Block #73,211

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 4:36:41 AM · Difficulty 8.9947 · 6,727,581 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cc8d52b7756548503a75f5fae0df01ed4e271f1b0d47c49b03bb695a3230f2ff

View on Chainz ↗

Height

#73,211

Difficulty

8.994657

Transactions

Size

203 B

Version

Bits

08fea1d4

Nonce

204

Timestamp

7/21/2013, 4:36:41 AM

Confirmations

6,727,581

Mined by

⛏️ P2SHALD4vzJs4Zwqrn14ZxtLe9UeDdGRCXP6ri

Merkle Root

a2eb20698b31cca39bd853ac6e3ba708ffb334ac26fe5090ee85d6b6ebe271f4

Transactions (1)

Coinbasea2eb20698b31cc…85d6b6ebe271f4

1 in → 1 out12.3400 XPM110 B

ALD4vzJs…GRCXP6ri

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.

4.048 × 10¹⁰²(103-digit number)

40485916184371205330…01592802682108114639

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

4.048 × 10¹⁰²(103-digit number)

40485916184371205330…01592802682108114639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.048 × 10¹⁰²(103-digit number)

40485916184371205330…01592802682108114641

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

8.097 × 10¹⁰²(103-digit number)

80971832368742410660…03185605364216229279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.097 × 10¹⁰²(103-digit number)

80971832368742410660…03185605364216229281

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

1.619 × 10¹⁰³(104-digit number)

16194366473748482132…06371210728432458559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.619 × 10¹⁰³(104-digit number)

16194366473748482132…06371210728432458561

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

3.238 × 10¹⁰³(104-digit number)

32388732947496964264…12742421456864917119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.238 × 10¹⁰³(104-digit number)

32388732947496964264…12742421456864917121

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

6.477 × 10¹⁰³(104-digit number)

64777465894993928528…25484842913729834239

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