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Block #46,388

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/15/2013, 6:21:00 AM Β· Difficulty 8.7905 Β· 6,768,458 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c5d35e7e9c018e5f41507696bfae91d7b2fb448f34997cab2b25a5a6a7067f35
View on Chainz β†—

Height

#46,388

Difficulty

8.790503

Transactions

2

Size

509 B

Version

2

Bits

08ca5e6b

Nonce

641

Timestamp

7/15/2013, 6:21:00 AM

Confirmations

6,768,458

Merkle Root

88c9c99c92ea94b03c505c1a8940dc33e90fb50b883e830d06dcfaff2b0adcf0
Transactions (2)
Coinbase0c7decb8034c7f…74537abe019ceb
1 in β†’ 1 out12.9300 XPM109 B
AJkys6Q5…hVcoruvt
749fd9ab2d80d4…a76346dc5ce755
2 in β†’ 1 out13.5200 XPM306 B
AScNu17i…EEtEnKS9
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.

1.157 Γ— 10¹⁰⁡(106-digit number)
11576080603255616895…73047280693375964220
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
1.157 Γ— 10¹⁰⁡(106-digit number)
11576080603255616895…73047280693375964219
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.157 Γ— 10¹⁰⁡(106-digit number)
11576080603255616895…73047280693375964221
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
2.315 Γ— 10¹⁰⁡(106-digit number)
23152161206511233791…46094561386751928439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.315 Γ— 10¹⁰⁡(106-digit number)
23152161206511233791…46094561386751928441
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
4.630 Γ— 10¹⁰⁡(106-digit number)
46304322413022467582…92189122773503856879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.630 Γ— 10¹⁰⁡(106-digit number)
46304322413022467582…92189122773503856881
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
9.260 Γ— 10¹⁰⁡(106-digit number)
92608644826044935165…84378245547007713759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.260 Γ— 10¹⁰⁡(106-digit number)
92608644826044935165…84378245547007713761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8
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 46388

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 c5d35e7e9c018e5f41507696bfae91d7b2fb448f34997cab2b25a5a6a7067f35

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 #46,388 on Chainz β†—
Circulating Supply:57,762,852 XPMΒ·at block #6,814,845 Β· updates every 60s
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