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Block #274,516

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 7:58:13 AM · Difficulty 9.9577 · 6,567,641 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8532f0997815ab3b8718d5bac79b7cc42ebfe2806c79095ec1fb7e6cd4889b11

View on Chainz ↗

Height

#274,516

Difficulty

9.957732

Transactions

Size

789 B

Version

Bits

09f52dea

Nonce

2,250

Timestamp

11/26/2013, 7:58:13 AM

Confirmations

6,567,641

Merkle Root

bdd43bdc4c9171ed9d6e5f97dc2425b94a11ecf1af134713a2a324aee2d85ce2

Transactions (2)

Coinbase56e5f1bc3cb6c8…48227cef85e644

1 in → 2 out10.0800 XPM140 B

AKcbk49N…GJbKa7j1 AHsw4d6U…EnM8UXNZ

ccb3fcc2441bdb…f4346b424a51ef

3 in → 3 out1150.7100 XPM555 B

AcgwRb9z…8nkKvtuL ATDg1wpK…dc5kwZ3e ARo32Xqg…2DSaRuZA

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.

9.263 × 10¹⁰⁴(105-digit number)

92638930126308773847…05484381836693510400

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

9.263 × 10¹⁰⁴(105-digit number)

92638930126308773847…05484381836693510399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.263 × 10¹⁰⁴(105-digit number)

92638930126308773847…05484381836693510401

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

1.852 × 10¹⁰⁵(106-digit number)

18527786025261754769…10968763673387020799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.852 × 10¹⁰⁵(106-digit number)

18527786025261754769…10968763673387020801

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

3.705 × 10¹⁰⁵(106-digit number)

37055572050523509538…21937527346774041599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.705 × 10¹⁰⁵(106-digit number)

37055572050523509538…21937527346774041601

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

7.411 × 10¹⁰⁵(106-digit number)

74111144101047019077…43875054693548083199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.411 × 10¹⁰⁵(106-digit number)

74111144101047019077…43875054693548083201

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

1.482 × 10¹⁰⁶(107-digit number)

14822228820209403815…87750109387096166399

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 274516

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 8532f0997815ab3b8718d5bac79b7cc42ebfe2806c79095ec1fb7e6cd4889b11

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 #274,516 on Chainz ↗

Block #274,516

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