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Block #679,206

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/15/2014, 7:18:23 PM Β· Difficulty 10.9632 Β· 6,121,846 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
053c4bb855b9f989f443545263da425f2fc8b1324baad52f599fc5229da17b37
View on Chainz β†—

Height

#679,206

Difficulty

10.963203

Transactions

2

Size

580 B

Version

2

Bits

0af6947f

Nonce

35,545,724

Timestamp

8/15/2014, 7:18:23 PM

Confirmations

6,121,846

Merkle Root

14963988729d04c4b8667cc22a171cefc9902f4e9aad41c67a127692ccf3e0b6
Transactions (2)
Coinbase44582382a70d41…bcce1ff04a606c
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
968686eb1ca9c1…d9da1e0d2ea7b3
2 in β†’ 2 out352.1717 XPM374 B
AQUC7Hue…LL2XMoNYAKmtPSzf…av7oDjkx
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.

1.287 Γ— 10⁹⁡(96-digit number)
12875554638831759562…96077579665392810850
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
1.287 Γ— 10⁹⁡(96-digit number)
12875554638831759562…96077579665392810849
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.287 Γ— 10⁹⁡(96-digit number)
12875554638831759562…96077579665392810851
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
2.575 Γ— 10⁹⁡(96-digit number)
25751109277663519125…92155159330785621699
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.575 Γ— 10⁹⁡(96-digit number)
25751109277663519125…92155159330785621701
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
5.150 Γ— 10⁹⁡(96-digit number)
51502218555327038251…84310318661571243399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.150 Γ— 10⁹⁡(96-digit number)
51502218555327038251…84310318661571243401
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
1.030 Γ— 10⁹⁢(97-digit number)
10300443711065407650…68620637323142486799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.030 Γ— 10⁹⁢(97-digit number)
10300443711065407650…68620637323142486801
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
2.060 Γ— 10⁹⁢(97-digit number)
20600887422130815300…37241274646284973599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.060 Γ— 10⁹⁢(97-digit number)
20600887422130815300…37241274646284973601
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 679206

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 053c4bb855b9f989f443545263da425f2fc8b1324baad52f599fc5229da17b37

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 #679,206 on Chainz β†—
Circulating Supply:57,652,482 XPMΒ·at block #6,801,051 Β· updates every 60s
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