Home/Chain Registry/Block #103,499

Block #103,499

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/7/2013, 3:14:35 PM · Difficulty 9.5271 · 6,688,434 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e0bc1e919cb87d2b674aa6a7f55ec4f18bee264c115a25c3c2efe028a446a895

View on Chainz ↗

Height

#103,499

Difficulty

9.527111

Transactions

Size

201 B

Version

Bits

0986f0b8

Nonce

156,378

Timestamp

8/7/2013, 3:14:35 PM

Confirmations

6,688,434

Merkle Root

aa6a780b35fc166b1b09ce8a201d7d25e0db59e81fa20e997d6f6142e24b2eeb

Transactions (1)

Coinbaseaa6a780b35fc16…6f6142e24b2eeb

1 in → 1 out11.0000 XPM109 B

AKPbouZZ…PsZpwHcc

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.

1.240 × 10¹⁰⁰(101-digit number)

12404379809001778318…85692391093770624800

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

1.240 × 10¹⁰⁰(101-digit number)

12404379809001778318…85692391093770624799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.240 × 10¹⁰⁰(101-digit number)

12404379809001778318…85692391093770624801

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

2.480 × 10¹⁰⁰(101-digit number)

24808759618003556637…71384782187541249599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.480 × 10¹⁰⁰(101-digit number)

24808759618003556637…71384782187541249601

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

4.961 × 10¹⁰⁰(101-digit number)

49617519236007113275…42769564375082499199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.961 × 10¹⁰⁰(101-digit number)

49617519236007113275…42769564375082499201

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

9.923 × 10¹⁰⁰(101-digit number)

99235038472014226550…85539128750164998399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.923 × 10¹⁰⁰(101-digit number)

99235038472014226550…85539128750164998401

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

1.984 × 10¹⁰¹(102-digit number)

19847007694402845310…71078257500329996799

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 103499

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 e0bc1e919cb87d2b674aa6a7f55ec4f18bee264c115a25c3c2efe028a446a895

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 #103,499 on Chainz ↗