Block #73,949

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 8:40:00 AM · Difficulty 8.9952 · 6,750,570 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

736bb983d350a5878677eb4406a4c396c7c352bd6320ebf00e57aa574cc3569e

View on Chainz ↗

Height

#73,949

Difficulty

8.995178

Transactions

Size

555 B

Version

Bits

08fec3f6

Nonce

1,063

Timestamp

7/21/2013, 8:40:00 AM

Confirmations

6,750,570

Mined by

⛏️ P2SHAb8afhHafmbY9dYeVWAE1EHd6ccNwnVLP1

Merkle Root

f9f886d1e71b9698d56462c188d39259406cf8940425a852a2d3d1138ef0d344

Transactions (3)

Coinbase7db65a4056a6a6…4f03e2b224910d

1 in → 1 out12.3600 XPM110 B

Ab8afhHa…cNwnVLP1

ef6d19bfe915e6…663a5e475b6bcf

1 in → 1 out12.3600 XPM159 B

AUfahFXS…8J91Aks8

6f223e0af3f959…efad70818c617b

1 in → 2 out12.3400 XPM192 B

AFuTrcG1…mV7W6Wfy ANBXgfaf…ZXqNYSdt

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.

8.902 × 10¹⁰³(104-digit number)

89020226633542747086…55338602438846473519

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

8.902 × 10¹⁰³(104-digit number)

89020226633542747086…55338602438846473519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.902 × 10¹⁰³(104-digit number)

89020226633542747086…55338602438846473521

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

1.780 × 10¹⁰⁴(105-digit number)

17804045326708549417…10677204877692947039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.780 × 10¹⁰⁴(105-digit number)

17804045326708549417…10677204877692947041

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

3.560 × 10¹⁰⁴(105-digit number)

35608090653417098834…21354409755385894079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.560 × 10¹⁰⁴(105-digit number)

35608090653417098834…21354409755385894081

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

7.121 × 10¹⁰⁴(105-digit number)

71216181306834197669…42708819510771788159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.121 × 10¹⁰⁴(105-digit number)

71216181306834197669…42708819510771788161

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

1.424 × 10¹⁰⁵(106-digit number)

14243236261366839533…85417639021543576319

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 #73,949

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