Block #1,084,238

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/31/2015, 11:09:22 AM · Difficulty 10.7708 · 5,711,550 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

572159b51b68e230acc194a944af6c19d1abcaccd28965e64638f4b038d6d3e6

View on Chainz ↗

Height

#1,084,238

Difficulty

10.770820

Transactions

Size

86.84 KB

Version

Bits

0ac55475

Nonce

428,500,762

Timestamp

5/31/2015, 11:09:22 AM

Confirmations

5,711,550

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b5bbb83cbadd54de7b696b4876843759a46f6acbf6a04ed6ff7769d1d336be9b

Transactions (2)

Coinbase403492f36936a8…40c2a537bbdee0

1 in → 1 out9.5100 XPM116 B

ANSXnLY2…Sd25TjkD

cfeb1015823c6d…0687c4f6b290e7

599 in → 2 out3500.0100 XPM86.64 KB

AVBDyetW…iVLnHuuV Ae5WFHbn…gBo7rvHr

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.

8.394 × 10⁹⁶(97-digit number)

83949933570152651496…66298298459739407359

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

8.394 × 10⁹⁶(97-digit number)

83949933570152651496…66298298459739407359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.394 × 10⁹⁶(97-digit number)

83949933570152651496…66298298459739407361

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

1.678 × 10⁹⁷(98-digit number)

16789986714030530299…32596596919478814719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.678 × 10⁹⁷(98-digit number)

16789986714030530299…32596596919478814721

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

3.357 × 10⁹⁷(98-digit number)

33579973428061060598…65193193838957629439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.357 × 10⁹⁷(98-digit number)

33579973428061060598…65193193838957629441

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

6.715 × 10⁹⁷(98-digit number)

67159946856122121197…30386387677915258879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.715 × 10⁹⁷(98-digit number)

67159946856122121197…30386387677915258881

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

1.343 × 10⁹⁸(99-digit number)

13431989371224424239…60772775355830517759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.343 × 10⁹⁸(99-digit number)

13431989371224424239…60772775355830517761

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