Block #425,702

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/2/2014, 3:05:46 AM · Difficulty 10.3570 · 6,384,186 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4e9525a26b410adc1208a8fa3c0a3bbd99a019a6c63fa7f24f9a103f655e2d7a

View on Chainz ↗

Height

#425,702

Difficulty

10.356976

Transactions

Size

1.17 KB

Version

Bits

0a5b62cf

Nonce

44,464

Timestamp

3/2/2014, 3:05:46 AM

Confirmations

6,384,186

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

50c29f2057f86956143474c069d4fdb79962556dddde8a5551015c13021ffbaf

Transactions (3)

Coinbasee244c271f846cd…8ac3e02285db70

1 in → 1 out9.3300 XPM116 B

AbwWkWZt…kawDhufa

90e683d16480da…8f7b377b56f12c

3 in → 10 out9.9368 XPM760 B

AJ7bwxHw…vy276KPV AMTcH6rD…J5EReFoC APPZLZRh…k8wT1gVi ASY5xqVU…DNRfWDXj AU8Gx9wF…Dof9VtwY

6eaaa62c64e25c…6e15c221de20f3

1 in → 2 out2.4579 XPM226 B

AYJqB6MZ…byGx7w48 AXnL68UR…jsxeGUhN

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.

9.114 × 10⁹⁷(98-digit number)

91149546606115318677…04047849289547476799

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

9.114 × 10⁹⁷(98-digit number)

91149546606115318677…04047849289547476799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.114 × 10⁹⁷(98-digit number)

91149546606115318677…04047849289547476801

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

1.822 × 10⁹⁸(99-digit number)

18229909321223063735…08095698579094953599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.822 × 10⁹⁸(99-digit number)

18229909321223063735…08095698579094953601

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

3.645 × 10⁹⁸(99-digit number)

36459818642446127470…16191397158189907199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.645 × 10⁹⁸(99-digit number)

36459818642446127470…16191397158189907201

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

7.291 × 10⁹⁸(99-digit number)

72919637284892254941…32382794316379814399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.291 × 10⁹⁸(99-digit number)

72919637284892254941…32382794316379814401

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

1.458 × 10⁹⁹(100-digit number)

14583927456978450988…64765588632759628799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.458 × 10⁹⁹(100-digit number)

14583927456978450988…64765588632759628801

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 #425,702

Cookie Preferences