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Block #667,477

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2014, 4:09:58 PM Β· Difficulty 10.9626 Β· 6,146,558 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1aa4eded5ab1db7cf13a7423cb5ddc91d33bc5465c446df7117f1fa90be0b88a
View on Chainz β†—

Height

#667,477

Difficulty

10.962648

Transactions

1

Size

208 B

Version

2

Bits

0af6701b

Nonce

276,653,877

Timestamp

8/7/2014, 4:09:58 PM

Confirmations

6,146,558

Merkle Root

35c461dfcf48baa293617063a5724bb87d9cf5b08f606bf9dddee6846597afb4
Transactions (1)
Coinbase35c461dfcf48ba…dee6846597afb4
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.504 Γ— 10¹⁰⁰(101-digit number)
15042957541353513679…25784033496609280000
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
1.504 Γ— 10¹⁰⁰(101-digit number)
15042957541353513679…25784033496609279999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.504 Γ— 10¹⁰⁰(101-digit number)
15042957541353513679…25784033496609280001
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
3.008 Γ— 10¹⁰⁰(101-digit number)
30085915082707027358…51568066993218559999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.008 Γ— 10¹⁰⁰(101-digit number)
30085915082707027358…51568066993218560001
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
6.017 Γ— 10¹⁰⁰(101-digit number)
60171830165414054716…03136133986437119999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.017 Γ— 10¹⁰⁰(101-digit number)
60171830165414054716…03136133986437120001
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
1.203 Γ— 10¹⁰¹(102-digit number)
12034366033082810943…06272267972874239999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.203 Γ— 10¹⁰¹(102-digit number)
12034366033082810943…06272267972874240001
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
2.406 Γ— 10¹⁰¹(102-digit number)
24068732066165621886…12544535945748479999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.406 Γ— 10¹⁰¹(102-digit number)
24068732066165621886…12544535945748480001
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 667477

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 1aa4eded5ab1db7cf13a7423cb5ddc91d33bc5465c446df7117f1fa90be0b88a

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 #667,477 on Chainz β†—
Circulating Supply:57,756,355 XPMΒ·at block #6,814,034 Β· updates every 60s
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