-digit number)

49516496496849696894…19430434472920319071

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

9.903 × 10¹⁰⁵(106-digit number)

99032992993699393789…38860868945840638139

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.903 × 10¹⁰⁵(106-digit number)

99032992993699393789…38860868945840638141

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

1.980 × 10¹⁰⁶(107-digit number)

19806598598739878757…77721737891681276279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.980 × 10¹⁰⁶(107-digit number)

19806598598739878757…77721737891681276281

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

3.961 × 10¹⁰⁶(107-digit number)

39613197197479757515…55443475783362552559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.961 × 10¹⁰⁶(107-digit number)

39613197197479757515…55443475783362552561

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

7.922 × 10¹⁰⁶(107-digit number)

79226394394959515031…10886951566725105119

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 #63,932

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