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Block #41,876

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 5:27:56 PM Β· Difficulty 8.5599 Β· 6,783,523 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3b29a22a2d33df763330b412b3d4b940a2044edee1024859a58b3e29bfc40b24
View on Chainz β†—

Height

#41,876

Difficulty

8.559902

Transactions

1

Size

196 B

Version

2

Bits

088f55c4

Nonce

173

Timestamp

7/14/2013, 5:27:56 PM

Confirmations

6,783,523

Merkle Root

0b50649d9e390f25724c765dd35bc9f2c373589e62395d64f527d91031a48a79
Transactions (1)
Coinbase0b50649d9e390f…27d91031a48a79
1 in β†’ 1 out13.6300 XPM109 B
APUHCRR1…V5wAzido
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.

2.070 Γ— 10⁸⁸(89-digit number)
20708073374014128328…15805602264498976710
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
2.070 Γ— 10⁸⁸(89-digit number)
20708073374014128328…15805602264498976709
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.070 Γ— 10⁸⁸(89-digit number)
20708073374014128328…15805602264498976711
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
4.141 Γ— 10⁸⁸(89-digit number)
41416146748028256656…31611204528997953419
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.141 Γ— 10⁸⁸(89-digit number)
41416146748028256656…31611204528997953421
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
8.283 Γ— 10⁸⁸(89-digit number)
82832293496056513312…63222409057995906839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.283 Γ— 10⁸⁸(89-digit number)
82832293496056513312…63222409057995906841
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
1.656 Γ— 10⁸⁹(90-digit number)
16566458699211302662…26444818115991813679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.656 Γ— 10⁸⁹(90-digit number)
16566458699211302662…26444818115991813681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8
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 41876

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 3b29a22a2d33df763330b412b3d4b940a2044edee1024859a58b3e29bfc40b24

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 #41,876 on Chainz β†—
Circulating Supply:57,847,292 XPMΒ·at block #6,825,398 Β· updates every 60s
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