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Home/Chain Registry/Block #2,859,007

Block #2,859,007

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/28/2018, 10:49:18 PM Β· Difficulty 11.6783 Β· 3,947,563 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
005689c87ee9b475b2a7e3424f23643e4772b25d03138771976cc3b00a18f26b
View on Chainz β†—

Difficulty

11.678340

Transactions

1

Size

199 B

Version

2

Bits

0bada7b4

Nonce

1,137,075,245

Timestamp

9/28/2018, 10:49:18 PM

Confirmations

3,947,563

Merkle Root

9d4e735f478e090c629d38803723281511f279e11210d8a8769b239dbccf82e4
Transactions (1)
Coinbase9d4e735f478e09…9b239dbccf82e4
1 in β†’ 1 out7.3200 XPM110 B
AWZ3upbX…fjUwEnjm
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.

8.115 Γ— 10⁹¹(92-digit number)
81158491418319788076…74882880140341572640
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
8.115 Γ— 10⁹¹(92-digit number)
81158491418319788076…74882880140341572639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.115 Γ— 10⁹¹(92-digit number)
81158491418319788076…74882880140341572641
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
1.623 Γ— 10⁹²(93-digit number)
16231698283663957615…49765760280683145279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.623 Γ— 10⁹²(93-digit number)
16231698283663957615…49765760280683145281
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
3.246 Γ— 10⁹²(93-digit number)
32463396567327915230…99531520561366290559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.246 Γ— 10⁹²(93-digit number)
32463396567327915230…99531520561366290561
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
6.492 Γ— 10⁹²(93-digit number)
64926793134655830461…99063041122732581119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.492 Γ— 10⁹²(93-digit number)
64926793134655830461…99063041122732581121
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
1.298 Γ— 10⁹³(94-digit number)
12985358626931166092…98126082245465162239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.298 Γ— 10⁹³(94-digit number)
12985358626931166092…98126082245465162241
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
2.597 Γ— 10⁹³(94-digit number)
25970717253862332184…96252164490930324479
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 2859007

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 005689c87ee9b475b2a7e3424f23643e4772b25d03138771976cc3b00a18f26b

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 #2,859,007 on Chainz β†—
Circulating Supply:57,696,657 XPMΒ·at block #6,806,569 Β· updates every 60s
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