Block #362,213

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/16/2014, 1:55:59 PM · Difficulty 10.4122 · 6,441,560 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ebc893bc12a10e36be63870b8b6102230e8f4d27c156f0546d12ba874208b794

View on Chainz ↗

Height

#362,213

Difficulty

10.412236

Transactions

Size

1.46 KB

Version

Bits

0a69884b

Nonce

11,313

Timestamp

1/16/2014, 1:55:59 PM

Confirmations

6,441,560

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

abdcfc4d62058912e744dd83896fdd3178c0cddc20f01ddbd6af4461f889b26a

Transactions (3)

Coinbaseb41b4753793a03…3c58d635c5dec1

1 in → 1 out9.2400 XPM116 B

AbwWkWZt…kawDhufa

7537529009f1b2…c8275f26a77688

1 in → 1 out2.9900 XPM193 B

AdwYsaaT…D6SV1XP6

f0fe9159812061…0e46dfea10a89b

5 in → 15 out46.5219 XPM1.06 KB

AeKNrjNj…1NEq95Ta AND9bh7f…Vq85QSAN AbpE83ia…CLwYTUjb AbRso1mW…qkEyGERy AQmbZZK2…8Hh6ZeM7

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.

6.311 × 10⁹⁸(99-digit number)

63116126487843139280…23518388219115627519

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

6.311 × 10⁹⁸(99-digit number)

63116126487843139280…23518388219115627519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.311 × 10⁹⁸(99-digit number)

63116126487843139280…23518388219115627521

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

1.262 × 10⁹⁹(100-digit number)

12623225297568627856…47036776438231255039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.262 × 10⁹⁹(100-digit number)

12623225297568627856…47036776438231255041

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

2.524 × 10⁹⁹(100-digit number)

25246450595137255712…94073552876462510079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.524 × 10⁹⁹(100-digit number)

25246450595137255712…94073552876462510081

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

5.049 × 10⁹⁹(100-digit number)

50492901190274511424…88147105752925020159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.049 × 10⁹⁹(100-digit number)

50492901190274511424…88147105752925020161

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

1.009 × 10¹⁰⁰(101-digit number)

10098580238054902284…76294211505850040319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.009 × 10¹⁰⁰(101-digit number)

10098580238054902284…76294211505850040321

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