Block #557,048

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/22/2014, 4:41:30 PM · Difficulty 10.9628 · 6,268,078 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c1c63ac21c35be7463cc383e9f7bceadcc3a6c39cdc1bb6383033b775a602960

View on Chainz ↗

Height

#557,048

Difficulty

10.962796

Transactions

Size

1.09 KB

Version

Bits

0af679c6

Nonce

530,545,719

Timestamp

5/22/2014, 4:41:30 PM

Confirmations

6,268,078

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9bc384167803c3d9885b1a675e366f9a6b47256a8ca17b224038090caf7c2651

Transactions (5)

Coinbase0b3ed260d7c1c3…80bcc5077d3e03

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

5ef636a746d354…388fc7cc67ac33

1 in → 2 out7.7056 XPM225 B

AbRWHhqf…LcYgxLfS AcRFxk9e…RTuJn1zH

ece82131d4c396…270f7abcd684bb

1 in → 2 out6.7673 XPM226 B

ANujDbh3…KMMryBNJ AWx4NR1x…msnH1t4Z

474ade33bd986e…95a732317bfe5c

1 in → 2 out4.0273 XPM226 B

ASrxCFyg…kB2T2Rfx AMUmstGS…XePJVTQg

5026c760018ed0…0a16a0b5831b47

1 in → 2 out6.6464 XPM227 B

AWr7QESV…T91HodnJ AS6Lf9mm…dtStZ3fd

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.

1.858 × 10¹⁰¹(102-digit number)

18580977230758446787…34834930916702904319

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

1.858 × 10¹⁰¹(102-digit number)

18580977230758446787…34834930916702904319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.858 × 10¹⁰¹(102-digit number)

18580977230758446787…34834930916702904321

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

3.716 × 10¹⁰¹(102-digit number)

37161954461516893575…69669861833405808639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.716 × 10¹⁰¹(102-digit number)

37161954461516893575…69669861833405808641

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

7.432 × 10¹⁰¹(102-digit number)

74323908923033787150…39339723666811617279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.432 × 10¹⁰¹(102-digit number)

74323908923033787150…39339723666811617281

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

1.486 × 10¹⁰²(103-digit number)

14864781784606757430…78679447333623234559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.486 × 10¹⁰²(103-digit number)

14864781784606757430…78679447333623234561

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

2.972 × 10¹⁰²(103-digit number)

29729563569213514860…57358894667246469119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.972 × 10¹⁰²(103-digit number)

29729563569213514860…57358894667246469121

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

5.945 × 10¹⁰²(103-digit number)

59459127138427029720…14717789334492938239

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 #557,048

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