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Block #378,060

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/27/2014, 1:28:41 PM Β· Difficulty 10.4218 Β· 6,448,138 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
18e7741b928257bad12b8be9e00e540566c3d0d27c16130df80c6433d61c49af
View on Chainz β†—

Height

#378,060

Difficulty

10.421785

Transactions

1

Size

202 B

Version

2

Bits

0a6bfa19

Nonce

227,145

Timestamp

1/27/2014, 1:28:41 PM

Confirmations

6,448,138

Merkle Root

38dc5005fcb3ca6d3afe1c0e3200f38e18bc33897bbd9479dab4bb365e6fbdb3
Transactions (1)
Coinbase38dc5005fcb3ca…b4bb365e6fbdb3
1 in β†’ 1 out9.1900 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.354 Γ— 10¹⁰⁰(101-digit number)
13543420579946600646…02643027646209280000
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
1.354 Γ— 10¹⁰⁰(101-digit number)
13543420579946600646…02643027646209279999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.354 Γ— 10¹⁰⁰(101-digit number)
13543420579946600646…02643027646209280001
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
2.708 Γ— 10¹⁰⁰(101-digit number)
27086841159893201293…05286055292418559999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.708 Γ— 10¹⁰⁰(101-digit number)
27086841159893201293…05286055292418560001
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
5.417 Γ— 10¹⁰⁰(101-digit number)
54173682319786402586…10572110584837119999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.417 Γ— 10¹⁰⁰(101-digit number)
54173682319786402586…10572110584837120001
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
1.083 Γ— 10¹⁰¹(102-digit number)
10834736463957280517…21144221169674239999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.083 Γ— 10¹⁰¹(102-digit number)
10834736463957280517…21144221169674240001
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
2.166 Γ— 10¹⁰¹(102-digit number)
21669472927914561034…42288442339348479999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.166 Γ— 10¹⁰¹(102-digit number)
21669472927914561034…42288442339348480001
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 378060

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 18e7741b928257bad12b8be9e00e540566c3d0d27c16130df80c6433d61c49af

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 #378,060 on Chainz β†—
Circulating Supply:57,853,714 XPMΒ·at block #6,826,197 Β· updates every 60s
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