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Home/Chain Registry/Block #2,601,723

Block #2,601,723

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/5/2018, 7:58:44 PM Β· Difficulty 11.3160 Β· 4,240,158 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6a927484a94f202993fc6d333ca3e042cbffadf18d35557682d954d50caa7d13
View on Chainz β†—

Difficulty

11.316022

Transactions

1

Size

200 B

Version

2

Bits

0b50e6ca

Nonce

1,001,951,171

Timestamp

4/5/2018, 7:58:44 PM

Confirmations

4,240,158

Merkle Root

510c8acd1f533729ebd2937ac095d790611b7535f5bcabec0dabbdf71f2f2ce1
Transactions (1)
Coinbase510c8acd1f5337…abbdf71f2f2ce1
1 in β†’ 1 out7.8000 XPM110 B
AWrK2rWc…tzv5PQXC
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.

9.731 Γ— 10⁹⁴(95-digit number)
97318481115830309354…60353060152616538480
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
9.731 Γ— 10⁹⁴(95-digit number)
97318481115830309354…60353060152616538479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.731 Γ— 10⁹⁴(95-digit number)
97318481115830309354…60353060152616538481
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
1.946 Γ— 10⁹⁡(96-digit number)
19463696223166061870…20706120305233076959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.946 Γ— 10⁹⁡(96-digit number)
19463696223166061870…20706120305233076961
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
3.892 Γ— 10⁹⁡(96-digit number)
38927392446332123741…41412240610466153919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.892 Γ— 10⁹⁡(96-digit number)
38927392446332123741…41412240610466153921
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
7.785 Γ— 10⁹⁡(96-digit number)
77854784892664247483…82824481220932307839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.785 Γ— 10⁹⁡(96-digit number)
77854784892664247483…82824481220932307841
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
1.557 Γ— 10⁹⁢(97-digit number)
15570956978532849496…65648962441864615679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.557 Γ— 10⁹⁢(97-digit number)
15570956978532849496…65648962441864615681
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
3.114 Γ— 10⁹⁢(97-digit number)
31141913957065698993…31297924883729231359
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 2601723

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 6a927484a94f202993fc6d333ca3e042cbffadf18d35557682d954d50caa7d13

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 #2,601,723 on Chainz β†—
Circulating Supply:57,979,423 XPMΒ·at block #6,841,880 Β· updates every 60s
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