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Block #854,242

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/15/2014, 11:52:26 AM Β· Difficulty 10.9686 Β· 5,973,156 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4f7ed726a36ba5bb22aeb9c501e512d7407125d858a071b98b45d87fd9d1fb0d
View on Chainz β†—

Height

#854,242

Difficulty

10.968631

Transactions

1

Size

200 B

Version

2

Bits

0af7f835

Nonce

533,597,429

Timestamp

12/15/2014, 11:52:26 AM

Confirmations

5,973,156

Merkle Root

69c6be5519de2b7e245826741957f850d68db58782121aee4579aa3efb3da98b
Transactions (1)
Coinbase69c6be5519de2b…79aa3efb3da98b
1 in β†’ 1 out8.3000 XPM110 B
AYZvn8kx…L2HzYoTq
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.

1.700 Γ— 10⁹⁡(96-digit number)
17003844009434096552…35355618041130681280
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
1.700 Γ— 10⁹⁡(96-digit number)
17003844009434096552…35355618041130681279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.700 Γ— 10⁹⁡(96-digit number)
17003844009434096552…35355618041130681281
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
3.400 Γ— 10⁹⁡(96-digit number)
34007688018868193104…70711236082261362559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.400 Γ— 10⁹⁡(96-digit number)
34007688018868193104…70711236082261362561
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
6.801 Γ— 10⁹⁡(96-digit number)
68015376037736386209…41422472164522725119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.801 Γ— 10⁹⁡(96-digit number)
68015376037736386209…41422472164522725121
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
1.360 Γ— 10⁹⁢(97-digit number)
13603075207547277241…82844944329045450239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.360 Γ— 10⁹⁢(97-digit number)
13603075207547277241…82844944329045450241
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
2.720 Γ— 10⁹⁢(97-digit number)
27206150415094554483…65689888658090900479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.720 Γ— 10⁹⁢(97-digit number)
27206150415094554483…65689888658090900481
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 854242

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 4f7ed726a36ba5bb22aeb9c501e512d7407125d858a071b98b45d87fd9d1fb0d

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 #854,242 on Chainz β†—
Circulating Supply:57,863,288 XPMΒ·at block #6,827,397 Β· updates every 60s
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