Block #74,909

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 1:38:59 PM · Difficulty 8.9958 · 6,743,066 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c73de0256e2b1c9fc2ffb13dae4ca529b26baae1e4864d51229379d6390e527b

View on Chainz ↗

Height

#74,909

Difficulty

8.995797

Transactions

Size

205 B

Version

Bits

08feec89

Nonce

Timestamp

7/21/2013, 1:38:59 PM

Confirmations

6,743,066

Mined by

⛏️ P2SHAHGPtSCNuYeecmqUQuK4cLJv6iGESamBFW

Merkle Root

d245905c36795d0cb73a3f5a1f1d7b362a0e45e38c09f6e87386004dd46e08f4

Transactions (1)

Coinbased245905c36795d…86004dd46e08f4

1 in → 1 out12.3400 XPM110 B

AHGPtSCN…GESamBFW

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.

1.047 × 10¹⁰⁷(108-digit number)

10471491655162667244…79830425595708948369

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

1.047 × 10¹⁰⁷(108-digit number)

10471491655162667244…79830425595708948369

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.047 × 10¹⁰⁷(108-digit number)

10471491655162667244…79830425595708948371

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

2.094 × 10¹⁰⁷(108-digit number)

20942983310325334488…59660851191417896739

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.094 × 10¹⁰⁷(108-digit number)

20942983310325334488…59660851191417896741

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

4.188 × 10¹⁰⁷(108-digit number)

41885966620650668976…19321702382835793479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.188 × 10¹⁰⁷(108-digit number)

41885966620650668976…19321702382835793481

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

8.377 × 10¹⁰⁷(108-digit number)

83771933241301337953…38643404765671586959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.377 × 10¹⁰⁷(108-digit number)

83771933241301337953…38643404765671586961

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

1.675 × 10¹⁰⁸(109-digit number)

16754386648260267590…77286809531343173919

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

Block #74,909

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