Block #550,063

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/17/2014, 11:06:38 PM · Difficulty 10.9613 · 6,246,566 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3d5607115da0916b2f40843caf7c446333fde35c9ed603307b4841bdf2a54600

View on Chainz ↗

Height

#550,063

Difficulty

10.961272

Transactions

Size

843 B

Version

Bits

0af615f2

Nonce

103,714,103

Timestamp

5/17/2014, 11:06:38 PM

Confirmations

6,246,566

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7f97f5d9cf1667034b97a4d3746bcb8c53127dacdb29274cafa1458b4a8ecd7e

Transactions (2)

Coinbase6b6ebfc86fcbe1…9759e3410f166a

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

599e459f0020a4…fabae114d17b6f

4 in → 1 out5.1786 XPM635 B

ASrCnREh…ueFjRQ5d

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.

3.174 × 10⁹⁹(100-digit number)

31743044079611795908…73459607078245169599

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

3.174 × 10⁹⁹(100-digit number)

31743044079611795908…73459607078245169599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.174 × 10⁹⁹(100-digit number)

31743044079611795908…73459607078245169601

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

6.348 × 10⁹⁹(100-digit number)

63486088159223591816…46919214156490339199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.348 × 10⁹⁹(100-digit number)

63486088159223591816…46919214156490339201

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

1.269 × 10¹⁰⁰(101-digit number)

12697217631844718363…93838428312980678399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.269 × 10¹⁰⁰(101-digit number)

12697217631844718363…93838428312980678401

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

2.539 × 10¹⁰⁰(101-digit number)

25394435263689436726…87676856625961356799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.539 × 10¹⁰⁰(101-digit number)

25394435263689436726…87676856625961356801

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

5.078 × 10¹⁰⁰(101-digit number)

50788870527378873453…75353713251922713599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.078 × 10¹⁰⁰(101-digit number)

50788870527378873453…75353713251922713601

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

1.015 × 10¹⁰¹(102-digit number)

10157774105475774690…50707426503845427199

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