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Home/Chain Registry/Block #2,159,787

Block #2,159,787

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/14/2017, 2:35:35 AM Β· Difficulty 10.9027 Β· 4,681,726 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
abb728c979956696eb7fa6042ed053abcfe3cfcc520f1988e5bcc7bee5be503c
View on Chainz β†—

Difficulty

10.902676

Transactions

1

Size

198 B

Version

2

Bits

0ae715c9

Nonce

349,304,663

Timestamp

6/14/2017, 2:35:35 AM

Confirmations

4,681,726

Merkle Root

ab3ec537ad5464d9d9bc4eef372d3211322143c409d080f63d7b05c5fbc5cb91
Transactions (1)
Coinbaseab3ec537ad5464…7b05c5fbc5cb91
1 in β†’ 1 out8.4000 XPM109 B
AREkVWmV…ZRMxXFDW
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.

4.528 Γ— 10⁹¹(92-digit number)
45285149103117248968…26032257144891725260
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
4.528 Γ— 10⁹¹(92-digit number)
45285149103117248968…26032257144891725259
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.528 Γ— 10⁹¹(92-digit number)
45285149103117248968…26032257144891725261
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
9.057 Γ— 10⁹¹(92-digit number)
90570298206234497937…52064514289783450519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.057 Γ— 10⁹¹(92-digit number)
90570298206234497937…52064514289783450521
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
1.811 Γ— 10⁹²(93-digit number)
18114059641246899587…04129028579566901039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.811 Γ— 10⁹²(93-digit number)
18114059641246899587…04129028579566901041
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
3.622 Γ— 10⁹²(93-digit number)
36228119282493799175…08258057159133802079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.622 Γ— 10⁹²(93-digit number)
36228119282493799175…08258057159133802081
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
7.245 Γ— 10⁹²(93-digit number)
72456238564987598350…16516114318267604159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.245 Γ— 10⁹²(93-digit number)
72456238564987598350…16516114318267604161
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
1.449 Γ— 10⁹³(94-digit number)
14491247712997519670…33032228636535208319
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 2159787

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 abb728c979956696eb7fa6042ed053abcfe3cfcc520f1988e5bcc7bee5be503c

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 #2,159,787 on Chainz β†—
Circulating Supply:57,976,484 XPMΒ·at block #6,841,512 Β· updates every 60s
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