Block #276,790

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 8:00:20 AM · Difficulty 9.9642 · 6,530,942 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7a349e3f8579aa5d7c2c3998d0e542706c4bc3a4d2ae77351d1ab929c1178cc4

View on Chainz ↗

Height

#276,790

Difficulty

9.964223

Transactions

Size

9.99 KB

Version

Bits

09f6d74c

Nonce

23,505

Timestamp

11/27/2013, 8:00:20 AM

Confirmations

6,530,942

Mined by

⛏️ 69aRAUSdJaErsBBYg47xHm7xkW1PfAY4n4oUzF

Merkle Root

97361a81f9e0e042636cab1bb235260b03cef67bbc3824e5034bc72bdcacef04

Transactions (2)

Coinbase65318ec4981854…1fe9669669913f

1 in → 24 out10.0600 XPM879 B

AUSdJaEr…Y4n4oUzF AScAzqGc…BZ6tV1vJ Abv8pzf1…t4zPXDTV Aaf3CsqS…k1Eu3vmJ AXsfu4E3…ZifoNcUa

d34140bc0ebe3a…00fea3b714a031

62 in → 2 out3.7940 XPM9.04 KB

AdUw2P8N…FVdMWv3n AGi5bgRv…BFQy9fy1

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.

1.208 × 10⁹⁴(95-digit number)

12088196445647307375…99378722722526566399

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

1.208 × 10⁹⁴(95-digit number)

12088196445647307375…99378722722526566399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.208 × 10⁹⁴(95-digit number)

12088196445647307375…99378722722526566401

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

2.417 × 10⁹⁴(95-digit number)

24176392891294614751…98757445445053132799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.417 × 10⁹⁴(95-digit number)

24176392891294614751…98757445445053132801

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

4.835 × 10⁹⁴(95-digit number)

48352785782589229502…97514890890106265599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.835 × 10⁹⁴(95-digit number)

48352785782589229502…97514890890106265601

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

9.670 × 10⁹⁴(95-digit number)

96705571565178459004…95029781780212531199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.670 × 10⁹⁴(95-digit number)

96705571565178459004…95029781780212531201

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

1.934 × 10⁹⁵(96-digit number)

19341114313035691800…90059563560425062399

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 #276,790

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