Home/Chain Registry/Block #207,993

Block #207,993

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/13/2013, 6:14:05 PM · Difficulty 9.9049 · 6,582,976 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1fa857409a215dd500289eb60d6f0bc75d726af7c5900355a421b3d012448727

View on Chainz ↗

Height

#207,993

Difficulty

9.904873

Transactions

Size

869 B

Version

Bits

09e7a5c1

Nonce

28,803

Timestamp

10/13/2013, 6:14:05 PM

Confirmations

6,582,976

Merkle Root

ba2f87284f3b618bbda7a21d0eb6ac31921633c56c7c8155a334614ff788457d

Transactions (2)

Coinbase5a4b728d4299d4…4ef5f96a092208

1 in → 1 out10.1900 XPM110 B

AbuU1HhS…JPwsJEbB

01d01366357e33…574468c09e4539

4 in → 2 out1769.2476 XPM669 B

APPCsnBS…UGgK7tMn ANq1QQuk…8tWqaoqq

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.

2.620 × 10⁹⁴(95-digit number)

26207986624830991707…10853767181094600960

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

2.620 × 10⁹⁴(95-digit number)

26207986624830991707…10853767181094600959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.620 × 10⁹⁴(95-digit number)

26207986624830991707…10853767181094600961

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

5.241 × 10⁹⁴(95-digit number)

52415973249661983414…21707534362189201919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.241 × 10⁹⁴(95-digit number)

52415973249661983414…21707534362189201921

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

1.048 × 10⁹⁵(96-digit number)

10483194649932396682…43415068724378403839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.048 × 10⁹⁵(96-digit number)

10483194649932396682…43415068724378403841

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

2.096 × 10⁹⁵(96-digit number)

20966389299864793365…86830137448756807679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.096 × 10⁹⁵(96-digit number)

20966389299864793365…86830137448756807681

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

4.193 × 10⁹⁵(96-digit number)

41932778599729586731…73660274897513615359

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 207993

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 1fa857409a215dd500289eb60d6f0bc75d726af7c5900355a421b3d012448727

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 #207,993 on Chainz ↗