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Block #487,460

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/12/2014, 4:04:49 AM Β· Difficulty 10.6410 Β· 6,309,035 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3ce148cc3c6fbc866607b0c94bcd13bd55fd3dfee990115d55e429482fe3e0e5
View on Chainz β†—

Height

#487,460

Difficulty

10.641004

Transactions

2

Size

542 B

Version

2

Bits

0aa418d8

Nonce

183,341,775

Timestamp

4/12/2014, 4:04:49 AM

Confirmations

6,309,035

Merkle Root

5d218a887ea82200a7370ee208f3b93019ce086b578e6372682d6e2a5e753884
Transactions (2)
Coinbase8726333fbd8495…85dfcd8e1198b8
1 in β†’ 1 out8.8300 XPM111 B
AXuF5m5z…xSZ42JSU
fc36d8698b04ea…4771c7693d3fb1
2 in β†’ 1 out54.9900 XPM339 B
ARqLqg7j…tcvtkFxP
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.

2.418 Γ— 10⁹⁹(100-digit number)
24181125347968550268…79881646672658872320
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
2.418 Γ— 10⁹⁹(100-digit number)
24181125347968550268…79881646672658872319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.418 Γ— 10⁹⁹(100-digit number)
24181125347968550268…79881646672658872321
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
4.836 Γ— 10⁹⁹(100-digit number)
48362250695937100537…59763293345317744639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.836 Γ— 10⁹⁹(100-digit number)
48362250695937100537…59763293345317744641
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
9.672 Γ— 10⁹⁹(100-digit number)
96724501391874201074…19526586690635489279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.672 Γ— 10⁹⁹(100-digit number)
96724501391874201074…19526586690635489281
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
1.934 Γ— 10¹⁰⁰(101-digit number)
19344900278374840214…39053173381270978559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.934 Γ— 10¹⁰⁰(101-digit number)
19344900278374840214…39053173381270978561
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
3.868 Γ— 10¹⁰⁰(101-digit number)
38689800556749680429…78106346762541957119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.868 Γ— 10¹⁰⁰(101-digit number)
38689800556749680429…78106346762541957121
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 487460

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 3ce148cc3c6fbc866607b0c94bcd13bd55fd3dfee990115d55e429482fe3e0e5

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 #487,460 on Chainz β†—
Circulating Supply:57,615,960 XPMΒ·at block #6,796,494 Β· updates every 60s
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