Block #625,181

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/9/2014, 12:06:46 PM · Difficulty 10.9591 · 6,218,794 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d9256b7d93e051c4aa17672c73150fd4a77a192baa0495b03617c8dde7b2fb3f

View on Chainz ↗

Height

#625,181

Difficulty

10.959128

Transactions

Size

1.38 KB

Version

Bits

0af58967

Nonce

130,734,503

Timestamp

7/9/2014, 12:06:46 PM

Confirmations

6,218,794

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

270dc27b7055d95820b3f160d70bc954d55189399e848bb29dd8fd9bd649fac3

Transactions (5)

Coinbase72d34180223e84…2f12903b5b9998

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

0af2706aebd7c9…1a6f73664f54dd

3 in → 2 out10.5770 XPM522 B

AVYi1Ne3…o5MBMUSM AR1X7PV9…Tmii63dD

54c08766ce81cc…eb74f18bf1a182

1 in → 2 out7.1048 XPM227 B

AXme6eTz…PLdysKBL ATBfxyc5…qSjbGwwe

86eb0fe765b467…ead5cca1b1cae4

1 in → 2 out6.0338 XPM226 B

AaPVSnjy…grkWjuQn AYU1Ynxb…6LNs2ZYM

acbea2721a20ee…b470a25de2a1c9

1 in → 2 out0.8043 XPM226 B

ASkuboV8…mBQxNm3J AYEqJQxr…mukGcfWG

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.

5.356 × 10⁹⁸(99-digit number)

53560013475440791459…11975310228594923519

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

5.356 × 10⁹⁸(99-digit number)

53560013475440791459…11975310228594923519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.356 × 10⁹⁸(99-digit number)

53560013475440791459…11975310228594923521

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

1.071 × 10⁹⁹(100-digit number)

10712002695088158291…23950620457189847039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.071 × 10⁹⁹(100-digit number)

10712002695088158291…23950620457189847041

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

2.142 × 10⁹⁹(100-digit number)

21424005390176316583…47901240914379694079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.142 × 10⁹⁹(100-digit number)

21424005390176316583…47901240914379694081

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

4.284 × 10⁹⁹(100-digit number)

42848010780352633167…95802481828759388159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.284 × 10⁹⁹(100-digit number)

42848010780352633167…95802481828759388161

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

8.569 × 10⁹⁹(100-digit number)

85696021560705266334…91604963657518776319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.569 × 10⁹⁹(100-digit number)

85696021560705266334…91604963657518776321

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 #625,181

Cookie Preferences