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Block #456,853

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/23/2014, 12:26:44 PM Β· Difficulty 10.4176 Β· 6,369,955 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
667d8e8a6430f0ea26a245106f8149b58ee1ea0ccdfecf6821c02918aa0aec39
View on Chainz β†—

Height

#456,853

Difficulty

10.417568

Transactions

1

Size

202 B

Version

2

Bits

0a6ae5c0

Nonce

170,834

Timestamp

3/23/2014, 12:26:44 PM

Confirmations

6,369,955

Merkle Root

4e31ca0c341520b268dcd0dfd2881ee65548a197894d1a6f7baf6cbb561c15bc
Transactions (1)
Coinbase4e31ca0c341520…af6cbb561c15bc
1 in β†’ 1 out9.2000 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.

6.469 Γ— 10⁹⁸(99-digit number)
64699679229519993902…82623144367807461480
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
6.469 Γ— 10⁹⁸(99-digit number)
64699679229519993902…82623144367807461479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.469 Γ— 10⁹⁸(99-digit number)
64699679229519993902…82623144367807461481
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
1.293 Γ— 10⁹⁹(100-digit number)
12939935845903998780…65246288735614922959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.293 Γ— 10⁹⁹(100-digit number)
12939935845903998780…65246288735614922961
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
2.587 Γ— 10⁹⁹(100-digit number)
25879871691807997560…30492577471229845919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.587 Γ— 10⁹⁹(100-digit number)
25879871691807997560…30492577471229845921
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
5.175 Γ— 10⁹⁹(100-digit number)
51759743383615995121…60985154942459691839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.175 Γ— 10⁹⁹(100-digit number)
51759743383615995121…60985154942459691841
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
1.035 Γ— 10¹⁰⁰(101-digit number)
10351948676723199024…21970309884919383679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.035 Γ— 10¹⁰⁰(101-digit number)
10351948676723199024…21970309884919383681
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 456853

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 667d8e8a6430f0ea26a245106f8149b58ee1ea0ccdfecf6821c02918aa0aec39

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 #456,853 on Chainz β†—
Circulating Supply:57,858,626 XPMΒ·at block #6,826,807 Β· updates every 60s
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