Block #550,161

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/18/2014, 12:25:09 AM · Difficulty 10.9614 · 6,259,448 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

79adee004d3114c291fb1673688b019f618aa05f7545a158c757cdb2b1e543c2

View on Chainz ↗

Height

#550,161

Difficulty

10.961427

Transactions

Size

616 B

Version

Bits

0af6200f

Nonce

41,090,140

Timestamp

5/18/2014, 12:25:09 AM

Confirmations

6,259,448

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

84351e7c13c8d093837dc218874c28b63963b04d4d8c4062c062fee612cb2a02

Transactions (2)

Coinbaseb2b859f93500a2…795d075e7a7788

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

ba114f61e963f1…0371055dbd03c3

2 in → 4 out9.3785 XPM407 B

AY1FuBSV…jEZrVd1U AWppzrSM…CxCJ4whA AeKNrjNj…1NEq95Ta AHDTi5u9…w5TNUkX7

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.

2.352 × 10¹⁰²(103-digit number)

23525795605392792306…76778992493056163839

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

2.352 × 10¹⁰²(103-digit number)

23525795605392792306…76778992493056163839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.352 × 10¹⁰²(103-digit number)

23525795605392792306…76778992493056163841

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

4.705 × 10¹⁰²(103-digit number)

47051591210785584613…53557984986112327679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.705 × 10¹⁰²(103-digit number)

47051591210785584613…53557984986112327681

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

9.410 × 10¹⁰²(103-digit number)

94103182421571169227…07115969972224655359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.410 × 10¹⁰²(103-digit number)

94103182421571169227…07115969972224655361

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

1.882 × 10¹⁰³(104-digit number)

18820636484314233845…14231939944449310719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.882 × 10¹⁰³(104-digit number)

18820636484314233845…14231939944449310721

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

3.764 × 10¹⁰³(104-digit number)

37641272968628467691…28463879888898621439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.764 × 10¹⁰³(104-digit number)

37641272968628467691…28463879888898621441

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

7.528 × 10¹⁰³(104-digit number)

75282545937256935382…56927759777797242879

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

Block #550,161

Cookie Preferences