Block #274,974

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 12:33:10 PM · Difficulty 9.9594 · 6,530,829 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d3d61620a3a77417e36371311719cd96524d4d70eb7ef10df6cdfddd32988f22

View on Chainz ↗

Height

#274,974

Difficulty

9.959351

Transactions

Size

1.11 KB

Version

Bits

09f5980e

Nonce

6,964

Timestamp

11/26/2013, 12:33:10 PM

Confirmations

6,530,829

Mined by

⛏️ 2aR:ZARpndEmcGyFUFhdFVbgqJiPBAmHg792kEk

Merkle Root

f78077275b33a63eee3242142e0d2e3e6fdf0f449e15a2e16a9da61146eec9e6

Transactions (1)

Coinbasef78077275b33a6…9da61146eec9e6

1 in → 29 out10.0409 XPM1.02 KB

ARpndEmc…Hg792kEk Ae2pnFaX…7SPtJMsm APeshfYV…3PKcKMKH AMbCuLHZ…WSoStwkc AT5oTsET…Pi5H6raU

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.

7.610 × 10⁹⁶(97-digit number)

76102114005578073278…42269143410919976959

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

7.610 × 10⁹⁶(97-digit number)

76102114005578073278…42269143410919976959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.610 × 10⁹⁶(97-digit number)

76102114005578073278…42269143410919976961

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

1.522 × 10⁹⁷(98-digit number)

15220422801115614655…84538286821839953919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.522 × 10⁹⁷(98-digit number)

15220422801115614655…84538286821839953921

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

3.044 × 10⁹⁷(98-digit number)

30440845602231229311…69076573643679907839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.044 × 10⁹⁷(98-digit number)

30440845602231229311…69076573643679907841

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

6.088 × 10⁹⁷(98-digit number)

60881691204462458622…38153147287359815679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.088 × 10⁹⁷(98-digit number)

60881691204462458622…38153147287359815681

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

1.217 × 10⁹⁸(99-digit number)

12176338240892491724…76306294574719631359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.217 × 10⁹⁸(99-digit number)

12176338240892491724…76306294574719631361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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