Block #541,477

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/13/2014, 1:05:37 PM · Difficulty 10.9394 · 6,257,739 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c346dc248bda48a7c54484db8aab0783c0a2a535396956d1dd547257bc6f394f

View on Chainz ↗

Height

#541,477

Difficulty

10.939421

Transactions

Size

697 B

Version

Bits

0af07dde

Nonce

109,794

Timestamp

5/13/2014, 1:05:37 PM

Confirmations

6,257,739

Mined by

⛏️ %CaSrAAdxPNkWDCvKeJZdYCNethssA1dZMa9u34q

Merkle Root

7ea8744690aab22999c0c95c896216badabbad78b12e5d64cc5b65310fd60095

Transactions (1)

Coinbase7ea8744690aab2…5b65310fd60095

1 in → 16 out8.3321 XPM607 B

AdxPNkWD…ZMa9u34q AQvZBsUo…hppgRZTJ AUbecsVa…i8zo8qRf AJtNW28X…Syb4Ph5j AQyr8Lw3…hs4nt3Pn

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.

2.381 × 10⁹⁵(96-digit number)

23813240450039733908…77700467151475374999

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

2.381 × 10⁹⁵(96-digit number)

23813240450039733908…77700467151475374999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.381 × 10⁹⁵(96-digit number)

23813240450039733908…77700467151475375001

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

4.762 × 10⁹⁵(96-digit number)

47626480900079467816…55400934302950749999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.762 × 10⁹⁵(96-digit number)

47626480900079467816…55400934302950750001

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

9.525 × 10⁹⁵(96-digit number)

95252961800158935632…10801868605901499999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.525 × 10⁹⁵(96-digit number)

95252961800158935632…10801868605901500001

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

1.905 × 10⁹⁶(97-digit number)

19050592360031787126…21603737211802999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.905 × 10⁹⁶(97-digit number)

19050592360031787126…21603737211803000001

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

3.810 × 10⁹⁶(97-digit number)

38101184720063574253…43207474423605999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.810 × 10⁹⁶(97-digit number)

38101184720063574253…43207474423606000001

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

7.620 × 10⁹⁶(97-digit number)

76202369440127148506…86414948847211999999

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