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Block #582,618

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/9/2014, 8:07:38 PM Β· Difficulty 10.9594 Β· 6,213,551 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
708592fffe3ed46cced637da3e8f05071ad74fbd9ce0ef08c23d209ca9ce1860
View on Chainz β†—

Height

#582,618

Difficulty

10.959446

Transactions

2

Size

582 B

Version

2

Bits

0af59e47

Nonce

57,562,368

Timestamp

6/9/2014, 8:07:38 PM

Confirmations

6,213,551

Merkle Root

c4c627feaece8f1b90b161882b030d8440bb4306091d31fdbb06b0dca1ea7ed8
Transactions (2)
Coinbase28ac95d8a90ee6…b44ae7d7bb1bee
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
848bb408294884…8709ae9c2c1ca3
2 in β†’ 2 out16.6500 XPM374 B
AbVPt3EM…Q5PU9SqVAJnLdNuf…3EQVEdGz
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.

2.984 Γ— 10⁹⁸(99-digit number)
29846469219091629725…51093481453663712000
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
2.984 Γ— 10⁹⁸(99-digit number)
29846469219091629725…51093481453663711999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.984 Γ— 10⁹⁸(99-digit number)
29846469219091629725…51093481453663712001
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
5.969 Γ— 10⁹⁸(99-digit number)
59692938438183259450…02186962907327423999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.969 Γ— 10⁹⁸(99-digit number)
59692938438183259450…02186962907327424001
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
1.193 Γ— 10⁹⁹(100-digit number)
11938587687636651890…04373925814654847999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.193 Γ— 10⁹⁹(100-digit number)
11938587687636651890…04373925814654848001
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
2.387 Γ— 10⁹⁹(100-digit number)
23877175375273303780…08747851629309695999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.387 Γ— 10⁹⁹(100-digit number)
23877175375273303780…08747851629309696001
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
4.775 Γ— 10⁹⁹(100-digit number)
47754350750546607560…17495703258619391999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.775 Γ— 10⁹⁹(100-digit number)
47754350750546607560…17495703258619392001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
9.550 Γ— 10⁹⁹(100-digit number)
95508701501093215120…34991406517238783999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 582618

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 708592fffe3ed46cced637da3e8f05071ad74fbd9ce0ef08c23d209ca9ce1860

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 #582,618 on Chainz β†—
Circulating Supply:57,613,350 XPMΒ·at block #6,796,168 Β· updates every 60s
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