Block #427,783

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2014, 2:36:42 PM · Difficulty 10.3517 · 6,364,025 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0d3ad0c884358769a5de45a9be5cec7d18d8542dbc12a4b189d3a239e39209d6

View on Chainz ↗

Height

#427,783

Difficulty

10.351663

Transactions

Size

2.44 KB

Version

Bits

0a5a068e

Nonce

15,410

Timestamp

3/3/2014, 2:36:42 PM

Confirmations

6,364,025

Merkle Root

99772ac27d9c3975182e207b0e549b6645c420261d4da4b45b2a80c9235005ac

Transactions (2)

Coinbasece504886d07ee7…8f0f1cf9ac9019

1 in → 1 out9.3500 XPM110 B

AeKNrjNj…1NEq95Ta

1281d729822a0e…2117aaa38cfa4e

12 in → 22 out69.1262 XPM2.24 KB

AaUXu2KR…T7BcctBi AbUeeSzh…AQKn5Nuq AeKNrjNj…1NEq95Ta AQDNUV7B…uQRit37C AUSw48r2…nRKXidTs

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.

1.858 × 10¹⁰¹(102-digit number)

18586991341860137123…05180814293060430559

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

1.858 × 10¹⁰¹(102-digit number)

18586991341860137123…05180814293060430559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.858 × 10¹⁰¹(102-digit number)

18586991341860137123…05180814293060430561

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

3.717 × 10¹⁰¹(102-digit number)

37173982683720274246…10361628586120861119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.717 × 10¹⁰¹(102-digit number)

37173982683720274246…10361628586120861121

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

7.434 × 10¹⁰¹(102-digit number)

74347965367440548493…20723257172241722239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.434 × 10¹⁰¹(102-digit number)

74347965367440548493…20723257172241722241

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

1.486 × 10¹⁰²(103-digit number)

14869593073488109698…41446514344483444479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.486 × 10¹⁰²(103-digit number)

14869593073488109698…41446514344483444481

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

2.973 × 10¹⁰²(103-digit number)

29739186146976219397…82893028688966888959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.973 × 10¹⁰²(103-digit number)

29739186146976219397…82893028688966888961

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