Block #59,969

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 5:17:32 AM · Difficulty 8.9673 · 6,729,902 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

345386513e90d138df64c5dad3e25b9a1dac0ad488e9d311dfd58f3b7fb7b15f

View on Chainz ↗

Height

#59,969

Difficulty

8.967255

Transactions

Size

724 B

Version

Bits

08f79e00

Nonce

210

Timestamp

7/18/2013, 5:17:32 AM

Confirmations

6,729,902

Merkle Root

84bcd4d2dcd9ae6d8b53f3961552c2a33f11bc8782536a9b0514036e647318f8

Transactions (2)

Coinbase69d6f026861868…eeb8287841901c

1 in → 1 out12.4300 XPM110 B

AKwH7f7i…jaaUhkWH

bea617fe5fff32…2743eda6cdae13

3 in → 2 out1000.3836 XPM522 B

Abwgb4M5…hvNpgSsE Acs9SHrk…QJSB8SFG

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.

1.317 × 10¹⁰⁰(101-digit number)

13176479257732513110…56732470550184462399

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

1.317 × 10¹⁰⁰(101-digit number)

13176479257732513110…56732470550184462399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.317 × 10¹⁰⁰(101-digit number)

13176479257732513110…56732470550184462401

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

2.635 × 10¹⁰⁰(101-digit number)

26352958515465026220…13464941100368924799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.635 × 10¹⁰⁰(101-digit number)

26352958515465026220…13464941100368924801

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

5.270 × 10¹⁰⁰(101-digit number)

52705917030930052441…26929882200737849599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.270 × 10¹⁰⁰(101-digit number)

52705917030930052441…26929882200737849601

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

1.054 × 10¹⁰¹(102-digit number)

10541183406186010488…53859764401475699199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.054 × 10¹⁰¹(102-digit number)

10541183406186010488…53859764401475699201

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

2.108 × 10¹⁰¹(102-digit number)

21082366812372020976…07719528802951398399

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