Block #558,579

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/23/2014, 3:46:07 PM · Difficulty 10.9639 · 6,286,150 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

88bd3a2e69d2c254ca20797a0f45257a13adbe69a5960a94e91c8cd960962fcb

View on Chainz ↗

Height

#558,579

Difficulty

10.963897

Transactions

Size

435 B

Version

Bits

0af6c1f4

Nonce

2,065,910,989

Timestamp

5/23/2014, 3:46:07 PM

Confirmations

6,286,150

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

66fec8f26312a62779e06e5609def3fc95612bc5c9b07d4c209925e6698ae206

Transactions (2)

Coinbase0c595f90d2a891…9fcaeaaaec501f

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

41b769fedab6db…9952a81431ebd0

1 in → 2 out4.1274 XPM226 B

AXGKTHwE…znvypgAW AMLssXBN…VZyLLL9Z

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.

2.006 × 10¹⁰²(103-digit number)

20061308057827241872…85720736945756897279

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

2.006 × 10¹⁰²(103-digit number)

20061308057827241872…85720736945756897279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.006 × 10¹⁰²(103-digit number)

20061308057827241872…85720736945756897281

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

4.012 × 10¹⁰²(103-digit number)

40122616115654483745…71441473891513794559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.012 × 10¹⁰²(103-digit number)

40122616115654483745…71441473891513794561

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

8.024 × 10¹⁰²(103-digit number)

80245232231308967491…42882947783027589119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.024 × 10¹⁰²(103-digit number)

80245232231308967491…42882947783027589121

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

1.604 × 10¹⁰³(104-digit number)

16049046446261793498…85765895566055178239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.604 × 10¹⁰³(104-digit number)

16049046446261793498…85765895566055178241

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

3.209 × 10¹⁰³(104-digit number)

32098092892523586996…71531791132110356479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.209 × 10¹⁰³(104-digit number)

32098092892523586996…71531791132110356481

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 #558,579

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