Block #444,589

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/15/2014, 8:39:26 AM · Difficulty 10.3476 · 6,349,921 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ad521ef646802e823fe886f4e4d6f833006e646dfbc73f5f24d6b62eb369646

View on Chainz ↗

Height

#444,589

Difficulty

10.347564

Transactions

Size

1.08 KB

Version

Bits

0a58f9f4

Nonce

213,125

Timestamp

3/15/2014, 8:39:26 AM

Confirmations

6,349,921

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

47ed462823831d7c34da04dcdc3d96ba3836cafbd00c007370dab97ad495bae2

Transactions (5)

Coinbase27668dde30f588…65cc07fdb7d879

1 in → 1 out9.3700 XPM110 B

AeKNrjNj…1NEq95Ta

f2a94d65156160…e4e5ee9d338c39

1 in → 2 out6.7240 XPM227 B

AbGt9ZPx…GZsvcChe ANECpbxd…XLvANQZs

62b2bb8079f1da…adc96e0d7fafc3

1 in → 2 out4.2102 XPM225 B

AGxMeQpn…PtE4vAxN AVAGEBmb…N5De2tdh

a6a1d2fbe26a7d…877f1ac898ac5d

1 in → 2 out2.2126 XPM225 B

AWSzUKEq…RXHRSaog AXrpVTHR…becWCfgp

abd7b943f91cb9…d361918a0ed6c3

1 in → 2 out3.1402 XPM227 B

ASyBMzB3…TAHXihWa ARo8EK3R…KHn666hV

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.

1.791 × 10⁹⁹(100-digit number)

17915184748264624277…27532022475144646399

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

1.791 × 10⁹⁹(100-digit number)

17915184748264624277…27532022475144646399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.791 × 10⁹⁹(100-digit number)

17915184748264624277…27532022475144646401

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

3.583 × 10⁹⁹(100-digit number)

35830369496529248554…55064044950289292799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.583 × 10⁹⁹(100-digit number)

35830369496529248554…55064044950289292801

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

7.166 × 10⁹⁹(100-digit number)

71660738993058497109…10128089900578585599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.166 × 10⁹⁹(100-digit number)

71660738993058497109…10128089900578585601

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

1.433 × 10¹⁰⁰(101-digit number)

14332147798611699421…20256179801157171199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.433 × 10¹⁰⁰(101-digit number)

14332147798611699421…20256179801157171201

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

2.866 × 10¹⁰⁰(101-digit number)

28664295597223398843…40512359602314342399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.866 × 10¹⁰⁰(101-digit number)

28664295597223398843…40512359602314342401

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