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Block #33,877

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 5:37:45 AM · Difficulty 7.9926 · 6,776,054 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

92eba8e41797dad3de0dd9fdfce2c52fea819c4edb77f948f9b0d25dde71a7de

View on Chainz ↗

Height

#33,877

Difficulty

7.992555

Transactions

Size

203 B

Version

Bits

07fe181b

Nonce

113

Timestamp

7/14/2013, 5:37:45 AM

Confirmations

6,776,054

Merkle Root

afb175c0a128100b187962789f887beca6956844d0ea96fc7c90b26a8c2eb815

Transactions (1)

Coinbaseafb175c0a12810…90b26a8c2eb815

1 in → 1 out15.6300 XPM110 B

AYrtgdMx…SnFDNzsA

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.

1.139 × 10¹⁰¹(102-digit number)

11395757463862392042…83661641352380365220

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

1.139 × 10¹⁰¹(102-digit number)

11395757463862392042…83661641352380365219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.139 × 10¹⁰¹(102-digit number)

11395757463862392042…83661641352380365221

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

2.279 × 10¹⁰¹(102-digit number)

22791514927724784084…67323282704760730439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.279 × 10¹⁰¹(102-digit number)

22791514927724784084…67323282704760730441

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

4.558 × 10¹⁰¹(102-digit number)

45583029855449568168…34646565409521460879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.558 × 10¹⁰¹(102-digit number)

45583029855449568168…34646565409521460881

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

9.116 × 10¹⁰¹(102-digit number)

91166059710899136337…69293130819042921759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.116 × 10¹⁰¹(102-digit number)

91166059710899136337…69293130819042921761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 33877

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 92eba8e41797dad3de0dd9fdfce2c52fea819c4edb77f948f9b0d25dde71a7de

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 #33,877 on Chainz ↗

Block #33,877

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