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Block #44,658

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/15/2013, 12:19:34 AM Β· Difficulty 8.7251 Β· 6,750,802 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
011fe3427f388caf5333513e7f565b0dc2bcb94bf921c85d50fd84ff2d0b278f
View on Chainz β†—

Height

#44,658

Difficulty

8.725132

Transactions

2

Size

540 B

Version

2

Bits

08b9a23f

Nonce

154

Timestamp

7/15/2013, 12:19:34 AM

Confirmations

6,750,802

Merkle Root

28b876fbf48ebec489720934578a814e2b15a2fa38e8b26d832082425a469776
Transactions (2)
Coinbasecc0550d45c7d81…a360f80ed268c1
1 in β†’ 1 out13.1300 XPM110 B
ARXW9nxx…wWS3FZFj
397b477bc48de1…757bbed6fd0cb1
2 in β†’ 1 out29.2600 XPM339 B
AJ5JDkMB…S91bdMiR
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.

3.903 Γ— 10⁹⁢(97-digit number)
39039128463821323546…72575581919450952360
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
3.903 Γ— 10⁹⁢(97-digit number)
39039128463821323546…72575581919450952359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.903 Γ— 10⁹⁢(97-digit number)
39039128463821323546…72575581919450952361
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
7.807 Γ— 10⁹⁢(97-digit number)
78078256927642647092…45151163838901904719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.807 Γ— 10⁹⁢(97-digit number)
78078256927642647092…45151163838901904721
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
1.561 Γ— 10⁹⁷(98-digit number)
15615651385528529418…90302327677803809439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.561 Γ— 10⁹⁷(98-digit number)
15615651385528529418…90302327677803809441
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
3.123 Γ— 10⁹⁷(98-digit number)
31231302771057058837…80604655355607618879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.123 Γ— 10⁹⁷(98-digit number)
31231302771057058837…80604655355607618881
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 44658

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 011fe3427f388caf5333513e7f565b0dc2bcb94bf921c85d50fd84ff2d0b278f

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 #44,658 on Chainz β†—
Circulating Supply:57,607,738 XPMΒ·at block #6,795,459 Β· updates every 60s
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