Block #468,500

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/31/2014, 1:27:28 PM · Difficulty 10.4315 · 6,333,991 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8bbe60b82abe783fbe7ab1d363af971d57499b7d88bf2365d294fd74af273fea

View on Chainz ↗

Height

#468,500

Difficulty

10.431538

Transactions

Size

2.01 KB

Version

Bits

0a6e7947

Nonce

67,097

Timestamp

3/31/2014, 1:27:28 PM

Confirmations

6,333,991

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

4232b57cb0d71c048fb957c64f1a9be470938fd5fe11c1e8435ec0af59bc2630

Transactions (3)

Coinbase1270c6a6a9080a…4e2f2c0d8b73de

1 in → 1 out9.2100 XPM110 B

AeKNrjNj…1NEq95Ta

e0c6278dc23aed…ae8659ec42309a

2 in → 1 out5.9913 XPM340 B

AejQsASd…1cR9CA4E

b5f50f4989e461…aa687608097090

9 in → 7 out19.3671 XPM1.48 KB

AbJ2m1AL…BeT5jPVi AdVJEi62…5WZTgbE1 AeKNrjNj…1NEq95Ta AQbUxPt2…aXzeQ1D4 ANQKf2g4…29NaVj23

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.

1.504 × 10¹⁰³(104-digit number)

15040950313946665720…83664478261083128499

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

1.504 × 10¹⁰³(104-digit number)

15040950313946665720…83664478261083128499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.504 × 10¹⁰³(104-digit number)

15040950313946665720…83664478261083128501

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

3.008 × 10¹⁰³(104-digit number)

30081900627893331440…67328956522166256999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.008 × 10¹⁰³(104-digit number)

30081900627893331440…67328956522166257001

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

6.016 × 10¹⁰³(104-digit number)

60163801255786662880…34657913044332513999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.016 × 10¹⁰³(104-digit number)

60163801255786662880…34657913044332514001

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

1.203 × 10¹⁰⁴(105-digit number)

12032760251157332576…69315826088665027999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.203 × 10¹⁰⁴(105-digit number)

12032760251157332576…69315826088665028001

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

2.406 × 10¹⁰⁴(105-digit number)

24065520502314665152…38631652177330055999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.406 × 10¹⁰⁴(105-digit number)

24065520502314665152…38631652177330056001

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