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Home/Chain Registry/Block #2,642,698

Block #2,642,698

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2018, 8:07:58 PM Β· Difficulty 11.6610 Β· 4,199,135 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
edaf53f7a0e5d4693fa4e01da0836c18a4742bac4e8af8b34f3643543e7155a4
View on Chainz β†—

Difficulty

11.661016

Transactions

1

Size

200 B

Version

2

Bits

0ba9385e

Nonce

423,220,042

Timestamp

5/1/2018, 8:07:58 PM

Confirmations

4,199,135

Merkle Root

c6b941adb4b05495097d57f3a098f0f244977bc3898d9ff3ebcb2797d4949ed1
Transactions (1)
Coinbasec6b941adb4b054…cb2797d4949ed1
1 in β†’ 1 out7.3400 XPM110 B
AYQ8W5sw…SYKd96MK
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.

2.258 Γ— 10⁹⁡(96-digit number)
22584846351054834628…23384384725678521620
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
2.258 Γ— 10⁹⁡(96-digit number)
22584846351054834628…23384384725678521619
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.258 Γ— 10⁹⁡(96-digit number)
22584846351054834628…23384384725678521621
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
4.516 Γ— 10⁹⁡(96-digit number)
45169692702109669256…46768769451357043239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.516 Γ— 10⁹⁡(96-digit number)
45169692702109669256…46768769451357043241
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
9.033 Γ— 10⁹⁡(96-digit number)
90339385404219338512…93537538902714086479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.033 Γ— 10⁹⁡(96-digit number)
90339385404219338512…93537538902714086481
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
1.806 Γ— 10⁹⁢(97-digit number)
18067877080843867702…87075077805428172959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.806 Γ— 10⁹⁢(97-digit number)
18067877080843867702…87075077805428172961
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
3.613 Γ— 10⁹⁢(97-digit number)
36135754161687735405…74150155610856345919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.613 Γ— 10⁹⁢(97-digit number)
36135754161687735405…74150155610856345921
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
7.227 Γ— 10⁹⁢(97-digit number)
72271508323375470810…48300311221712691839
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 2642698

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 edaf53f7a0e5d4693fa4e01da0836c18a4742bac4e8af8b34f3643543e7155a4

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 #2,642,698 on Chainz β†—
Circulating Supply:57,979,037 XPMΒ·at block #6,841,832 Β· updates every 60s
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