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Block #534,480

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/10/2014, 8:38:20 AM Β· Difficulty 10.9020 Β· 6,290,206 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2df97df8b46d6902bbb31dfe5d7978a2df25add89665707c7c5b61b4f44aaf48
View on Chainz β†—

Height

#534,480

Difficulty

10.901977

Transactions

1

Size

209 B

Version

2

Bits

0ae6e7f6

Nonce

114,784,489

Timestamp

5/10/2014, 8:38:20 AM

Confirmations

6,290,206

Merkle Root

3c97a9a2bfa53575300003a45e0d6fa4c191006be84f89aa51a4ed1f9ca3f77f
Transactions (1)
Coinbase3c97a9a2bfa535…a4ed1f9ca3f77f
1 in β†’ 1 out8.4000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

6.238 Γ— 10¹⁰⁰(101-digit number)
62388982435126611650…59956328324118118400
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
6.238 Γ— 10¹⁰⁰(101-digit number)
62388982435126611650…59956328324118118399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.238 Γ— 10¹⁰⁰(101-digit number)
62388982435126611650…59956328324118118401
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
1.247 Γ— 10¹⁰¹(102-digit number)
12477796487025322330…19912656648236236799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.247 Γ— 10¹⁰¹(102-digit number)
12477796487025322330…19912656648236236801
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
2.495 Γ— 10¹⁰¹(102-digit number)
24955592974050644660…39825313296472473599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.495 Γ— 10¹⁰¹(102-digit number)
24955592974050644660…39825313296472473601
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
4.991 Γ— 10¹⁰¹(102-digit number)
49911185948101289320…79650626592944947199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.991 Γ— 10¹⁰¹(102-digit number)
49911185948101289320…79650626592944947201
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
9.982 Γ— 10¹⁰¹(102-digit number)
99822371896202578640…59301253185889894399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.982 Γ— 10¹⁰¹(102-digit number)
99822371896202578640…59301253185889894401
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 534480

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 2df97df8b46d6902bbb31dfe5d7978a2df25add89665707c7c5b61b4f44aaf48

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 #534,480 on Chainz β†—
Circulating Supply:57,841,554 XPMΒ·at block #6,824,685 Β· updates every 60s
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