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Home/Chain Registry/Block #2,849,507

Block #2,849,507

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/21/2018, 5:19:00 PM Β· Difficulty 11.7312 Β· 3,983,491 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1d4568a5879bdc47910f69269c74dceeda5dc89e65d0e5305b5ac2f19d5e1fec
View on Chainz β†—

Difficulty

11.731217

Transactions

1

Size

200 B

Version

2

Bits

0bbb310d

Nonce

1,950,917,236

Timestamp

9/21/2018, 5:19:00 PM

Confirmations

3,983,491

Merkle Root

15cb713b0f0bb57a8ddf5816c00058323d0b82f40e4fb5c867c35f3747c3d74d
Transactions (1)
Coinbase15cb713b0f0bb5…c35f3747c3d74d
1 in β†’ 1 out7.2500 XPM109 B
AeRVJzRC…Cnqiy1WW
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.

2.830 Γ— 10⁹⁢(97-digit number)
28308602782436732203…43940277024926689280
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
2.830 Γ— 10⁹⁢(97-digit number)
28308602782436732203…43940277024926689279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.830 Γ— 10⁹⁢(97-digit number)
28308602782436732203…43940277024926689281
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
5.661 Γ— 10⁹⁢(97-digit number)
56617205564873464406…87880554049853378559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.661 Γ— 10⁹⁢(97-digit number)
56617205564873464406…87880554049853378561
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
1.132 Γ— 10⁹⁷(98-digit number)
11323441112974692881…75761108099706757119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.132 Γ— 10⁹⁷(98-digit number)
11323441112974692881…75761108099706757121
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
2.264 Γ— 10⁹⁷(98-digit number)
22646882225949385762…51522216199413514239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.264 Γ— 10⁹⁷(98-digit number)
22646882225949385762…51522216199413514241
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
4.529 Γ— 10⁹⁷(98-digit number)
45293764451898771525…03044432398827028479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.529 Γ— 10⁹⁷(98-digit number)
45293764451898771525…03044432398827028481
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
9.058 Γ— 10⁹⁷(98-digit number)
90587528903797543050…06088864797654056959
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 2849507

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 1d4568a5879bdc47910f69269c74dceeda5dc89e65d0e5305b5ac2f19d5e1fec

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 #2,849,507 on Chainz β†—
Circulating Supply:57,908,156 XPMΒ·at block #6,832,997 Β· updates every 60s
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