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Home/Chain Registry/Block #569,623

Block #569,623

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/31/2014, 6:40:32 AM Β· Difficulty 10.9648 Β· 6,242,616 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c5e5fcb622103d90f33693e71574b42ea6f0562d18f950dfb20a9b77e53b0aaa
View on Chainz β†—

Height

#569,623

Difficulty

10.964773

Transactions

1

Size

243 B

Version

2

Bits

0af6fb5b

Nonce

961,691,378

Timestamp

5/31/2014, 6:40:32 AM

Confirmations

6,242,616

Merkle Root

c7fcf94553486564a07403308751377496ba9fbf17be389dad2852b974a2e0ee
Transactions (1)
Coinbasec7fcf945534865…2852b974a2e0ee
1 in β†’ 2 out8.3000 XPM152 B
Aa3wSAXq…mqUhuJLqALPu3s2c…EJXLjVFh
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.

1.439 Γ— 10⁹⁷(98-digit number)
14393116738398876266…71958008887577225500
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
1.439 Γ— 10⁹⁷(98-digit number)
14393116738398876266…71958008887577225499
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.439 Γ— 10⁹⁷(98-digit number)
14393116738398876266…71958008887577225501
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
2.878 Γ— 10⁹⁷(98-digit number)
28786233476797752532…43916017775154450999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.878 Γ— 10⁹⁷(98-digit number)
28786233476797752532…43916017775154451001
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
5.757 Γ— 10⁹⁷(98-digit number)
57572466953595505064…87832035550308901999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.757 Γ— 10⁹⁷(98-digit number)
57572466953595505064…87832035550308902001
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
1.151 Γ— 10⁹⁸(99-digit number)
11514493390719101012…75664071100617803999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.151 Γ— 10⁹⁸(99-digit number)
11514493390719101012…75664071100617804001
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
2.302 Γ— 10⁹⁸(99-digit number)
23028986781438202025…51328142201235607999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.302 Γ— 10⁹⁸(99-digit number)
23028986781438202025…51328142201235608001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.605 Γ— 10⁹⁸(99-digit number)
46057973562876404051…02656284402471215999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 569623

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 c5e5fcb622103d90f33693e71574b42ea6f0562d18f950dfb20a9b77e53b0aaa

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 #569,623 on Chainz β†—
Circulating Supply:57,741,929 XPMΒ·at block #6,812,238 Β· updates every 60s
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