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Block #679,579

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/16/2014, 1:46:28 AM Β· Difficulty 10.9631 Β· 6,132,822 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
886fb446f0a99057e2cf5a51345434bcca0ed09d7b51c3fecfe5cca53b6afef7
View on Chainz β†—

Height

#679,579

Difficulty

10.963103

Transactions

1

Size

207 B

Version

2

Bits

0af68de8

Nonce

408,808,125

Timestamp

8/16/2014, 1:46:28 AM

Confirmations

6,132,822

Merkle Root

d55f87381c6ecfce1319d0551bd86b2ac471b604d18fd119065cd18667c86c80
Transactions (1)
Coinbased55f87381c6ecf…5cd18667c86c80
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.

2.891 Γ— 10⁹⁢(97-digit number)
28919289710724044295…82810974644153802240
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
2.891 Γ— 10⁹⁢(97-digit number)
28919289710724044295…82810974644153802239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.891 Γ— 10⁹⁢(97-digit number)
28919289710724044295…82810974644153802241
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
5.783 Γ— 10⁹⁢(97-digit number)
57838579421448088591…65621949288307604479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.783 Γ— 10⁹⁢(97-digit number)
57838579421448088591…65621949288307604481
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
1.156 Γ— 10⁹⁷(98-digit number)
11567715884289617718…31243898576615208959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.156 Γ— 10⁹⁷(98-digit number)
11567715884289617718…31243898576615208961
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
2.313 Γ— 10⁹⁷(98-digit number)
23135431768579235436…62487797153230417919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.313 Γ— 10⁹⁷(98-digit number)
23135431768579235436…62487797153230417921
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
4.627 Γ— 10⁹⁷(98-digit number)
46270863537158470873…24975594306460835839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.627 Γ— 10⁹⁷(98-digit number)
46270863537158470873…24975594306460835841
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 679579

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 886fb446f0a99057e2cf5a51345434bcca0ed09d7b51c3fecfe5cca53b6afef7

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 #679,579 on Chainz β†—
Circulating Supply:57,743,234 XPMΒ·at block #6,812,400 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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