Home/Chain Registry/Block #101,862

Block #101,862

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/6/2013, 8:36:00 PM · Difficulty 9.4752 · 6,700,557 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

6,700,557

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…38739377463130410490

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.

View full Prime Chain Discovery page →

★☆☆☆☆

Rarity

CommonChain length 9

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 101862

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 459c191857ea26b65130d7aeb4b0a3806815e363d65cf55770f406b7ad8e05de

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #101,862 on Chainz ↗