Block #68,258

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 3:10:01 AM · Difficulty 8.9893 · 6,749,048 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

998a02b1c77300d88af21a3b48b3068b5ba9ea7cd7d553358b43b9db14492d02

View on Chainz ↗

Height

#68,258

Difficulty

8.989251

Transactions

Size

363 B

Version

Bits

08fd3f8d

Nonce

195

Timestamp

7/20/2013, 3:10:01 AM

Confirmations

6,749,048

Mined by

⛏️ P2SHAHouzGdBvFee2HLCeT9rNAGtc38VinDX7w

Merkle Root

ec595a201303265124406729055756821ea07c67c2bc8865af39b58180036d28

Transactions (2)

Coinbase2acc9d0cd3d646…ee7096bdd4d081

1 in → 1 out12.3700 XPM110 B

AHouzGdB…8VinDX7w

7fd9cf114980c3…a6a76e1bb9fe9a

1 in → 1 out12.3800 XPM159 B

AXPRySWh…GeFZKjLU

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.

1.132 × 10¹⁰³(104-digit number)

11321945527505475934…19859800727412069699

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

1.132 × 10¹⁰³(104-digit number)

11321945527505475934…19859800727412069699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.132 × 10¹⁰³(104-digit number)

11321945527505475934…19859800727412069701

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

2.264 × 10¹⁰³(104-digit number)

22643891055010951869…39719601454824139399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.264 × 10¹⁰³(104-digit number)

22643891055010951869…39719601454824139401

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

4.528 × 10¹⁰³(104-digit number)

45287782110021903739…79439202909648278799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.528 × 10¹⁰³(104-digit number)

45287782110021903739…79439202909648278801

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

9.057 × 10¹⁰³(104-digit number)

90575564220043807478…58878405819296557599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.057 × 10¹⁰³(104-digit number)

90575564220043807478…58878405819296557601

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

1.811 × 10¹⁰⁴(105-digit number)

18115112844008761495…17756811638593115199

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 #68,258

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