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Block #556,351

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/22/2014, 5:11:59 AM Β· Difficulty 10.9627 Β· 6,238,480 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7fe2316aed4222293d7fd08629d2198f18e19df24ef367b7b0ce4f8823763a1a
View on Chainz β†—

Height

#556,351

Difficulty

10.962729

Transactions

1

Size

209 B

Version

2

Bits

0af67567

Nonce

103,281,589

Timestamp

5/22/2014, 5:11:59 AM

Confirmations

6,238,480

Merkle Root

c0b8a8d82023058ebec9d107308409e61bc580537e0d4619f7f5fe98a8787396
Transactions (1)
Coinbasec0b8a8d8202305…f5fe98a8787396
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.009 Γ— 10¹⁰⁰(101-digit number)
70097662458334758407…82665570256612464640
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
7.009 Γ— 10¹⁰⁰(101-digit number)
70097662458334758407…82665570256612464639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.009 Γ— 10¹⁰⁰(101-digit number)
70097662458334758407…82665570256612464641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.401 Γ— 10¹⁰¹(102-digit number)
14019532491666951681…65331140513224929279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.401 Γ— 10¹⁰¹(102-digit number)
14019532491666951681…65331140513224929281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.803 Γ— 10¹⁰¹(102-digit number)
28039064983333903363…30662281026449858559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.803 Γ— 10¹⁰¹(102-digit number)
28039064983333903363…30662281026449858561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
5.607 Γ— 10¹⁰¹(102-digit number)
56078129966667806726…61324562052899717119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.607 Γ— 10¹⁰¹(102-digit number)
56078129966667806726…61324562052899717121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.121 Γ— 10¹⁰²(103-digit number)
11215625993333561345…22649124105799434239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.121 Γ— 10¹⁰²(103-digit number)
11215625993333561345…22649124105799434241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 β€” the large number shown above β€” 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 β†’
β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 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 556351

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 7fe2316aed4222293d7fd08629d2198f18e19df24ef367b7b0ce4f8823763a1a

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 β†’ Debug Window β†’ 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 #556,351 on Chainz β†—
Circulating Supply:57,602,698 XPMΒ·at block #6,794,830 Β· updates every 60s
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