Block #462,898

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/27/2014, 5:57:16 PM · Difficulty 10.4163 · 6,347,360 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aef94161445164d9f89f7ef91a35260b0038311919adc41bf79b052392f1692e

View on Chainz ↗

Height

#462,898

Difficulty

10.416292

Transactions

Size

1.26 KB

Version

Bits

0a6a921b

Nonce

234,404

Timestamp

3/27/2014, 5:57:16 PM

Confirmations

6,347,360

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

0c13a94c5ac1b9ac3fa7ac53b91c143362ab5deec49d359428681e160580da94

Transactions (2)

Coinbased0a8d4e45c47f4…67e03e8cdc7996

1 in → 1 out9.2200 XPM110 B

AeKNrjNj…1NEq95Ta

b59600d08ebb2f…3e0f30ae471185

5 in → 15 out46.0200 XPM1.07 KB

AesAVNRf…eAXARtnF Aevqk5D4…9EsVdRX7 AM6JvF6Y…u5DULnSo AcGCmc9D…1fUXRBUx Ac5Sc2Mv…q4gm41o8

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.

5.273 × 10¹⁰⁰(101-digit number)

52731127724694539556…34298787637444375039

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

5.273 × 10¹⁰⁰(101-digit number)

52731127724694539556…34298787637444375039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.273 × 10¹⁰⁰(101-digit number)

52731127724694539556…34298787637444375041

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

1.054 × 10¹⁰¹(102-digit number)

10546225544938907911…68597575274888750079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.054 × 10¹⁰¹(102-digit number)

10546225544938907911…68597575274888750081

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

2.109 × 10¹⁰¹(102-digit number)

21092451089877815822…37195150549777500159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.109 × 10¹⁰¹(102-digit number)

21092451089877815822…37195150549777500161

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

4.218 × 10¹⁰¹(102-digit number)

42184902179755631645…74390301099555000319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.218 × 10¹⁰¹(102-digit number)

42184902179755631645…74390301099555000321

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

8.436 × 10¹⁰¹(102-digit number)

84369804359511263290…48780602199110000639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.436 × 10¹⁰¹(102-digit number)

84369804359511263290…48780602199110000641

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 #462,898

Cookie Preferences