Block #840,575

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/5/2014, 6:22:33 AM · Difficulty 10.9742 · 6,004,198 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

433374665cb8501bc94be9909b4660392bb61d50f01e76a1f224a7b1ddb8c5cd

View on Chainz ↗

Height

#840,575

Difficulty

10.974223

Transactions

Size

1.09 KB

Version

Bits

0af966b6

Nonce

1,114,680,930

Timestamp

12/5/2014, 6:22:33 AM

Confirmations

6,004,198

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

dbb25da8bdbab20f9dd0a2b3df15f6177385bb79258bfc7c40be9226c8084b0d

Transactions (5)

Coinbase28ee6d593d988f…70e6eaee0b06c4

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

3185f04096a542…9819d5968d9d09

1 in → 2 out0.4053 XPM227 B

ASPWKyRG…RpF51FhT AMr737oS…s4AFUBi5

499486bde22e4f…1704c6e0f0d0e6

1 in → 2 out0.4454 XPM226 B

AMJwSnTg…YcWAujpp ANPue7vr…veZKL2Yf

f286ecabf1867d…5e55a1c446b553

1 in → 2 out0.2574 XPM226 B

AHsdoFke…r9wu57Fx ANGAnEVR…ZQh9kmGe

2446aa4892dd8d…df06201b423902

1 in → 2 out0.3214 XPM227 B

Aef4jsqe…cu2Jibg8 AXwUSPQ9…Z4D9X2WS

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.

1.457 × 10⁹⁷(98-digit number)

14576736757856912039…81268721581402118399

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

1.457 × 10⁹⁷(98-digit number)

14576736757856912039…81268721581402118399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.457 × 10⁹⁷(98-digit number)

14576736757856912039…81268721581402118401

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

2.915 × 10⁹⁷(98-digit number)

29153473515713824079…62537443162804236799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.915 × 10⁹⁷(98-digit number)

29153473515713824079…62537443162804236801

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

5.830 × 10⁹⁷(98-digit number)

58306947031427648158…25074886325608473599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.830 × 10⁹⁷(98-digit number)

58306947031427648158…25074886325608473601

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

1.166 × 10⁹⁸(99-digit number)

11661389406285529631…50149772651216947199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.166 × 10⁹⁸(99-digit number)

11661389406285529631…50149772651216947201

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

2.332 × 10⁹⁸(99-digit number)

23322778812571059263…00299545302433894399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.332 × 10⁹⁸(99-digit number)

23322778812571059263…00299545302433894401

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 #840,575

Cookie Preferences