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Block #581,171

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/8/2014, 11:49:58 AM Β· Difficulty 10.9631 Β· 6,225,356 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
68ed249281dfd4e08e267c51c0ec3bd2fd3ee8f40bb5df6a9a110825a8b83999
View on Chainz β†—

Height

#581,171

Difficulty

10.963126

Transactions

1

Size

208 B

Version

2

Bits

0af68f68

Nonce

1,640,588,080

Timestamp

6/8/2014, 11:49:58 AM

Confirmations

6,225,356

Merkle Root

f6e4274bc43c8d8b0f584d420b8fce7bcb0a3141b64d744844ffe7aa37900b4b
Transactions (1)
Coinbasef6e4274bc43c8d…ffe7aa37900b4b
1 in β†’ 1 out8.3100 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.

1.832 Γ— 10¹⁰⁰(101-digit number)
18321786417842126809…65793597501784299520
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
1.832 Γ— 10¹⁰⁰(101-digit number)
18321786417842126809…65793597501784299519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.832 Γ— 10¹⁰⁰(101-digit number)
18321786417842126809…65793597501784299521
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
3.664 Γ— 10¹⁰⁰(101-digit number)
36643572835684253618…31587195003568599039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.664 Γ— 10¹⁰⁰(101-digit number)
36643572835684253618…31587195003568599041
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
7.328 Γ— 10¹⁰⁰(101-digit number)
73287145671368507236…63174390007137198079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.328 Γ— 10¹⁰⁰(101-digit number)
73287145671368507236…63174390007137198081
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
1.465 Γ— 10¹⁰¹(102-digit number)
14657429134273701447…26348780014274396159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.465 Γ— 10¹⁰¹(102-digit number)
14657429134273701447…26348780014274396161
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
2.931 Γ— 10¹⁰¹(102-digit number)
29314858268547402894…52697560028548792319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.931 Γ— 10¹⁰¹(102-digit number)
29314858268547402894…52697560028548792321
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
5.862 Γ— 10¹⁰¹(102-digit number)
58629716537094805789…05395120057097584639
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 581171

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 68ed249281dfd4e08e267c51c0ec3bd2fd3ee8f40bb5df6a9a110825a8b83999

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 #581,171 on Chainz β†—
Circulating Supply:57,696,316 XPMΒ·at block #6,806,526 Β· updates every 60s
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