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Block #74,909

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2013, 1:38:59 PM Β· Difficulty 8.9958 Β· 6,738,132 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c73de0256e2b1c9fc2ffb13dae4ca529b26baae1e4864d51229379d6390e527b
View on Chainz β†—

Height

#74,909

Difficulty

8.995797

Transactions

1

Size

205 B

Version

2

Bits

08feec89

Nonce

29

Timestamp

7/21/2013, 1:38:59 PM

Confirmations

6,738,132

Merkle Root

d245905c36795d0cb73a3f5a1f1d7b362a0e45e38c09f6e87386004dd46e08f4
Transactions (1)
Coinbased245905c36795d…86004dd46e08f4
1 in β†’ 1 out12.3400 XPM110 B
AHGPtSCN…GESamBFW
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.

1.047 Γ— 10¹⁰⁷(108-digit number)
10471491655162667244…79830425595708948370
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
1.047 Γ— 10¹⁰⁷(108-digit number)
10471491655162667244…79830425595708948369
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.047 Γ— 10¹⁰⁷(108-digit number)
10471491655162667244…79830425595708948371
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
2.094 Γ— 10¹⁰⁷(108-digit number)
20942983310325334488…59660851191417896739
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.094 Γ— 10¹⁰⁷(108-digit number)
20942983310325334488…59660851191417896741
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
4.188 Γ— 10¹⁰⁷(108-digit number)
41885966620650668976…19321702382835793479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.188 Γ— 10¹⁰⁷(108-digit number)
41885966620650668976…19321702382835793481
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
8.377 Γ— 10¹⁰⁷(108-digit number)
83771933241301337953…38643404765671586959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.377 Γ— 10¹⁰⁷(108-digit number)
83771933241301337953…38643404765671586961
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
1.675 Γ— 10¹⁰⁸(109-digit number)
16754386648260267590…77286809531343173919
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9
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 74909

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 c73de0256e2b1c9fc2ffb13dae4ca529b26baae1e4864d51229379d6390e527b

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 #74,909 on Chainz β†—
Circulating Supply:57,748,372 XPMΒ·at block #6,813,040 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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