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Home/Chain Registry/Block #3,476,723

Block #3,476,723

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/15/2019, 9:25:46 AM Β· Difficulty 10.9791 Β· 3,349,906 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
89c1ead4e34c88afbf5fb64c00921233548bf7dc67964acd6183d6940539bb73
View on Chainz β†—

Difficulty

10.979103

Transactions

1

Size

200 B

Version

2

Bits

0afaa682

Nonce

310,333,056

Timestamp

12/15/2019, 9:25:46 AM

Confirmations

3,349,906

Merkle Root

c68a33ceeeef3576a3e953e7952638fce1a0d7fa46f71515f718b5c34069c540
Transactions (1)
Coinbasec68a33ceeeef35…18b5c34069c540
1 in β†’ 1 out8.2800 XPM110 B
ASiq2qtK…VMhmk7yL
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.

8.945 Γ— 10⁹⁴(95-digit number)
89452335457208986930…15355922961231959440
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
8.945 Γ— 10⁹⁴(95-digit number)
89452335457208986930…15355922961231959439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.945 Γ— 10⁹⁴(95-digit number)
89452335457208986930…15355922961231959441
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
1.789 Γ— 10⁹⁡(96-digit number)
17890467091441797386…30711845922463918879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.789 Γ— 10⁹⁡(96-digit number)
17890467091441797386…30711845922463918881
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
3.578 Γ— 10⁹⁡(96-digit number)
35780934182883594772…61423691844927837759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.578 Γ— 10⁹⁡(96-digit number)
35780934182883594772…61423691844927837761
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
7.156 Γ— 10⁹⁡(96-digit number)
71561868365767189544…22847383689855675519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.156 Γ— 10⁹⁡(96-digit number)
71561868365767189544…22847383689855675521
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
1.431 Γ— 10⁹⁢(97-digit number)
14312373673153437908…45694767379711351039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.431 Γ— 10⁹⁢(97-digit number)
14312373673153437908…45694767379711351041
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
2.862 Γ— 10⁹⁢(97-digit number)
28624747346306875817…91389534759422702079
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 3476723

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 89c1ead4e34c88afbf5fb64c00921233548bf7dc67964acd6183d6940539bb73

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 #3,476,723 on Chainz β†—
Circulating Supply:57,857,177 XPMΒ·at block #6,826,628 Β· updates every 60s
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