Block #545,203

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/15/2014, 6:36:46 AM · Difficulty 10.9527 · 6,264,356 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0f8f0da25386763c66c1f5830e9464dc07ed129c4527603b91a21b74cff1029b

View on Chainz ↗

Height

#545,203

Difficulty

10.952700

Transactions

Size

245 B

Version

Bits

0af3e424

Nonce

253,730,422

Timestamp

5/15/2014, 6:36:46 AM

Confirmations

6,264,356

Mined by

⛏️ P2SHARzmpY4cAhz8WiJkMBTqRELns6fvx8bF9t

Merkle Root

d5e4806c8cf40d70d9716ab3a415b9030fbdfe7efc2dbdc47afd868bbdcf8c01

Transactions (1)

Coinbased5e4806c8cf40d…fd868bbdcf8c01

1 in → 2 out8.3200 XPM152 B

ARzmpY4c…fvx8bF9t ALPu3s2c…EJXLjVFh

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.

5.317 × 10¹⁰⁰(101-digit number)

53173853939816130004…75442306691849809919

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

5.317 × 10¹⁰⁰(101-digit number)

53173853939816130004…75442306691849809919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.317 × 10¹⁰⁰(101-digit number)

53173853939816130004…75442306691849809921

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

1.063 × 10¹⁰¹(102-digit number)

10634770787963226000…50884613383699619839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.063 × 10¹⁰¹(102-digit number)

10634770787963226000…50884613383699619841

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

2.126 × 10¹⁰¹(102-digit number)

21269541575926452001…01769226767399239679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.126 × 10¹⁰¹(102-digit number)

21269541575926452001…01769226767399239681

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

4.253 × 10¹⁰¹(102-digit number)

42539083151852904003…03538453534798479359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.253 × 10¹⁰¹(102-digit number)

42539083151852904003…03538453534798479361

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

8.507 × 10¹⁰¹(102-digit number)

85078166303705808006…07076907069596958719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.507 × 10¹⁰¹(102-digit number)

85078166303705808006…07076907069596958721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #545,203

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