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Home/Chain Registry/Block #2,679,142

Block #2,679,142

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/26/2018, 7:33:21 PM Β· Difficulty 11.6931 Β· 4,163,012 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8d14aea1ea7d9e5aa8df4c75537c9d378ba29fdd859e8b21d1b571fbf0fe89b9
View on Chainz β†—

Difficulty

11.693053

Transactions

1

Size

201 B

Version

2

Bits

0bb16bf3

Nonce

1,777,667,294

Timestamp

5/26/2018, 7:33:21 PM

Confirmations

4,163,012

Merkle Root

6a9443c2871071f19911b24cdc0a38770f52c95dce667136cc87f1c4640959ac
Transactions (1)
Coinbase6a9443c2871071…87f1c4640959ac
1 in β†’ 1 out7.3000 XPM110 B
Adqah8zh…1WwoHJ9t
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.

6.685 Γ— 10⁹⁷(98-digit number)
66851324599144950522…37982558354387435520
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
6.685 Γ— 10⁹⁷(98-digit number)
66851324599144950522…37982558354387435519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.685 Γ— 10⁹⁷(98-digit number)
66851324599144950522…37982558354387435521
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
1.337 Γ— 10⁹⁸(99-digit number)
13370264919828990104…75965116708774871039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.337 Γ— 10⁹⁸(99-digit number)
13370264919828990104…75965116708774871041
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
2.674 Γ— 10⁹⁸(99-digit number)
26740529839657980208…51930233417549742079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.674 Γ— 10⁹⁸(99-digit number)
26740529839657980208…51930233417549742081
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
5.348 Γ— 10⁹⁸(99-digit number)
53481059679315960417…03860466835099484159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.348 Γ— 10⁹⁸(99-digit number)
53481059679315960417…03860466835099484161
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
1.069 Γ— 10⁹⁹(100-digit number)
10696211935863192083…07720933670198968319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.069 Γ— 10⁹⁹(100-digit number)
10696211935863192083…07720933670198968321
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
2.139 Γ— 10⁹⁹(100-digit number)
21392423871726384167…15441867340397936639
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 2679142

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 8d14aea1ea7d9e5aa8df4c75537c9d378ba29fdd859e8b21d1b571fbf0fe89b9

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 #2,679,142 on Chainz β†—
Circulating Supply:57,981,622 XPMΒ·at block #6,842,153 Β· updates every 60s
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