Block #146,610

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/2/2013, 2:58:29 PM · Difficulty 9.8483 · 6,670,656 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

521c17068f845e549044a3892453cd0cfbff101162c4b600503367f885a15ddd

View on Chainz ↗

Height

#146,610

Difficulty

9.848338

Transactions

Size

719 B

Version

Bits

09d92cb3

Nonce

186,196

Timestamp

9/2/2013, 2:58:29 PM

Confirmations

6,670,656

Mined by

⛏️ P2SHAKUegfDdkwE8cLmJU3Kgt3YKpswwHBC13P

Merkle Root

a091ad2b5f49e98bfd817ad0f591d2c9c219b76dec3e396c271434c5b07afb9b

Transactions (2)

Coinbasee17637fd20281a…31fd6462b11799

1 in → 1 out10.3100 XPM109 B

AKUegfDd…wwHBC13P

dbf19095c3a0ee…e4d02466c7aa84

3 in → 2 out270.2079 XPM521 B

AX76edCW…wbrzSDcf AUWSUEty…fhtKxRFm

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.

4.146 × 10⁹²(93-digit number)

41468812178996240309…41252932219184109119

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

4.146 × 10⁹²(93-digit number)

41468812178996240309…41252932219184109119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.146 × 10⁹²(93-digit number)

41468812178996240309…41252932219184109121

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

8.293 × 10⁹²(93-digit number)

82937624357992480619…82505864438368218239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.293 × 10⁹²(93-digit number)

82937624357992480619…82505864438368218241

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

1.658 × 10⁹³(94-digit number)

16587524871598496123…65011728876736436479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.658 × 10⁹³(94-digit number)

16587524871598496123…65011728876736436481

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

3.317 × 10⁹³(94-digit number)

33175049743196992247…30023457753472872959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.317 × 10⁹³(94-digit number)

33175049743196992247…30023457753472872961

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

6.635 × 10⁹³(94-digit number)

66350099486393984495…60046915506945745919

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

Block #146,610

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