Block #578,681

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/6/2014, 6:22:41 AM · Difficulty 10.9679 · 6,224,015 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b361269ad4876cb4a74a7415124564ea4ed30696b42c237c3d1c8073f2d8f18b

View on Chainz ↗

Height

#578,681

Difficulty

10.967942

Transactions

Size

1.09 KB

Version

Bits

0af7cb12

Nonce

480,629,946

Timestamp

6/6/2014, 6:22:41 AM

Confirmations

6,224,015

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b1d5ad7471923821e330fab2965637b5d7699e3cb73a1286c0551cfe0036b5c9

Transactions (5)

Coinbase0a6700152bffb0…75b295508b5c3e

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

af03a95577bee4…cefa662508c968

1 in → 2 out8.2900 XPM227 B

AGEed55R…9o5EJWws AQUu2XkX…1iBGTyGM

6c8ce0ad53b539…f4ec602c4eab8f

1 in → 2 out6.6498 XPM226 B

AQYfM6tR…wtD7VsKo APLGLGBo…cz9dwyzK

8ece098025a390…3dbd596dd34830

1 in → 2 out5.5397 XPM226 B

AdSgTDFv…guJRFFfi AM8GuxnN…AfjbhWoV

d941db49564324…5e03543fbe4225

1 in → 2 out1.5410 XPM227 B

AKir3A4g…1Zd4H8ZU AekdwfxU…kbhJFGTn

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.

5.028 × 10⁹⁷(98-digit number)

50287061436182227742…66021833556576665039

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

5.028 × 10⁹⁷(98-digit number)

50287061436182227742…66021833556576665039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.028 × 10⁹⁷(98-digit number)

50287061436182227742…66021833556576665041

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

1.005 × 10⁹⁸(99-digit number)

10057412287236445548…32043667113153330079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.005 × 10⁹⁸(99-digit number)

10057412287236445548…32043667113153330081

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

2.011 × 10⁹⁸(99-digit number)

20114824574472891097…64087334226306660159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.011 × 10⁹⁸(99-digit number)

20114824574472891097…64087334226306660161

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

4.022 × 10⁹⁸(99-digit number)

40229649148945782194…28174668452613320319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.022 × 10⁹⁸(99-digit number)

40229649148945782194…28174668452613320321

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

8.045 × 10⁹⁸(99-digit number)

80459298297891564388…56349336905226640639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.045 × 10⁹⁸(99-digit number)

80459298297891564388…56349336905226640641

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.609 × 10⁹⁹(100-digit number)

16091859659578312877…12698673810453281279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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