Block #496,172

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/16/2014, 11:25:44 PM · Difficulty 10.7499 · 6,307,834 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40a6450b78a857f6f235cf687ed304a0d450e6132de5c2519a714279d40abe9a

View on Chainz ↗

Height

#496,172

Difficulty

10.749891

Transactions

Size

1.72 KB

Version

Bits

0abff8db

Nonce

74,148,194

Timestamp

4/16/2014, 11:25:44 PM

Confirmations

6,307,834

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

aac64b4093c9daa21cfba1e0f6692341c44102c92a0b23655cc44db8743758ca

Transactions (4)

Coinbase9c66312ca144cc…1de2fb19f0109c

1 in → 1 out8.6800 XPM116 B

AbwWkWZt…kawDhufa

3a7399f387b6eb…7845e95a950c8b

6 in → 9 out27.9014 XPM1.08 KB

AJ4n9kZS…SnX6JMpQ AeKNrjNj…1NEq95Ta AMeyeZ9L…gJoDemgf ALNTdrTH…hyfEy639 AGw7KuTT…ZfJmwhoB

db132bf77823f9…b5f85f584bd3cd

1 in → 2 out6.6963 XPM225 B

APhyxg3g…LNqfRJSZ AJRAKoca…2Ahyq3dg

fbfd432138e7d9…8909146f8282d2

1 in → 2 out1.4676 XPM225 B

AYhN9yGp…VLF2up9Y ATbwaXYH…XwadvCv7

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.

9.706 × 10⁹⁷(98-digit number)

97067013156539327582…31504739937280447599

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

9.706 × 10⁹⁷(98-digit number)

97067013156539327582…31504739937280447599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.706 × 10⁹⁷(98-digit number)

97067013156539327582…31504739937280447601

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

1.941 × 10⁹⁸(99-digit number)

19413402631307865516…63009479874560895199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.941 × 10⁹⁸(99-digit number)

19413402631307865516…63009479874560895201

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

3.882 × 10⁹⁸(99-digit number)

38826805262615731032…26018959749121790399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.882 × 10⁹⁸(99-digit number)

38826805262615731032…26018959749121790401

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

7.765 × 10⁹⁸(99-digit number)

77653610525231462065…52037919498243580799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.765 × 10⁹⁸(99-digit number)

77653610525231462065…52037919498243580801

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

1.553 × 10⁹⁹(100-digit number)

15530722105046292413…04075838996487161599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.553 × 10⁹⁹(100-digit number)

15530722105046292413…04075838996487161601

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