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Block #46,016

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/15/2013, 4:54:51 AM Β· Difficulty 8.7783 Β· 6,760,294 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c189b23c6908ae735324eb3c178d40bdafa23fe3cb38ac48d1a2c0c074a0e718
View on Chainz β†—

Height

#46,016

Difficulty

8.778267

Transactions

1

Size

198 B

Version

2

Bits

08c73c89

Nonce

95

Timestamp

7/15/2013, 4:54:51 AM

Confirmations

6,760,294

Merkle Root

3942073e37b149e127e675c472729cd9515789397417ee819ccf61e820fd3c97
Transactions (1)
Coinbase3942073e37b149…cf61e820fd3c97
1 in β†’ 1 out12.9600 XPM109 B
AM6VRLKv…ByN91i1u
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.

2.530 Γ— 10⁹¹(92-digit number)
25305890523490076706…21016120710166555390
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
2.530 Γ— 10⁹¹(92-digit number)
25305890523490076706…21016120710166555389
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.530 Γ— 10⁹¹(92-digit number)
25305890523490076706…21016120710166555391
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
5.061 Γ— 10⁹¹(92-digit number)
50611781046980153412…42032241420333110779
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.061 Γ— 10⁹¹(92-digit number)
50611781046980153412…42032241420333110781
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
1.012 Γ— 10⁹²(93-digit number)
10122356209396030682…84064482840666221559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.012 Γ— 10⁹²(93-digit number)
10122356209396030682…84064482840666221561
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
2.024 Γ— 10⁹²(93-digit number)
20244712418792061364…68128965681332443119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.024 Γ— 10⁹²(93-digit number)
20244712418792061364…68128965681332443121
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
4.048 Γ— 10⁹²(93-digit number)
40489424837584122729…36257931362664886239
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 46016

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 c189b23c6908ae735324eb3c178d40bdafa23fe3cb38ac48d1a2c0c074a0e718

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 #46,016 on Chainz β†—
Circulating Supply:57,694,568 XPMΒ·at block #6,806,309 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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