Block #578,334

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/5/2014, 11:33:21 PM · Difficulty 10.9683 · 6,223,482 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d409ed501b2da49d2de259004eb58cda88641ddc1538a5277f2cfc83cbe9bc64

View on Chainz ↗

Height

#578,334

Difficulty

10.968332

Transactions

Size

807 B

Version

Bits

0af7e494

Nonce

148,436,238

Timestamp

6/5/2014, 11:33:21 PM

Confirmations

6,223,482

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4aa385e2a9974138d5a211f2ca364f93793eed781643e05ae0c21e37a0322e4a

Transactions (3)

Coinbase4f7db9370e147e…759b9aabba6b63

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

c2fe3843f3696c…2872b2682cf85c

2 in → 2 out540.9100 XPM373 B

APuz5Ldg…aRFjQAHk AJ5xWTLy…U77cqd1f

515b1acb2ee0cf…dadb1a0ae6aa5a

1 in → 2 out2.6066 XPM226 B

AYz8XXeX…wUExhw54 ARZNHcGp…oqZwJqL4

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.

1.349 × 10⁹⁹(100-digit number)

13491194538123112050…75282582984870871039

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

1.349 × 10⁹⁹(100-digit number)

13491194538123112050…75282582984870871039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.349 × 10⁹⁹(100-digit number)

13491194538123112050…75282582984870871041

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

2.698 × 10⁹⁹(100-digit number)

26982389076246224101…50565165969741742079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.698 × 10⁹⁹(100-digit number)

26982389076246224101…50565165969741742081

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

5.396 × 10⁹⁹(100-digit number)

53964778152492448202…01130331939483484159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.396 × 10⁹⁹(100-digit number)

53964778152492448202…01130331939483484161

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

1.079 × 10¹⁰⁰(101-digit number)

10792955630498489640…02260663878966968319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.079 × 10¹⁰⁰(101-digit number)

10792955630498489640…02260663878966968321

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

2.158 × 10¹⁰⁰(101-digit number)

21585911260996979280…04521327757933936639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.158 × 10¹⁰⁰(101-digit number)

21585911260996979280…04521327757933936641

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