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Block #858,123

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/18/2014, 8:53:13 AM Β· Difficulty 10.9671 Β· 5,985,100 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
36e0c223bc81685d244ac9f0bab7024c8f079ff90a7c72808995a5fc2ccdb890
View on Chainz β†—

Height

#858,123

Difficulty

10.967090

Transactions

1

Size

243 B

Version

2

Bits

0af79335

Nonce

940,806,558

Timestamp

12/18/2014, 8:53:13 AM

Confirmations

5,985,100

Merkle Root

66c99711cd138ea7781a5448b8c760b69045ee6c4db291e8bcd3bd5a07e5a2a2
Transactions (1)
Coinbase66c99711cd138e…d3bd5a07e5a2a2
1 in β†’ 2 out8.3000 XPM152 B
AK6BxZXL…UXnxyXDBALPu3s2c…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.

2.336 Γ— 10⁹⁢(97-digit number)
23360618199995761011…15965713594131299200
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
2.336 Γ— 10⁹⁢(97-digit number)
23360618199995761011…15965713594131299199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.336 Γ— 10⁹⁢(97-digit number)
23360618199995761011…15965713594131299201
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
4.672 Γ— 10⁹⁢(97-digit number)
46721236399991522023…31931427188262598399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.672 Γ— 10⁹⁢(97-digit number)
46721236399991522023…31931427188262598401
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
9.344 Γ— 10⁹⁢(97-digit number)
93442472799983044046…63862854376525196799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.344 Γ— 10⁹⁢(97-digit number)
93442472799983044046…63862854376525196801
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
1.868 Γ— 10⁹⁷(98-digit number)
18688494559996608809…27725708753050393599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.868 Γ— 10⁹⁷(98-digit number)
18688494559996608809…27725708753050393601
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
3.737 Γ— 10⁹⁷(98-digit number)
37376989119993217618…55451417506100787199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.737 Γ— 10⁹⁷(98-digit number)
37376989119993217618…55451417506100787201
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
7.475 Γ— 10⁹⁷(98-digit number)
74753978239986435237…10902835012201574399
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 858123

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 36e0c223bc81685d244ac9f0bab7024c8f079ff90a7c72808995a5fc2ccdb890

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 #858,123 on Chainz β†—
Circulating Supply:57,990,158 XPMΒ·at block #6,843,222 Β· updates every 60s
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