Block #565,290

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/28/2014, 5:37:54 AM · Difficulty 10.9649 · 6,243,701 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c825c0635065dfb23f21e0e7afa789d22bb49c2eb71947c58287d5e0be254668

View on Chainz ↗

Height

#565,290

Difficulty

10.964948

Transactions

Size

808 B

Version

Bits

0af706d2

Nonce

919,587,382

Timestamp

5/28/2014, 5:37:54 AM

Confirmations

6,243,701

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

886989afa88d5ba4be484d8d90f94b23e3da74a52760b333f95710d452fa617e

Transactions (3)

Coinbase3d628b00395dcc…ed4f9a20e6cf52

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

a4ddb76bb2c260…84c21b4c50dc6d

2 in → 2 out11.9883 XPM375 B

ASUbvGQ3…eWcvX9ZX AT2Y4r9b…8KfxjrbJ

f36b9e32d05f4d…69bd87532f8f09

1 in → 2 out4.9475 XPM225 B

AcVexCzF…SY75pd2v AQtmnYbC…CqjZFwWY

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.

2.231 × 10⁹⁸(99-digit number)

22319585981308923651…69079103857136712959

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

2.231 × 10⁹⁸(99-digit number)

22319585981308923651…69079103857136712959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.231 × 10⁹⁸(99-digit number)

22319585981308923651…69079103857136712961

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

4.463 × 10⁹⁸(99-digit number)

44639171962617847302…38158207714273425919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.463 × 10⁹⁸(99-digit number)

44639171962617847302…38158207714273425921

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

8.927 × 10⁹⁸(99-digit number)

89278343925235694604…76316415428546851839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.927 × 10⁹⁸(99-digit number)

89278343925235694604…76316415428546851841

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

1.785 × 10⁹⁹(100-digit number)

17855668785047138920…52632830857093703679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.785 × 10⁹⁹(100-digit number)

17855668785047138920…52632830857093703681

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

3.571 × 10⁹⁹(100-digit number)

35711337570094277841…05265661714187407359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.571 × 10⁹⁹(100-digit number)

35711337570094277841…05265661714187407361

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

7.142 × 10⁹⁹(100-digit number)

71422675140188555683…10531323428374814719

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 #565,290

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