Block #78,916

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/23/2013, 4:38:03 AM · Difficulty 9.2313 · 6,715,544 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

970b2c79ea1e0ea8e43c026986e09d94d88ef66a3d37a7f11a872f3ad47b856b

View on Chainz ↗

Height

#78,916

Difficulty

9.231274

Transactions

Size

397 B

Version

Bits

093b34c5

Nonce

Timestamp

7/23/2013, 4:38:03 AM

Confirmations

6,715,544

Mined by

⛏️ P2SHAHpT5Ubr7tyJrMtf8YgCHZoPSbErRZ8yTA

Merkle Root

b286b89396c431fedae7dcc69ef909135a8274d64403688722771ad1f65709b4

Transactions (2)

Coinbaseb2fe764297bd59…ec5c052b8deb3b

1 in → 1 out11.7300 XPM110 B

AHpT5Ubr…ErRZ8yTA

4731f83590f174…4a9b03052d003f

1 in → 2 out12.4700 XPM193 B

AbTc6dkp…fyH1XN1u APwLy6FT…Yzbdv5Mc

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.

3.001 × 10¹⁰⁵(106-digit number)

30010491868301900482…75207393856393640959

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

3.001 × 10¹⁰⁵(106-digit number)

30010491868301900482…75207393856393640959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.001 × 10¹⁰⁵(106-digit number)

30010491868301900482…75207393856393640961

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

6.002 × 10¹⁰⁵(106-digit number)

60020983736603800964…50414787712787281919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.002 × 10¹⁰⁵(106-digit number)

60020983736603800964…50414787712787281921

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

1.200 × 10¹⁰⁶(107-digit number)

12004196747320760192…00829575425574563839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.200 × 10¹⁰⁶(107-digit number)

12004196747320760192…00829575425574563841

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

2.400 × 10¹⁰⁶(107-digit number)

24008393494641520385…01659150851149127679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.400 × 10¹⁰⁶(107-digit number)

24008393494641520385…01659150851149127681

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

4.801 × 10¹⁰⁶(107-digit number)

48016786989283040771…03318301702298255359

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