Block #510,846

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/25/2014, 9:36:23 PM · Difficulty 10.8274 · 6,303,491 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

17bb7d247b6921e4bec723fe7088efcf2728f7f3806a789cd6f4e26bd373a58a

View on Chainz ↗

Height

#510,846

Difficulty

10.827444

Transactions

Size

764 B

Version

Bits

0ad3d358

Nonce

99,315

Timestamp

4/25/2014, 9:36:23 PM

Confirmations

6,303,491

Mined by

⛏️ ~aSZ9AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

b7ee2c63e838254eef85ea21a362653128f73a6ff2df8f289c4f22225c4938ad

Transactions (1)

Coinbaseb7ee2c63e83825…4f22225c4938ad

1 in → 18 out8.5200 XPM675 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AJtNW28X…Syb4Ph5j ATKK7iFz…wZm46KN1 AdxPNkWD…ZMa9u34q

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.

5.686 × 10⁹¹(92-digit number)

56863587526018684853…89652298233538776559

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

5.686 × 10⁹¹(92-digit number)

56863587526018684853…89652298233538776559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.686 × 10⁹¹(92-digit number)

56863587526018684853…89652298233538776561

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

1.137 × 10⁹²(93-digit number)

11372717505203736970…79304596467077553119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.137 × 10⁹²(93-digit number)

11372717505203736970…79304596467077553121

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

2.274 × 10⁹²(93-digit number)

22745435010407473941…58609192934155106239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.274 × 10⁹²(93-digit number)

22745435010407473941…58609192934155106241

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

4.549 × 10⁹²(93-digit number)

45490870020814947882…17218385868310212479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.549 × 10⁹²(93-digit number)

45490870020814947882…17218385868310212481

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

9.098 × 10⁹²(93-digit number)

90981740041629895765…34436771736620424959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.098 × 10⁹²(93-digit number)

90981740041629895765…34436771736620424961

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

Block #510,846

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