Block #497,112

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/17/2014, 10:40:26 AM · Difficulty 10.7629 · 6,299,728 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1fd04a2ebbeda2e171d2dbef1313e3d6ae2b95508150106dd200193869e693d8

View on Chainz ↗

Height

#497,112

Difficulty

10.762855

Transactions

Size

869 B

Version

Bits

0ac34a73

Nonce

41,440

Timestamp

4/17/2014, 10:40:26 AM

Confirmations

6,299,728

Mined by

⛏️ aSORAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

92bf056adf4d786f21ea5a148cf0efd0884fc2f43bf5aa3df447a69e753e3fec

Transactions (1)

Coinbase92bf056adf4d78…47a69e753e3fec

1 in → 21 out8.6200 XPM776 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q ATKK7iFz…wZm46KN1 AJtNW28X…Syb4Ph5j

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.

9.278 × 10¹⁰⁰(101-digit number)

92781584484170894926…05137679137008844799

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

9.278 × 10¹⁰⁰(101-digit number)

92781584484170894926…05137679137008844799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.278 × 10¹⁰⁰(101-digit number)

92781584484170894926…05137679137008844801

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

1.855 × 10¹⁰¹(102-digit number)

18556316896834178985…10275358274017689599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.855 × 10¹⁰¹(102-digit number)

18556316896834178985…10275358274017689601

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

3.711 × 10¹⁰¹(102-digit number)

37112633793668357970…20550716548035379199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.711 × 10¹⁰¹(102-digit number)

37112633793668357970…20550716548035379201

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

7.422 × 10¹⁰¹(102-digit number)

74225267587336715941…41101433096070758399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.422 × 10¹⁰¹(102-digit number)

74225267587336715941…41101433096070758401

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

1.484 × 10¹⁰²(103-digit number)

14845053517467343188…82202866192141516799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.484 × 10¹⁰²(103-digit number)

14845053517467343188…82202866192141516801

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