Block #58,866

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/17/2013, 11:02:28 PM · Difficulty 8.9621 · 6,730,883 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2d0731c2e2b584b396de1a280caae43050b4acb7f72b58b45f015f6f67c07182

View on Chainz ↗

Height

#58,866

Difficulty

8.962135

Transactions

Size

1.37 KB

Version

Bits

08f64e7e

Nonce

1,140

Timestamp

7/17/2013, 11:02:28 PM

Confirmations

6,730,883

Merkle Root

c98b8d59c90be100da57da73f511131bba8ec098c2e5db842cf16ece79ffcb2e

Transactions (5)

Coinbase824b7591f329e1…3ba83417626784

1 in → 1 out12.4700 XPM110 B

AbgDPBu9…fCCFrSbs

a4e48ed5bf0e7e…57d6f4a98d2625

3 in → 2 out112.2160 XPM523 B

APUSs5i1…ZEuvWLXa AL5iHwkH…YGkGxDZC

66d19db1ae08fd…e8b76f4d956239

1 in → 2 out37.4500 XPM226 B

AXf8d9Cn…6fQBues7 AUnpqXJn…xjzBeGzg

ac10b130b82b32…37f9881a0541ac

1 in → 2 out0.0900 XPM225 B

AdqsnYr7…rTLXWZ6m AQ2SbjYw…Aux2S9zX

35dffe966cc059…1cc9a55973ca4c

1 in → 2 out0.0650 XPM226 B

AQ2SbjYw…Aux2S9zX AMv3aC57…Mbg5dUja

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.

2.186 × 10¹⁰¹(102-digit number)

21868600412045405392…49064316545310265429

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

2.186 × 10¹⁰¹(102-digit number)

21868600412045405392…49064316545310265429

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.186 × 10¹⁰¹(102-digit number)

21868600412045405392…49064316545310265431

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

4.373 × 10¹⁰¹(102-digit number)

43737200824090810784…98128633090620530859

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.373 × 10¹⁰¹(102-digit number)

43737200824090810784…98128633090620530861

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

8.747 × 10¹⁰¹(102-digit number)

87474401648181621569…96257266181241061719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.747 × 10¹⁰¹(102-digit number)

87474401648181621569…96257266181241061721

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

1.749 × 10¹⁰²(103-digit number)

17494880329636324313…92514532362482123439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.749 × 10¹⁰²(103-digit number)

17494880329636324313…92514532362482123441

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

3.498 × 10¹⁰²(103-digit number)

34989760659272648627…85029064724964246879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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