Block #517,396

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/29/2014, 10:25:26 PM · Difficulty 10.8512 · 6,277,989 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cf12153e85c033d29260aa62fa37d236e558eafebea3762ccb40a19e59526dc0

View on Chainz ↗

Height

#517,396

Difficulty

10.851183

Transactions

Size

614 B

Version

Bits

0ad9e726

Nonce

238,668,028

Timestamp

4/29/2014, 10:25:26 PM

Confirmations

6,277,989

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

50cf2835007b89db1ee5fe407f75ba6b8f7e35adb06b3dc84260a5e1301d4d57

Transactions (2)

Coinbaseb1254585578f76…1335d51c27982b

1 in → 1 out8.4900 XPM116 B

AbwWkWZt…kawDhufa

7357fb4d54c1ed…db40403915b4a2

2 in → 4 out10.0159 XPM407 B

AdL7suF5…ksXj79Un AKTrH22f…o8JQ4BHw AeKNrjNj…1NEq95Ta AU8K9zCe…2NaCayba

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.

1.313 × 10⁹⁷(98-digit number)

13133053421313378211…07918422770263893099

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

1.313 × 10⁹⁷(98-digit number)

13133053421313378211…07918422770263893099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.313 × 10⁹⁷(98-digit number)

13133053421313378211…07918422770263893101

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

2.626 × 10⁹⁷(98-digit number)

26266106842626756423…15836845540527786199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.626 × 10⁹⁷(98-digit number)

26266106842626756423…15836845540527786201

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

5.253 × 10⁹⁷(98-digit number)

52532213685253512847…31673691081055572399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.253 × 10⁹⁷(98-digit number)

52532213685253512847…31673691081055572401

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

1.050 × 10⁹⁸(99-digit number)

10506442737050702569…63347382162111144799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.050 × 10⁹⁸(99-digit number)

10506442737050702569…63347382162111144801

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

2.101 × 10⁹⁸(99-digit number)

21012885474101405138…26694764324222289599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.101 × 10⁹⁸(99-digit number)

21012885474101405138…26694764324222289601

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