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Block #44,807

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/15/2013, 12:47:12 AM Β· Difficulty 8.7316 Β· 6,767,984 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3ee42ac0889dbe345cf50f1d2052ce9d0f98da27d089107af4528ad5c5ec124c
View on Chainz β†—

Height

#44,807

Difficulty

8.731635

Transactions

1

Size

199 B

Version

2

Bits

08bb4c68

Nonce

1,011

Timestamp

7/15/2013, 12:47:12 AM

Confirmations

6,767,984

Merkle Root

27f9a51d700cd56a0aff19a66e285f88c837c17b4225c674aebb209e3a685890
Transactions (1)
Coinbase27f9a51d700cd5…bb209e3a685890
1 in β†’ 1 out13.1000 XPM110 B
AWeEPkwu…2eMpSWHE
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.

7.857 Γ— 10⁹¹(92-digit number)
78578249278129324003…10981695274143650520
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
7.857 Γ— 10⁹¹(92-digit number)
78578249278129324003…10981695274143650519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.857 Γ— 10⁹¹(92-digit number)
78578249278129324003…10981695274143650521
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
1.571 Γ— 10⁹²(93-digit number)
15715649855625864800…21963390548287301039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.571 Γ— 10⁹²(93-digit number)
15715649855625864800…21963390548287301041
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
3.143 Γ— 10⁹²(93-digit number)
31431299711251729601…43926781096574602079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.143 Γ— 10⁹²(93-digit number)
31431299711251729601…43926781096574602081
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
6.286 Γ— 10⁹²(93-digit number)
62862599422503459203…87853562193149204159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.286 Γ— 10⁹²(93-digit number)
62862599422503459203…87853562193149204161
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 44807

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 3ee42ac0889dbe345cf50f1d2052ce9d0f98da27d089107af4528ad5c5ec124c

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 #44,807 on Chainz β†—
Circulating Supply:57,746,370 XPMΒ·at block #6,812,790 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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