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Home/Chain Registry/Block #1,878,481

Block #1,878,481

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/4/2016, 3:43:46 PM Β· Difficulty 10.6843 Β· 4,962,288 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d7d9bb7d0cf31575232202fd9af770689b5064092643d6a72dcc4a08a4d5d409
View on Chainz β†—

Difficulty

10.684312

Transactions

1

Size

200 B

Version

2

Bits

0aaf2f0c

Nonce

1,175,287,137

Timestamp

12/4/2016, 3:43:46 PM

Confirmations

4,962,288

Merkle Root

31b4027f5326275812ae9577f24a3aa28a0d2befc24fa12a2f7f9eeb3cf09b1f
Transactions (1)
Coinbase31b4027f532627…7f9eeb3cf09b1f
1 in β†’ 1 out8.7500 XPM110 B
AZEs1P9H…iqpm2exF
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.

9.138 Γ— 10⁹⁴(95-digit number)
91381170587507575745…86408116804993581440
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
9.138 Γ— 10⁹⁴(95-digit number)
91381170587507575745…86408116804993581439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.138 Γ— 10⁹⁴(95-digit number)
91381170587507575745…86408116804993581441
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
1.827 Γ— 10⁹⁡(96-digit number)
18276234117501515149…72816233609987162879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.827 Γ— 10⁹⁡(96-digit number)
18276234117501515149…72816233609987162881
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
3.655 Γ— 10⁹⁡(96-digit number)
36552468235003030298…45632467219974325759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.655 Γ— 10⁹⁡(96-digit number)
36552468235003030298…45632467219974325761
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
7.310 Γ— 10⁹⁡(96-digit number)
73104936470006060596…91264934439948651519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.310 Γ— 10⁹⁡(96-digit number)
73104936470006060596…91264934439948651521
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
1.462 Γ— 10⁹⁢(97-digit number)
14620987294001212119…82529868879897303039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.462 Γ— 10⁹⁢(97-digit number)
14620987294001212119…82529868879897303041
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 1878481

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 d7d9bb7d0cf31575232202fd9af770689b5064092643d6a72dcc4a08a4d5d409

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 #1,878,481 on Chainz β†—
Circulating Supply:57,970,495 XPMΒ·at block #6,840,768 Β· updates every 60s
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