Block #508,109

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/24/2014, 4:28:08 AM · Difficulty 10.8177 · 6,292,414 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a4ef772de20a1117d66cf5e6509552d35827f2543e40450699452346c6419b0b

View on Chainz ↗

Height

#508,109

Difficulty

10.817677

Transactions

Size

1.02 KB

Version

Bits

0ad1534b

Nonce

67,528

Timestamp

4/24/2014, 4:28:08 AM

Confirmations

6,292,414

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

b7a118d81374822703ca08f0782b01bbcc059d1d25acc8896f4f632792da0c65

Transactions (2)

Coinbase77869554faf4f4…1209d1f444692c

1 in → 1 out8.5400 XPM116 B

AbwWkWZt…kawDhufa

17017f98c97c91…cc2fe4b9fe54e2

4 in → 10 out30.4827 XPM838 B

ALzeejWz…d7byrHth AVy7vA87…WkzNt12Y Acn35Cbn…kDx6QvGN AdL7suF5…ksXj79Un AP8xnw8a…fhaMMjoo

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.

9.872 × 10¹⁰⁴(105-digit number)

98723088451403734875…80516929837824801439

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

9.872 × 10¹⁰⁴(105-digit number)

98723088451403734875…80516929837824801439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.872 × 10¹⁰⁴(105-digit number)

98723088451403734875…80516929837824801441

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

1.974 × 10¹⁰⁵(106-digit number)

19744617690280746975…61033859675649602879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.974 × 10¹⁰⁵(106-digit number)

19744617690280746975…61033859675649602881

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

3.948 × 10¹⁰⁵(106-digit number)

39489235380561493950…22067719351299205759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.948 × 10¹⁰⁵(106-digit number)

39489235380561493950…22067719351299205761

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

7.897 × 10¹⁰⁵(106-digit number)

78978470761122987900…44135438702598411519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.897 × 10¹⁰⁵(106-digit number)

78978470761122987900…44135438702598411521

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

1.579 × 10¹⁰⁶(107-digit number)

15795694152224597580…88270877405196823039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.579 × 10¹⁰⁶(107-digit number)

15795694152224597580…88270877405196823041

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