Block #579,026

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/6/2014, 1:09:56 PM · Difficulty 10.9676 · 6,231,827 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5dad807c86346f826242a3cee6fb822c333eba5b53ea753b7287313af0af1f6f

View on Chainz ↗

Height

#579,026

Difficulty

10.967551

Transactions

Size

92.20 KB

Version

Bits

0af7b16d

Nonce

1,196,891,691

Timestamp

6/6/2014, 1:09:56 PM

Confirmations

6,231,827

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5852e27bf2337ee6983286a37fee960f6fa8893f13f89b1f09ca4d8a892191e9

Transactions (2)

Coinbase63a1bc49cec4db…e8a21cd55c217e

1 in → 1 out9.2500 XPM116 B

ANSXnLY2…Sd25TjkD

91f2d0382dcbfa…f30f7a46b595df

636 in → 2 out240.0100 XPM92.00 KB

AchmN8LE…XpHijvds ARAQGi2n…LGJgCbHw

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.

2.471 × 10⁹⁸(99-digit number)

24713608774307501297…41886756923104092799

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

2.471 × 10⁹⁸(99-digit number)

24713608774307501297…41886756923104092799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.471 × 10⁹⁸(99-digit number)

24713608774307501297…41886756923104092801

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

4.942 × 10⁹⁸(99-digit number)

49427217548615002594…83773513846208185599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.942 × 10⁹⁸(99-digit number)

49427217548615002594…83773513846208185601

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

9.885 × 10⁹⁸(99-digit number)

98854435097230005188…67547027692416371199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.885 × 10⁹⁸(99-digit number)

98854435097230005188…67547027692416371201

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

1.977 × 10⁹⁹(100-digit number)

19770887019446001037…35094055384832742399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.977 × 10⁹⁹(100-digit number)

19770887019446001037…35094055384832742401

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

3.954 × 10⁹⁹(100-digit number)

39541774038892002075…70188110769665484799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.954 × 10⁹⁹(100-digit number)

39541774038892002075…70188110769665484801

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

7.908 × 10⁹⁹(100-digit number)

79083548077784004151…40376221539330969599

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 #579,026

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