Block #549,014

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/17/2014, 8:19:30 AM · Difficulty 10.9600 · 6,253,539 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

23d673d38bb65e49663619aa51dd46f6ca3d847561348316c1280613ee37620d

View on Chainz ↗

Height

#549,014

Difficulty

10.959964

Transactions

Size

3.77 KB

Version

Bits

0af5c031

Nonce

5,307,950

Timestamp

5/17/2014, 8:19:30 AM

Confirmations

6,253,539

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3feba654024f3b86fc3c6a424419808d43a6353809b2ed016c2b95904a8190a6

Transactions (5)

Coinbase6ab39b14cea0e3…23f6b9ab531932

1 in → 1 out8.3700 XPM116 B

ANSXnLY2…Sd25TjkD

fd8c440e4d9680…e92cff5ce471bc

3 in → 1 out7590.0000 XPM488 B

AFtwRAEY…gp4etVu7

c8e74118b2e6c9…e6995e1c7cde51

11 in → 2 out242.0000 XPM1.67 KB

AUtMUHVY…KervxBbW AZ4gbyKx…ZCo23QHF

354b9e8634de4d…423383b0dc23f1

8 in → 1 out8.0543 XPM1.20 KB

AacwPYzW…EdjJgrkS

557aa32a9dc77b…73dd22563f7ea5

1 in → 2 out5.6326 XPM226 B

AGswXtkK…MRVmV1Kz AYmzMKCN…UT8QN8Vt

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.

1.671 × 10¹⁰¹(102-digit number)

16713003643836025793…92265167158758440959

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

1.671 × 10¹⁰¹(102-digit number)

16713003643836025793…92265167158758440959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.671 × 10¹⁰¹(102-digit number)

16713003643836025793…92265167158758440961

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

3.342 × 10¹⁰¹(102-digit number)

33426007287672051586…84530334317516881919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.342 × 10¹⁰¹(102-digit number)

33426007287672051586…84530334317516881921

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

6.685 × 10¹⁰¹(102-digit number)

66852014575344103172…69060668635033763839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.685 × 10¹⁰¹(102-digit number)

66852014575344103172…69060668635033763841

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

1.337 × 10¹⁰²(103-digit number)

13370402915068820634…38121337270067527679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.337 × 10¹⁰²(103-digit number)

13370402915068820634…38121337270067527681

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

2.674 × 10¹⁰²(103-digit number)

26740805830137641269…76242674540135055359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.674 × 10¹⁰²(103-digit number)

26740805830137641269…76242674540135055361

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