Block #75,089

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 2:34:27 PM · Difficulty 8.9959 · 6,716,394 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9daae9d366f9397641bd6843e591dad61058abcba06f611eb1a618f0bfac17b4

View on Chainz ↗

Height

#75,089

Difficulty

8.995904

Transactions

Size

204 B

Version

Bits

08fef396

Nonce

151

Timestamp

7/21/2013, 2:34:27 PM

Confirmations

6,716,394

Merkle Root

bdd0d1f53360bae7018f8148a5bbce94bd49091632c2d841db29af408ea3c6ef

Transactions (1)

Coinbasebdd0d1f53360ba…29af408ea3c6ef

1 in → 1 out12.3400 XPM110 B

Aa1wHdNK…T2sXvFwJ

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.

1.030 × 10¹⁰⁴(105-digit number)

10301967584557349948…45336548245359504999

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

1.030 × 10¹⁰⁴(105-digit number)

10301967584557349948…45336548245359504999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.030 × 10¹⁰⁴(105-digit number)

10301967584557349948…45336548245359505001

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

2.060 × 10¹⁰⁴(105-digit number)

20603935169114699897…90673096490719009999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.060 × 10¹⁰⁴(105-digit number)

20603935169114699897…90673096490719010001

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

4.120 × 10¹⁰⁴(105-digit number)

41207870338229399795…81346192981438019999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.120 × 10¹⁰⁴(105-digit number)

41207870338229399795…81346192981438020001

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

8.241 × 10¹⁰⁴(105-digit number)

82415740676458799590…62692385962876039999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.241 × 10¹⁰⁴(105-digit number)

82415740676458799590…62692385962876040001

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

1.648 × 10¹⁰⁵(106-digit number)

16483148135291759918…25384771925752079999

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