Block #559,830

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/24/2014, 10:56:21 AM · Difficulty 10.9647 · 6,266,591 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c27e5be3945f84a4295f501d1313d5aea9ce315a0d769905d3fb752bc07147ba

View on Chainz ↗

Height

#559,830

Difficulty

10.964653

Transactions

Size

883 B

Version

Bits

0af6f379

Nonce

2,131,424,992

Timestamp

5/24/2014, 10:56:21 AM

Confirmations

6,266,591

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

bfa33bb066f9afa7de45b4098841c10f73ff85af4b6eda6a292d8b034236c411

Transactions (4)

Coinbasef3d1c418be85f0…dbaff51c50379b

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

d1ec410a46dcea…59d0bfa8b1f2ab

1 in → 3 out8.3000 XPM226 B

AH5UDi4x…oKfPMbfn AetRjmdA…xa7RReBc AeKNrjNj…1NEq95Ta

7ddbe2da929f50…0b4d529abdd10a

1 in → 2 out5.6221 XPM225 B

Aasjrw9j…twYwVAij AWr7QESV…T91HodnJ

4b3b061840e791…ff818324f99933

1 in → 2 out4.1610 XPM225 B

AKSxx7e4…KG7Pey6E AT2k6SUV…XZuaP1uA

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.

8.786 × 10⁹⁷(98-digit number)

87862219509061556137…09019260241849063039

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

8.786 × 10⁹⁷(98-digit number)

87862219509061556137…09019260241849063039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.786 × 10⁹⁷(98-digit number)

87862219509061556137…09019260241849063041

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

1.757 × 10⁹⁸(99-digit number)

17572443901812311227…18038520483698126079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.757 × 10⁹⁸(99-digit number)

17572443901812311227…18038520483698126081

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

3.514 × 10⁹⁸(99-digit number)

35144887803624622455…36077040967396252159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.514 × 10⁹⁸(99-digit number)

35144887803624622455…36077040967396252161

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

7.028 × 10⁹⁸(99-digit number)

70289775607249244910…72154081934792504319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.028 × 10⁹⁸(99-digit number)

70289775607249244910…72154081934792504321

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

1.405 × 10⁹⁹(100-digit number)

14057955121449848982…44308163869585008639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.405 × 10⁹⁹(100-digit number)

14057955121449848982…44308163869585008641

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 #559,830

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