Block #560,984

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/25/2014, 5:30:40 AM · Difficulty 10.9650 · 6,242,515 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

987e60c48f0efae93a9ee7be81e3c32f77848f425133c04cfe993feec8ce48e4

View on Chainz ↗

Height

#560,984

Difficulty

10.964972

Transactions

Size

1.08 KB

Version

Bits

0af70865

Nonce

308,259,716

Timestamp

5/25/2014, 5:30:40 AM

Confirmations

6,242,515

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2b44c1eed5437e01a9de58145fe6e8963ecc8f73ca67ab4e315b74ae37b8b76c

Transactions (3)

Coinbasebaa68fd286a60b…6965be52fd9d79

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

f7de99fad9a5f9…32ed125defce3e

4 in → 2 out20.2878 XPM667 B

AG5uHL9x…tdDFRE42 AW6Cei3u…fGJvgpw8

fb452ad3f88ca3…59ca5df96c061b

1 in → 2 out6.2124 XPM227 B

APwZjrX3…VWBykQA5 AdobpKjj…M9auVuzw

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.

7.300 × 10⁹⁸(99-digit number)

73008810372854033639…33262583038947190399

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

7.300 × 10⁹⁸(99-digit number)

73008810372854033639…33262583038947190399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.300 × 10⁹⁸(99-digit number)

73008810372854033639…33262583038947190401

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

1.460 × 10⁹⁹(100-digit number)

14601762074570806727…66525166077894380799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.460 × 10⁹⁹(100-digit number)

14601762074570806727…66525166077894380801

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

2.920 × 10⁹⁹(100-digit number)

29203524149141613455…33050332155788761599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.920 × 10⁹⁹(100-digit number)

29203524149141613455…33050332155788761601

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

5.840 × 10⁹⁹(100-digit number)

58407048298283226911…66100664311577523199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.840 × 10⁹⁹(100-digit number)

58407048298283226911…66100664311577523201

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

1.168 × 10¹⁰⁰(101-digit number)

11681409659656645382…32201328623155046399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.168 × 10¹⁰⁰(101-digit number)

11681409659656645382…32201328623155046401

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

2.336 × 10¹⁰⁰(101-digit number)

23362819319313290764…64402657246310092799

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