Block #561,549

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/25/2014, 2:08:51 PM · Difficulty 10.9653 · 6,248,445 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

76018ec428132ad643915bbae177204bdaef374522347d75404fdb356e752982

View on Chainz ↗

Height

#561,549

Difficulty

10.965316

Transactions

Size

15.54 KB

Version

Bits

0af71ef4

Nonce

190,206,904

Timestamp

5/25/2014, 2:08:51 PM

Confirmations

6,248,445

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b0ed1900f4c20d089c1fd89ef75f096a201de40fea17ffaa6657ac3c86a210c0

Transactions (5)

Coinbasef29ff4efca2fd3…0b8fb5550a2f76

1 in → 1 out8.4900 XPM116 B

ANSXnLY2…Sd25TjkD

22b143fec82c8c…40f53d92a0812e

101 in → 2 out100.0314 XPM14.68 KB

ALtPV4KN…xN24yLMY ANyw1EmT…GEZJMwRt

d02fcbd8dfb028…7430f55720b9e4

1 in → 2 out2.2394 XPM226 B

AcFbA7pV…WsQyy6G9 AG8u7ddV…cU5QJSqk

8ad4419c07981d…a72c10893990ee

1 in → 2 out0.7340 XPM225 B

APHx196W…DwkgXfoX AFtGobMM…D8uBYdH4

ef5df29e566868…feddefe508d720

1 in → 2 out1.5152 XPM226 B

AM23VEk3…q622MtoH AVdh5FJP…FL5FSQEh

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.

1.140 × 10⁹⁹(100-digit number)

11403323615682890860…23652936093745276159

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

1.140 × 10⁹⁹(100-digit number)

11403323615682890860…23652936093745276159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.140 × 10⁹⁹(100-digit number)

11403323615682890860…23652936093745276161

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

2.280 × 10⁹⁹(100-digit number)

22806647231365781720…47305872187490552319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.280 × 10⁹⁹(100-digit number)

22806647231365781720…47305872187490552321

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

4.561 × 10⁹⁹(100-digit number)

45613294462731563440…94611744374981104639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.561 × 10⁹⁹(100-digit number)

45613294462731563440…94611744374981104641

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

9.122 × 10⁹⁹(100-digit number)

91226588925463126881…89223488749962209279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.122 × 10⁹⁹(100-digit number)

91226588925463126881…89223488749962209281

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

1.824 × 10¹⁰⁰(101-digit number)

18245317785092625376…78446977499924418559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.824 × 10¹⁰⁰(101-digit number)

18245317785092625376…78446977499924418561

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

3.649 × 10¹⁰⁰(101-digit number)

36490635570185250752…56893954999848837119

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 #561,549

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