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Home/Chain Registry/Block #3,002,677

Block #3,002,677

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/9/2019, 10:34:40 PM Β· Difficulty 11.2017 Β· 3,837,952 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4b6c9ada998008f14d9eba71e5194dbd3b7232c9aff499616e4841e164193e8e
View on Chainz β†—

Difficulty

11.201731

Transactions

1

Size

201 B

Version

2

Bits

0b33a4ac

Nonce

406,548,677

Timestamp

1/9/2019, 10:34:40 PM

Confirmations

3,837,952

Merkle Root

cb8e1cf68ea553906f965372ac5cffd7352cc6f78f742a00aee556db2c7671b1
Transactions (1)
Coinbasecb8e1cf68ea553…e556db2c7671b1
1 in β†’ 1 out7.9600 XPM110 B
AUMQRepm…tAfKmdW1
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.

1.094 Γ— 10⁹⁢(97-digit number)
10947549871201494491…20397132258758438400
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
1.094 Γ— 10⁹⁢(97-digit number)
10947549871201494491…20397132258758438399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.094 Γ— 10⁹⁢(97-digit number)
10947549871201494491…20397132258758438401
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
2.189 Γ— 10⁹⁢(97-digit number)
21895099742402988982…40794264517516876799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.189 Γ— 10⁹⁢(97-digit number)
21895099742402988982…40794264517516876801
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
4.379 Γ— 10⁹⁢(97-digit number)
43790199484805977965…81588529035033753599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.379 Γ— 10⁹⁢(97-digit number)
43790199484805977965…81588529035033753601
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
8.758 Γ— 10⁹⁢(97-digit number)
87580398969611955930…63177058070067507199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.758 Γ— 10⁹⁢(97-digit number)
87580398969611955930…63177058070067507201
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
1.751 Γ— 10⁹⁷(98-digit number)
17516079793922391186…26354116140135014399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.751 Γ— 10⁹⁷(98-digit number)
17516079793922391186…26354116140135014401
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
3.503 Γ— 10⁹⁷(98-digit number)
35032159587844782372…52708232280270028799
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 3002677

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 4b6c9ada998008f14d9eba71e5194dbd3b7232c9aff499616e4841e164193e8e

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 #3,002,677 on Chainz β†—
Circulating Supply:57,969,372 XPMΒ·at block #6,840,628 Β· updates every 60s
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