Block #562,727

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/26/2014, 8:29:42 AM · Difficulty 10.9659 · 6,233,175 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1b3cb19ca44e6e05018d382f6771c0f671597265678b115edf2643b3bf7a12fb

View on Chainz ↗

Height

#562,727

Difficulty

10.965865

Transactions

Size

658 B

Version

Bits

0af742e9

Nonce

14,556,124

Timestamp

5/26/2014, 8:29:42 AM

Confirmations

6,233,175

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a5b8356156fe212f9622c3ae17aefd67b737b29870b8a0cb112ec8b3b437004a

Transactions (3)

Coinbasefa814934990dfc…319ed23501c419

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

cc3bad8c711f05…e0538426d923e3

1 in → 2 out8.2900 XPM225 B

APY6bU6F…oQXHVm48 AMBQ24q8…vfguRsg9

fe290ef5d1571c…dd3c3da89b97b2

1 in → 2 out8.2900 XPM225 B

AZ5yfXce…ZzKvjLPF AMAxLjXk…843iHH6r

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.

1.707 × 10¹⁰⁰(101-digit number)

17075348444609245036…86016436900790251519

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

1.707 × 10¹⁰⁰(101-digit number)

17075348444609245036…86016436900790251519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.707 × 10¹⁰⁰(101-digit number)

17075348444609245036…86016436900790251521

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

3.415 × 10¹⁰⁰(101-digit number)

34150696889218490072…72032873801580503039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.415 × 10¹⁰⁰(101-digit number)

34150696889218490072…72032873801580503041

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

6.830 × 10¹⁰⁰(101-digit number)

68301393778436980144…44065747603161006079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.830 × 10¹⁰⁰(101-digit number)

68301393778436980144…44065747603161006081

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

1.366 × 10¹⁰¹(102-digit number)

13660278755687396028…88131495206322012159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.366 × 10¹⁰¹(102-digit number)

13660278755687396028…88131495206322012161

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

2.732 × 10¹⁰¹(102-digit number)

27320557511374792057…76262990412644024319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.732 × 10¹⁰¹(102-digit number)

27320557511374792057…76262990412644024321

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

5.464 × 10¹⁰¹(102-digit number)

54641115022749584115…52525980825288048639

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