Block #548,314

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/16/2014, 10:49:34 PM · Difficulty 10.9589 · 6,245,995 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7a7243552ec300f5f9ad151b3b6761ae64b72064da8045bb49727c107ca37b23

View on Chainz ↗

Height

#548,314

Difficulty

10.958902

Transactions

Size

401 B

Version

Bits

0af57a9c

Nonce

84,355

Timestamp

5/16/2014, 10:49:34 PM

Confirmations

6,245,995

Merkle Root

44f4d98941d6d9b6555543e38aeea7e97dbabc810750be391c78476b382fdef6

Transactions (2)

Coinbased727b01a30ab45…45646e0403b3af

1 in → 1 out8.3215 XPM116 B

ANSXnLY2…Sd25TjkD

c8bf3a22496b9a…16cef5a6156b7e

1 in → 1 out1.0700 XPM193 B

AbXCqCAU…8ikSsoVn

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.

4.668 × 10⁹⁹(100-digit number)

46689365793090314008…68030232591150766079

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

4.668 × 10⁹⁹(100-digit number)

46689365793090314008…68030232591150766079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.668 × 10⁹⁹(100-digit number)

46689365793090314008…68030232591150766081

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

9.337 × 10⁹⁹(100-digit number)

93378731586180628016…36060465182301532159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.337 × 10⁹⁹(100-digit number)

93378731586180628016…36060465182301532161

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

1.867 × 10¹⁰⁰(101-digit number)

18675746317236125603…72120930364603064319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.867 × 10¹⁰⁰(101-digit number)

18675746317236125603…72120930364603064321

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

3.735 × 10¹⁰⁰(101-digit number)

37351492634472251206…44241860729206128639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.735 × 10¹⁰⁰(101-digit number)

37351492634472251206…44241860729206128641

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

7.470 × 10¹⁰⁰(101-digit number)

74702985268944502413…88483721458412257279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.470 × 10¹⁰⁰(101-digit number)

74702985268944502413…88483721458412257281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.494 × 10¹⁰¹(102-digit number)

14940597053788900482…76967442916824514559

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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