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Home/Chain Registry/Block #2,556,059

Block #2,556,059

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/8/2018, 9:52:58 PM Β· Difficulty 10.9911 Β· 4,288,425 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
58fe638f41dabe7f916db1316f85967e4fa1837347724c044913a852c8f96ee3
View on Chainz β†—

Difficulty

10.991116

Transactions

1

Size

199 B

Version

2

Bits

0afdb9ca

Nonce

1,467,733,603

Timestamp

3/8/2018, 9:52:58 PM

Confirmations

4,288,425

Merkle Root

b658ad6da5350d20e752a338abcae12d6bff667c9a8f0b8130c69112c3522fcd
Transactions (1)
Coinbaseb658ad6da5350d…c69112c3522fcd
1 in β†’ 1 out8.2600 XPM110 B
AJYpfu7n…NPybXapg
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.

1.083 Γ— 10⁹³(94-digit number)
10834959145214474377…83714283285634083040
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
1.083 Γ— 10⁹³(94-digit number)
10834959145214474377…83714283285634083039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.083 Γ— 10⁹³(94-digit number)
10834959145214474377…83714283285634083041
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
2.166 Γ— 10⁹³(94-digit number)
21669918290428948754…67428566571268166079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.166 Γ— 10⁹³(94-digit number)
21669918290428948754…67428566571268166081
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
4.333 Γ— 10⁹³(94-digit number)
43339836580857897509…34857133142536332159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.333 Γ— 10⁹³(94-digit number)
43339836580857897509…34857133142536332161
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
8.667 Γ— 10⁹³(94-digit number)
86679673161715795019…69714266285072664319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.667 Γ— 10⁹³(94-digit number)
86679673161715795019…69714266285072664321
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
1.733 Γ— 10⁹⁴(95-digit number)
17335934632343159003…39428532570145328639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.733 Γ— 10⁹⁴(95-digit number)
17335934632343159003…39428532570145328641
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
3.467 Γ— 10⁹⁴(95-digit number)
34671869264686318007…78857065140290657279
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 2556059

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 58fe638f41dabe7f916db1316f85967e4fa1837347724c044913a852c8f96ee3

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 #2,556,059 on Chainz β†—
Circulating Supply:58,000,268 XPMΒ·at block #6,844,483 Β· updates every 60s
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