Block #493,775

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/15/2014, 8:35:00 PM · Difficulty 10.7071 · 6,301,099 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

331d5b228eb6bfb1862c7adc0b5e8401cd3f823ae115e8cc66c92eb4a9122ea9

View on Chainz ↗

Height

#493,775

Difficulty

10.707076

Transactions

Size

1.23 KB

Version

Bits

0ab502e8

Nonce

18,360,682

Timestamp

4/15/2014, 8:35:00 PM

Confirmations

6,301,099

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

65a84356326cc8baa3d97d59bb15a80899f269e107dbd05b48515129b8a2c383

Transactions (5)

Coinbased8553f4edb81c1…80c5fb786dffc9

1 in → 1 out8.7500 XPM116 B

AbwWkWZt…kawDhufa

d2010ce1a1ae41…d3b4358ddca8f0

1 in → 2 out7.6229 XPM226 B

AbHpQaD4…Giwt7ntR AHj8ktDG…crPtB4sf

813196eb318dbf…e88a1c70002395

1 in → 2 out5.6948 XPM225 B

ARx8qEy1…7wSuBMfq ATH2UEva…DVMtoM4W

11d527d923dbae…b9981ea0024ca3

1 in → 2 out3.6497 XPM225 B

APnrrLui…ptQwdG5B AdzraYFj…Sy4N9fSh

425d48df632c8c…3c09e3c8649ab2

2 in → 2 out0.5406 XPM374 B

AFpeLMG7…ohHdpcba AKUvR6c6…PjpFWiw2

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.

2.605 × 10⁹⁷(98-digit number)

26051406185905418726…72398778980162558079

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

2.605 × 10⁹⁷(98-digit number)

26051406185905418726…72398778980162558079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.605 × 10⁹⁷(98-digit number)

26051406185905418726…72398778980162558081

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

5.210 × 10⁹⁷(98-digit number)

52102812371810837452…44797557960325116159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.210 × 10⁹⁷(98-digit number)

52102812371810837452…44797557960325116161

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

1.042 × 10⁹⁸(99-digit number)

10420562474362167490…89595115920650232319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.042 × 10⁹⁸(99-digit number)

10420562474362167490…89595115920650232321

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

2.084 × 10⁹⁸(99-digit number)

20841124948724334981…79190231841300464639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.084 × 10⁹⁸(99-digit number)

20841124948724334981…79190231841300464641

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

4.168 × 10⁹⁸(99-digit number)

41682249897448669962…58380463682600929279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.168 × 10⁹⁸(99-digit number)

41682249897448669962…58380463682600929281

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