Block #64,990

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 10:09:06 AM · Difficulty 8.9831 · 6,727,851 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ea9244b7e4136cdc338a947cdb8a0890be2e6459a037e8ce8564838675c2fffe

View on Chainz ↗

Height

#64,990

Difficulty

8.983068

Transactions

Size

199 B

Version

Bits

08fbaa5d

Nonce

135

Timestamp

7/19/2013, 10:09:06 AM

Confirmations

6,727,851

Merkle Root

a1ef6c608935751874f520ce1a5f198050ca028629870ef5013e02cc15ae7919

Transactions (1)

Coinbasea1ef6c60893575…3e02cc15ae7919

1 in → 1 out12.3700 XPM109 B

AGY4TBx7…YfD8h7Va

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.

5.159 × 10⁹⁴(95-digit number)

51596328104324004855…67904417454755673699

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

5.159 × 10⁹⁴(95-digit number)

51596328104324004855…67904417454755673699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.159 × 10⁹⁴(95-digit number)

51596328104324004855…67904417454755673701

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

1.031 × 10⁹⁵(96-digit number)

10319265620864800971…35808834909511347399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.031 × 10⁹⁵(96-digit number)

10319265620864800971…35808834909511347401

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

2.063 × 10⁹⁵(96-digit number)

20638531241729601942…71617669819022694799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.063 × 10⁹⁵(96-digit number)

20638531241729601942…71617669819022694801

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

4.127 × 10⁹⁵(96-digit number)

41277062483459203884…43235339638045389599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.127 × 10⁹⁵(96-digit number)

41277062483459203884…43235339638045389601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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