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Block #556,280

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/22/2014, 3:48:49 AM · Difficulty 10.9628 · 6,239,325 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e7bc627f8d1ecf574d89d42e4550a8c2b59e88c9ec3e4d8e17ec41759474f741

View on Chainz ↗

Height

#556,280

Difficulty

10.962819

Transactions

Size

435 B

Version

Bits

0af67b4e

Nonce

1,174,656,056

Timestamp

5/22/2014, 3:48:49 AM

Confirmations

6,239,325

Merkle Root

7691d00902b10c3149f389729e485d4a78e4dcff35ce0376c77057c6172bf029

Transactions (2)

Coinbase0bebb8e98c6e08…87b5588ad17122

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

e6a0959cb26ab6…9074223dc484ce

1 in → 2 out1.9809 XPM227 B

AYqCBgAL…NRLHcPSk AL4RdTaL…RQtoEqnD

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.

1.924 × 10¹⁰⁰(101-digit number)

19249455308895153241…89756482061154001920

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

1.924 × 10¹⁰⁰(101-digit number)

19249455308895153241…89756482061154001919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.924 × 10¹⁰⁰(101-digit number)

19249455308895153241…89756482061154001921

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

3.849 × 10¹⁰⁰(101-digit number)

38498910617790306483…79512964122308003839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.849 × 10¹⁰⁰(101-digit number)

38498910617790306483…79512964122308003841

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

7.699 × 10¹⁰⁰(101-digit number)

76997821235580612967…59025928244616007679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.699 × 10¹⁰⁰(101-digit number)

76997821235580612967…59025928244616007681

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

1.539 × 10¹⁰¹(102-digit number)

15399564247116122593…18051856489232015359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.539 × 10¹⁰¹(102-digit number)

15399564247116122593…18051856489232015361

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

3.079 × 10¹⁰¹(102-digit number)

30799128494232245186…36103712978464030719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.079 × 10¹⁰¹(102-digit number)

30799128494232245186…36103712978464030721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 556280

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 e7bc627f8d1ecf574d89d42e4550a8c2b59e88c9ec3e4d8e17ec41759474f741

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 #556,280 on Chainz ↗