Block #71,246

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 5:44:42 PM · Difficulty 8.9930 · 6,755,069 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6a92522b12afa4ffedb5121ce4c9e33fbeafeb959f5e7c0affbd5e46f11e02b9

View on Chainz ↗

Height

#71,246

Difficulty

8.992998

Transactions

Size

203 B

Version

Bits

08fe3521

Nonce

582

Timestamp

7/20/2013, 5:44:42 PM

Confirmations

6,755,069

Mined by

⛏️ P2SHAPZw681PDHXiNBLN7jvKQAVJndYv3wDWd9

Merkle Root

d4677409d0595b475c577f0642c4b1237440d706e4d5920216ffb67dcf466e6f

Transactions (1)

Coinbased4677409d0595b…ffb67dcf466e6f

1 in → 1 out12.3500 XPM110 B

APZw681P…Yv3wDWd9

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.

9.981 × 10¹⁰¹(102-digit number)

99817415120338002011…65582104755512398199

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

9.981 × 10¹⁰¹(102-digit number)

99817415120338002011…65582104755512398199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.981 × 10¹⁰¹(102-digit number)

99817415120338002011…65582104755512398201

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

1.996 × 10¹⁰²(103-digit number)

19963483024067600402…31164209511024796399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.996 × 10¹⁰²(103-digit number)

19963483024067600402…31164209511024796401

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

3.992 × 10¹⁰²(103-digit number)

39926966048135200804…62328419022049592799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.992 × 10¹⁰²(103-digit number)

39926966048135200804…62328419022049592801

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

7.985 × 10¹⁰²(103-digit number)

79853932096270401609…24656838044099185599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.985 × 10¹⁰²(103-digit number)

79853932096270401609…24656838044099185601

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 #71,246

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