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Block #2,851,519

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/23/2018, 4:28:00 AM Β· Difficulty 11.7260 Β· 3,981,818 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e3b025902a074a1754d97f823872b87f459e1323b089088906b4ba51228db14a
View on Chainz β†—

Difficulty

11.726016

Transactions

1

Size

198 B

Version

2

Bits

0bb9dc29

Nonce

1,332,783,527

Timestamp

9/23/2018, 4:28:00 AM

Confirmations

3,981,818

Merkle Root

d74fe0e053d6f6676513d04e757fadedcf7e7f5ce75dec58fa979a20394c0713
Transactions (1)
Coinbased74fe0e053d6f6…979a20394c0713
1 in β†’ 1 out7.2600 XPM109 B
AXqCgEPt…aQ2uFooC
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.

2.295 Γ— 10⁹³(94-digit number)
22956408702833786474…69873961232589913200
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
2.295 Γ— 10⁹³(94-digit number)
22956408702833786474…69873961232589913199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.295 Γ— 10⁹³(94-digit number)
22956408702833786474…69873961232589913201
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
4.591 Γ— 10⁹³(94-digit number)
45912817405667572948…39747922465179826399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.591 Γ— 10⁹³(94-digit number)
45912817405667572948…39747922465179826401
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
9.182 Γ— 10⁹³(94-digit number)
91825634811335145897…79495844930359652799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.182 Γ— 10⁹³(94-digit number)
91825634811335145897…79495844930359652801
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
1.836 Γ— 10⁹⁴(95-digit number)
18365126962267029179…58991689860719305599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.836 Γ— 10⁹⁴(95-digit number)
18365126962267029179…58991689860719305601
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
3.673 Γ— 10⁹⁴(95-digit number)
36730253924534058358…17983379721438611199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.673 Γ— 10⁹⁴(95-digit number)
36730253924534058358…17983379721438611201
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
7.346 Γ— 10⁹⁴(95-digit number)
73460507849068116717…35966759442877222399
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 2851519

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 e3b025902a074a1754d97f823872b87f459e1323b089088906b4ba51228db14a

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 #2,851,519 on Chainz β†—
Circulating Supply:57,910,891 XPMΒ·at block #6,833,336 Β· updates every 60s
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