Block #554,174

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/20/2014, 3:40:07 PM · Difficulty 10.9632 · 6,249,315 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9e11b5b28d8377f033b8a692547234d7634a342427d8fee6ce51c8f3a1642583

View on Chainz ↗

Height

#554,174

Difficulty

10.963191

Transactions

Size

661 B

Version

Bits

0af693a8

Nonce

1,920,232,360

Timestamp

5/20/2014, 3:40:07 PM

Confirmations

6,249,315

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

edc5ac9e4261ca1be85dd7538e814feb54b7f7894f8f65b542f98935cc0343b7

Transactions (3)

Coinbase5eb19e8c925b98…fa2e994a3802a5

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

1812474b30cd42…bae279a932fa36

1 in → 2 out2.8723 XPM226 B

AHgUr66c…sxbG8CH5 AGdWVjRk…LFVsqCnK

ab4af7796778b6…eb0361756bf546

1 in → 2 out1.9823 XPM226 B

AcQfxVUD…vQnNph4X AUTBxqq3…cjGo9NNj

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.

2.183 × 10¹⁰¹(102-digit number)

21832866051486686747…26459340816480706559

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

2.183 × 10¹⁰¹(102-digit number)

21832866051486686747…26459340816480706559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.183 × 10¹⁰¹(102-digit number)

21832866051486686747…26459340816480706561

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

4.366 × 10¹⁰¹(102-digit number)

43665732102973373494…52918681632961413119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.366 × 10¹⁰¹(102-digit number)

43665732102973373494…52918681632961413121

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

8.733 × 10¹⁰¹(102-digit number)

87331464205946746989…05837363265922826239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.733 × 10¹⁰¹(102-digit number)

87331464205946746989…05837363265922826241

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

1.746 × 10¹⁰²(103-digit number)

17466292841189349397…11674726531845652479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.746 × 10¹⁰²(103-digit number)

17466292841189349397…11674726531845652481

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

3.493 × 10¹⁰²(103-digit number)

34932585682378698795…23349453063691304959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.493 × 10¹⁰²(103-digit number)

34932585682378698795…23349453063691304961

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

6.986 × 10¹⁰²(103-digit number)

69865171364757397591…46698906127382609919

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