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Block #716,086

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/11/2014, 8:12:53 AM Β· Difficulty 10.9534 Β· 6,110,887 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d6f36b145495916ade1f2d081c09bb5416c1d72c297ef7b3479882ea116a0117
View on Chainz β†—

Height

#716,086

Difficulty

10.953369

Transactions

1

Size

207 B

Version

2

Bits

0af41001

Nonce

1,683,825,694

Timestamp

9/11/2014, 8:12:53 AM

Confirmations

6,110,887

Merkle Root

f005eea37c1741150071ba1d540499225599563ce7238ebb838cea59f733babe
Transactions (1)
Coinbasef005eea37c1741…8cea59f733babe
1 in β†’ 1 out8.3200 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.

2.863 Γ— 10⁹⁷(98-digit number)
28638209716668386436…52442161931526374400
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
2.863 Γ— 10⁹⁷(98-digit number)
28638209716668386436…52442161931526374399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.863 Γ— 10⁹⁷(98-digit number)
28638209716668386436…52442161931526374401
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
5.727 Γ— 10⁹⁷(98-digit number)
57276419433336772873…04884323863052748799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.727 Γ— 10⁹⁷(98-digit number)
57276419433336772873…04884323863052748801
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
1.145 Γ— 10⁹⁸(99-digit number)
11455283886667354574…09768647726105497599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.145 Γ— 10⁹⁸(99-digit number)
11455283886667354574…09768647726105497601
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
2.291 Γ— 10⁹⁸(99-digit number)
22910567773334709149…19537295452210995199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.291 Γ— 10⁹⁸(99-digit number)
22910567773334709149…19537295452210995201
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
4.582 Γ— 10⁹⁸(99-digit number)
45821135546669418298…39074590904421990399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.582 Γ— 10⁹⁸(99-digit number)
45821135546669418298…39074590904421990401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
9.164 Γ— 10⁹⁸(99-digit number)
91642271093338836597…78149181808843980799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 716086

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 d6f36b145495916ade1f2d081c09bb5416c1d72c297ef7b3479882ea116a0117

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 #716,086 on Chainz β†—
Circulating Supply:57,859,959 XPMΒ·at block #6,826,972 Β· updates every 60s
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