Block #64,222

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 6:22:48 AM · Difficulty 8.9811 · 6,752,654 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ea4347d22986737065d1b44c7926552afaae45dab978a767c55dd06933362485

View on Chainz ↗

Height

#64,222

Difficulty

8.981123

Transactions

Size

872 B

Version

Bits

08fb2ae2

Nonce

Timestamp

7/19/2013, 6:22:48 AM

Confirmations

6,752,654

Mined by

⛏️ P2SHAafQth8ZdRJHXBpH2Yns3ixjSohxjRwe8k

Merkle Root

836a9e117cab019704fcc4bd89fa0cff8061eae8c7ff95f7c6d26f79566c9271

Transactions (2)

Coinbase51538abe35c3ac…11f612232d3e2d

1 in → 1 out12.3900 XPM110 B

AafQth8Z…hxjRwe8k

df403a3c9a00ae…8c0921fa7d58d6

4 in → 2 out79.9153 XPM669 B

AS4Uy8Wo…3kmV8XFd Aa4mQ8oN…LKM4opZF

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.

3.930 × 10¹⁰¹(102-digit number)

39302003121502524299…39994395859417567129

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

3.930 × 10¹⁰¹(102-digit number)

39302003121502524299…39994395859417567129

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.930 × 10¹⁰¹(102-digit number)

39302003121502524299…39994395859417567131

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

7.860 × 10¹⁰¹(102-digit number)

78604006243005048599…79988791718835134259

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.860 × 10¹⁰¹(102-digit number)

78604006243005048599…79988791718835134261

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

1.572 × 10¹⁰²(103-digit number)

15720801248601009719…59977583437670268519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.572 × 10¹⁰²(103-digit number)

15720801248601009719…59977583437670268521

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

3.144 × 10¹⁰²(103-digit number)

31441602497202019439…19955166875340537039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.144 × 10¹⁰²(103-digit number)

31441602497202019439…19955166875340537041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 #64,222

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