Block #101,862

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/6/2013, 8:36:00 PM · Difficulty 9.4752 · 6,695,955 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

459c191857ea26b65130d7aeb4b0a3806815e363d65cf55770f406b7ad8e05de

View on Chainz ↗

Height

#101,862

Difficulty

9.475177

Transactions

Size

723 B

Version

Bits

0979a536

Nonce

15,461

Timestamp

8/6/2013, 8:36:00 PM

Confirmations

6,695,955

Mined by

⛏️ P2SHAStN5M7dSHwrGDLXDmXXry9hQ2LZLG6TzR

Merkle Root

fa67b5807b4a5b9ae6694cf7d4002c77535cb8ddc96a0b9fdf44efc5ac3d35c5

Transactions (2)

Coinbase6a81f2ff161cb4…a2789528ee65e4

1 in → 1 out11.1300 XPM109 B

AStN5M7d…LZLG6TzR

1882dbe4bb2b2a…a65e10cdf95581

3 in → 2 out101.1202 XPM523 B

AFxeKXgU…ig8jLrGN AakmwZ5k…bkVkBwwU

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.

2.082 × 10⁹⁶(97-digit number)

20822980987048531317…38739377463130410489

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

2.082 × 10⁹⁶(97-digit number)

20822980987048531317…38739377463130410489

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.082 × 10⁹⁶(97-digit number)

20822980987048531317…38739377463130410491

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

4.164 × 10⁹⁶(97-digit number)

41645961974097062634…77478754926260820979

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.164 × 10⁹⁶(97-digit number)

41645961974097062634…77478754926260820981

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

8.329 × 10⁹⁶(97-digit number)

83291923948194125269…54957509852521641959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.329 × 10⁹⁶(97-digit number)

83291923948194125269…54957509852521641961

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

1.665 × 10⁹⁷(98-digit number)

16658384789638825053…09915019705043283919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.665 × 10⁹⁷(98-digit number)

16658384789638825053…09915019705043283921

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

3.331 × 10⁹⁷(98-digit number)

33316769579277650107…19830039410086567839

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