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Block #851,971

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/13/2014, 5:24:50 PM Β· Difficulty 10.9702 Β· 5,991,834 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3d93728f3c93cfa32e45aca031b190f31ecb8ec7d9ce3484c44b5b8d89d5dc50
View on Chainz β†—

Height

#851,971

Difficulty

10.970238

Transactions

1

Size

200 B

Version

2

Bits

0af86180

Nonce

1,305,762,983

Timestamp

12/13/2014, 5:24:50 PM

Confirmations

5,991,834

Merkle Root

5208ba1f8253bef6cc892623304e7a859c28d885cdfc50afaae4067128296118
Transactions (1)
Coinbase5208ba1f8253be…e4067128296118
1 in β†’ 1 out8.3000 XPM110 B
ATtnMtqz…tiLdT2Zc
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.

9.482 Γ— 10⁹⁴(95-digit number)
94826874861726489167…15699789187991124480
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
9.482 Γ— 10⁹⁴(95-digit number)
94826874861726489167…15699789187991124479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.482 Γ— 10⁹⁴(95-digit number)
94826874861726489167…15699789187991124481
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
1.896 Γ— 10⁹⁡(96-digit number)
18965374972345297833…31399578375982248959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.896 Γ— 10⁹⁡(96-digit number)
18965374972345297833…31399578375982248961
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
3.793 Γ— 10⁹⁡(96-digit number)
37930749944690595667…62799156751964497919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.793 Γ— 10⁹⁡(96-digit number)
37930749944690595667…62799156751964497921
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
7.586 Γ— 10⁹⁡(96-digit number)
75861499889381191334…25598313503928995839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.586 Γ— 10⁹⁡(96-digit number)
75861499889381191334…25598313503928995841
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
1.517 Γ— 10⁹⁢(97-digit number)
15172299977876238266…51196627007857991679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.517 Γ— 10⁹⁢(97-digit number)
15172299977876238266…51196627007857991681
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
3.034 Γ— 10⁹⁢(97-digit number)
30344599955752476533…02393254015715983359
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 851971

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 3d93728f3c93cfa32e45aca031b190f31ecb8ec7d9ce3484c44b5b8d89d5dc50

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 #851,971 on Chainz β†—
Circulating Supply:57,994,814 XPMΒ·at block #6,843,804 Β· updates every 60s
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