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Home/Chain Registry/Block #2,272,042

Block #2,272,042

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2017, 3:31:28 PM Β· Difficulty 10.9541 Β· 4,570,030 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cb07f686d48c7274985a2a38f461ed3f55291a4dc06c17cb478dc159b47d23fb
View on Chainz β†—

Difficulty

10.954079

Transactions

1

Size

201 B

Version

2

Bits

0af43e83

Nonce

1,972,846,664

Timestamp

8/28/2017, 3:31:28 PM

Confirmations

4,570,030

Merkle Root

defa4f89d758a999f8a17e96a4eeca78bf1506ba410bab9dec9c1a4b346a0c1c
Transactions (1)
Coinbasedefa4f89d758a9…9c1a4b346a0c1c
1 in β†’ 1 out8.3200 XPM110 B
AQE7dBdu…fbsPkiH5
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.

2.136 Γ— 10⁹⁷(98-digit number)
21366419443259099693…53484427516078899200
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
2.136 Γ— 10⁹⁷(98-digit number)
21366419443259099693…53484427516078899199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.136 Γ— 10⁹⁷(98-digit number)
21366419443259099693…53484427516078899201
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
4.273 Γ— 10⁹⁷(98-digit number)
42732838886518199386…06968855032157798399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.273 Γ— 10⁹⁷(98-digit number)
42732838886518199386…06968855032157798401
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
8.546 Γ— 10⁹⁷(98-digit number)
85465677773036398772…13937710064315596799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.546 Γ— 10⁹⁷(98-digit number)
85465677773036398772…13937710064315596801
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
1.709 Γ— 10⁹⁸(99-digit number)
17093135554607279754…27875420128631193599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.709 Γ— 10⁹⁸(99-digit number)
17093135554607279754…27875420128631193601
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
3.418 Γ— 10⁹⁸(99-digit number)
34186271109214559509…55750840257262387199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.418 Γ— 10⁹⁸(99-digit number)
34186271109214559509…55750840257262387201
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
6.837 Γ— 10⁹⁸(99-digit number)
68372542218429119018…11501680514524774399
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 2272042

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 cb07f686d48c7274985a2a38f461ed3f55291a4dc06c17cb478dc159b47d23fb

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 #2,272,042 on Chainz β†—
Circulating Supply:57,980,960 XPMΒ·at block #6,842,071 Β· updates every 60s
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