Block #75,245

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 3:26:11 PM · Difficulty 8.9960 · 6,734,292 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c2bdb610c5c058ba13e301844ded961f7cf5aa303330653e6f10f99f643fdfe4

View on Chainz ↗

Height

#75,245

Difficulty

8.995993

Transactions

Size

360 B

Version

Bits

08fef969

Nonce

590

Timestamp

7/21/2013, 3:26:11 PM

Confirmations

6,734,292

Mined by

⛏️ P2SHAFyH24t7snpCzfZK3DEQSSKvCuFypwiQVM

Merkle Root

55bf8b4542625b4987b60f347467dd45695ea39a9755968d0ebba8b68fa15243

Transactions (2)

Coinbase3376867645a8f9…97842dfca21615

1 in → 1 out12.5900 XPM110 B

AFyH24t7…FypwiQVM

1cc53f177dfaf8…c7dcd5458746c1

1 in → 1 out12.1000 XPM158 B

AWgqwfyG…7sLAZbuJ

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.

6.570 × 10⁹⁹(100-digit number)

65703264562002708227…69425459905109922979

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

6.570 × 10⁹⁹(100-digit number)

65703264562002708227…69425459905109922979

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.570 × 10⁹⁹(100-digit number)

65703264562002708227…69425459905109922981

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

1.314 × 10¹⁰⁰(101-digit number)

13140652912400541645…38850919810219845959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.314 × 10¹⁰⁰(101-digit number)

13140652912400541645…38850919810219845961

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

2.628 × 10¹⁰⁰(101-digit number)

26281305824801083291…77701839620439691919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.628 × 10¹⁰⁰(101-digit number)

26281305824801083291…77701839620439691921

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

5.256 × 10¹⁰⁰(101-digit number)

52562611649602166582…55403679240879383839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.256 × 10¹⁰⁰(101-digit number)

52562611649602166582…55403679240879383841

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

1.051 × 10¹⁰¹(102-digit number)

10512522329920433316…10807358481758767679

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 #75,245

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