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Block #665,537

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/6/2014, 1:34:00 PM Β· Difficulty 10.9600 Β· 6,159,043 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fcf422b4195fac29add3d64a6f7915b450f33f137ec2488d2388bf7134fdc4e7
View on Chainz β†—

Height

#665,537

Difficulty

10.959961

Transactions

1

Size

207 B

Version

2

Bits

0af5c002

Nonce

1,180,570,010

Timestamp

8/6/2014, 1:34:00 PM

Confirmations

6,159,043

Merkle Root

5199cd0f0b8666723408e4814f85a59edbb9827178b7ca040368807b8bfd313b
Transactions (1)
Coinbase5199cd0f0b8666…68807b8bfd313b
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.

6.059 Γ— 10⁹⁢(97-digit number)
60596158398343546467…07400699694484651200
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
6.059 Γ— 10⁹⁢(97-digit number)
60596158398343546467…07400699694484651199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.059 Γ— 10⁹⁢(97-digit number)
60596158398343546467…07400699694484651201
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
1.211 Γ— 10⁹⁷(98-digit number)
12119231679668709293…14801399388969302399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.211 Γ— 10⁹⁷(98-digit number)
12119231679668709293…14801399388969302401
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
2.423 Γ— 10⁹⁷(98-digit number)
24238463359337418586…29602798777938604799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.423 Γ— 10⁹⁷(98-digit number)
24238463359337418586…29602798777938604801
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
4.847 Γ— 10⁹⁷(98-digit number)
48476926718674837173…59205597555877209599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.847 Γ— 10⁹⁷(98-digit number)
48476926718674837173…59205597555877209601
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
9.695 Γ— 10⁹⁷(98-digit number)
96953853437349674347…18411195111754419199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.695 Γ— 10⁹⁷(98-digit number)
96953853437349674347…18411195111754419201
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 665537

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 fcf422b4195fac29add3d64a6f7915b450f33f137ec2488d2388bf7134fdc4e7

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 #665,537 on Chainz β†—
Circulating Supply:57,840,707 XPMΒ·at block #6,824,579 Β· updates every 60s
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