Block #495,417

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/16/2014, 3:06:37 PM · Difficulty 10.7368 · 6,309,789 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d09af2c5aaa88a4c9d307c6650d29b5c1e16539a09be3bd3b323519df1b80047

View on Chainz ↗

Height

#495,417

Difficulty

10.736768

Transactions

Size

3.27 KB

Version

Bits

0abc9cd9

Nonce

26,669

Timestamp

4/16/2014, 3:06:37 PM

Confirmations

6,309,789

Mined by

AGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

4d8167c1669acf566eb3ffe7c3240b2d7913efb013995957303d39869d892155

Transactions (2)

Coinbaseb6e0c3a8652271…17596defc2c4c8

1 in → 22 out8.6900 XPM811 B

AGz9gyZW…bo8NYQpw ASgUri65…C7NLcyBg AMVf7Jrg…xd5AVR7C AXCpMYgL…1r94ZQDa AbPcCMg4…719q6mAX

f1be775057f79e…dd5463bd9fb908

16 in → 2 out142.5573 XPM2.39 KB

AR5yT6bB…CakY9nXA AJ3Ex8Eq…CU3PNKgn

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.

2.470 × 10⁹⁴(95-digit number)

24709590188628030335…63189772733373691519

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

2.470 × 10⁹⁴(95-digit number)

24709590188628030335…63189772733373691519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.470 × 10⁹⁴(95-digit number)

24709590188628030335…63189772733373691521

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

4.941 × 10⁹⁴(95-digit number)

49419180377256060671…26379545466747383039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.941 × 10⁹⁴(95-digit number)

49419180377256060671…26379545466747383041

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

9.883 × 10⁹⁴(95-digit number)

98838360754512121342…52759090933494766079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.883 × 10⁹⁴(95-digit number)

98838360754512121342…52759090933494766081

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

1.976 × 10⁹⁵(96-digit number)

19767672150902424268…05518181866989532159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.976 × 10⁹⁵(96-digit number)

19767672150902424268…05518181866989532161

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

3.953 × 10⁹⁵(96-digit number)

39535344301804848536…11036363733979064319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.953 × 10⁹⁵(96-digit number)

39535344301804848536…11036363733979064321

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