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Block #857,042

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/17/2014, 1:21:27 PM Β· Difficulty 10.9677 Β· 5,986,323 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cf6439de58d4512d8b6c665d9e65447a548d60bfc17fbc4b3eeb915decc28d0d
View on Chainz β†—

Height

#857,042

Difficulty

10.967655

Transactions

1

Size

241 B

Version

2

Bits

0af7b835

Nonce

710,669,048

Timestamp

12/17/2014, 1:21:27 PM

Confirmations

5,986,323

Merkle Root

f2b2409ead49ee23e1f99ec5c48dc33a3bb5da667813530522876c08b071a025
Transactions (1)
Coinbasef2b2409ead49ee…876c08b071a025
1 in β†’ 2 out8.3000 XPM152 B
AK95bFBZ…LGYP2X93ALPu3s2c…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.

1.161 Γ— 10⁹³(94-digit number)
11614659685737650160…59341586438473837280
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
1.161 Γ— 10⁹³(94-digit number)
11614659685737650160…59341586438473837279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.161 Γ— 10⁹³(94-digit number)
11614659685737650160…59341586438473837281
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
2.322 Γ— 10⁹³(94-digit number)
23229319371475300320…18683172876947674559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.322 Γ— 10⁹³(94-digit number)
23229319371475300320…18683172876947674561
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
4.645 Γ— 10⁹³(94-digit number)
46458638742950600640…37366345753895349119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.645 Γ— 10⁹³(94-digit number)
46458638742950600640…37366345753895349121
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
9.291 Γ— 10⁹³(94-digit number)
92917277485901201281…74732691507790698239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.291 Γ— 10⁹³(94-digit number)
92917277485901201281…74732691507790698241
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
1.858 Γ— 10⁹⁴(95-digit number)
18583455497180240256…49465383015581396479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.858 Γ— 10⁹⁴(95-digit number)
18583455497180240256…49465383015581396481
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
3.716 Γ— 10⁹⁴(95-digit number)
37166910994360480512…98930766031162792959
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 857042

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 cf6439de58d4512d8b6c665d9e65447a548d60bfc17fbc4b3eeb915decc28d0d

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 #857,042 on Chainz β†—
Circulating Supply:57,991,283 XPMΒ·at block #6,843,364 Β· updates every 60s
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