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Block #117,641

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/15/2013, 5:03:16 AM Β· Difficulty 9.7518 Β· 6,677,845 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3a64cad63f2bc42fbdb00f658172f4bcbb2b2d5f38dd95abfc8cab7bf719d70a
View on Chainz β†—

Height

#117,641

Difficulty

9.751758

Transactions

1

Size

203 B

Version

2

Bits

09c0733e

Nonce

2,570,285

Timestamp

8/15/2013, 5:03:16 AM

Confirmations

6,677,845

Merkle Root

629fe7ea0695dc48b94f8d846d31d29a0bb88482e807c6a7c24f81d4f1ff8eac
Transactions (1)
Coinbase629fe7ea0695dc…4f81d4f1ff8eac
1 in β†’ 1 out10.5000 XPM112 B
AT5A2KL6…CT16n6i2
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.

1.998 Γ— 10⁹⁸(99-digit number)
19988277697959055666…01339036021216964530
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
1.998 Γ— 10⁹⁸(99-digit number)
19988277697959055666…01339036021216964529
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.998 Γ— 10⁹⁸(99-digit number)
19988277697959055666…01339036021216964531
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
3.997 Γ— 10⁹⁸(99-digit number)
39976555395918111332…02678072042433929059
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.997 Γ— 10⁹⁸(99-digit number)
39976555395918111332…02678072042433929061
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
7.995 Γ— 10⁹⁸(99-digit number)
79953110791836222664…05356144084867858119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.995 Γ— 10⁹⁸(99-digit number)
79953110791836222664…05356144084867858121
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
1.599 Γ— 10⁹⁹(100-digit number)
15990622158367244532…10712288169735716239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.599 Γ— 10⁹⁹(100-digit number)
15990622158367244532…10712288169735716241
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
3.198 Γ— 10⁹⁹(100-digit number)
31981244316734489065…21424576339471432479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.198 Γ— 10⁹⁹(100-digit number)
31981244316734489065…21424576339471432481
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 117641

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 3a64cad63f2bc42fbdb00f658172f4bcbb2b2d5f38dd95abfc8cab7bf719d70a

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 #117,641 on Chainz β†—
Circulating Supply:57,607,950 XPMΒ·at block #6,795,485 Β· updates every 60s
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