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Block #94,875

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/3/2013, 8:59:52 AM Β· Difficulty 9.2100 Β· 6,731,285 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2ea175cac1d3b10380efc3b78218883fbb443133025ca2d9e6755cc98b316478
View on Chainz β†—

Height

#94,875

Difficulty

9.210026

Transactions

1

Size

200 B

Version

2

Bits

0935c43f

Nonce

118,761

Timestamp

8/3/2013, 8:59:52 AM

Confirmations

6,731,285

Merkle Root

e0eb78f61bd1a5d9ff7f1c17a17f9294f8c70d98cd6a3ede5a0c2738ca532b1b
Transactions (1)
Coinbasee0eb78f61bd1a5…0c2738ca532b1b
1 in β†’ 1 out11.7700 XPM109 B
APs5EWFs…Wbyy5LtD
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.

2.901 Γ— 10⁹⁢(97-digit number)
29016112354578955254…18236862505021503660
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
2.901 Γ— 10⁹⁢(97-digit number)
29016112354578955254…18236862505021503659
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.901 Γ— 10⁹⁢(97-digit number)
29016112354578955254…18236862505021503661
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
5.803 Γ— 10⁹⁢(97-digit number)
58032224709157910508…36473725010043007319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.803 Γ— 10⁹⁢(97-digit number)
58032224709157910508…36473725010043007321
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
1.160 Γ— 10⁹⁷(98-digit number)
11606444941831582101…72947450020086014639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.160 Γ— 10⁹⁷(98-digit number)
11606444941831582101…72947450020086014641
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
2.321 Γ— 10⁹⁷(98-digit number)
23212889883663164203…45894900040172029279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.321 Γ— 10⁹⁷(98-digit number)
23212889883663164203…45894900040172029281
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
4.642 Γ— 10⁹⁷(98-digit number)
46425779767326328406…91789800080344058559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.642 Γ— 10⁹⁷(98-digit number)
46425779767326328406…91789800080344058561
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 94875

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 2ea175cac1d3b10380efc3b78218883fbb443133025ca2d9e6755cc98b316478

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 #94,875 on Chainz β†—
Circulating Supply:57,853,407 XPMΒ·at block #6,826,159 Β· updates every 60s
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