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Block #984,635

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/21/2015, 7:40:11 PM Β· Difficulty 10.8475 Β· 5,841,468 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d3821be443272de8d98722057c4c4279555e4d27d9ec195b497d4f46c0df12ee
View on Chainz β†—

Height

#984,635

Difficulty

10.847457

Transactions

1

Size

207 B

Version

2

Bits

0ad8f2f4

Nonce

2,670,025,491

Timestamp

3/21/2015, 7:40:11 PM

Confirmations

5,841,468

Merkle Root

d7f78369452cb4e8864395b29d7fa82fbc478b59a03f5287cb9753c3a47d5a74
Transactions (1)
Coinbased7f78369452cb4…9753c3a47d5a74
1 in β†’ 1 out8.4900 XPM116 B
ANSXnLY2…Sd25TjkD
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.

2.291 Γ— 10⁹⁢(97-digit number)
22917226648963445941…78819170851065274560
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
2.291 Γ— 10⁹⁢(97-digit number)
22917226648963445941…78819170851065274559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.291 Γ— 10⁹⁢(97-digit number)
22917226648963445941…78819170851065274561
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
4.583 Γ— 10⁹⁢(97-digit number)
45834453297926891882…57638341702130549119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.583 Γ— 10⁹⁢(97-digit number)
45834453297926891882…57638341702130549121
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
9.166 Γ— 10⁹⁢(97-digit number)
91668906595853783764…15276683404261098239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.166 Γ— 10⁹⁢(97-digit number)
91668906595853783764…15276683404261098241
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
1.833 Γ— 10⁹⁷(98-digit number)
18333781319170756752…30553366808522196479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.833 Γ— 10⁹⁷(98-digit number)
18333781319170756752…30553366808522196481
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
3.666 Γ— 10⁹⁷(98-digit number)
36667562638341513505…61106733617044392959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.666 Γ— 10⁹⁷(98-digit number)
36667562638341513505…61106733617044392961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 984635

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 d3821be443272de8d98722057c4c4279555e4d27d9ec195b497d4f46c0df12ee

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 #984,635 on Chainz β†—
Circulating Supply:57,852,947 XPMΒ·at block #6,826,102 Β· updates every 60s
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