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Block #118,218

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/15/2013, 3:04:55 PM Β· Difficulty 9.7506 Β· 6,696,328 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
15a47835336097c0fdb774eec03a5f0e79b93f93760dace90f84442fce2e37c1
View on Chainz β†—

Height

#118,218

Difficulty

9.750577

Transactions

1

Size

200 B

Version

2

Bits

09c025d5

Nonce

69,548

Timestamp

8/15/2013, 3:04:55 PM

Confirmations

6,696,328

Merkle Root

08e4554e8382d4f4150f38ce434c8e248f8751bb8ad29f96f3ea117eaed1187d
Transactions (1)
Coinbase08e4554e8382d4…ea117eaed1187d
1 in β†’ 1 out10.5000 XPM109 B
AeEXQxqG…J2q5dxWc
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.

9.318 Γ— 10⁹⁢(97-digit number)
93188761192496648957…32264775444008583680
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
9.318 Γ— 10⁹⁢(97-digit number)
93188761192496648957…32264775444008583679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.318 Γ— 10⁹⁢(97-digit number)
93188761192496648957…32264775444008583681
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
1.863 Γ— 10⁹⁷(98-digit number)
18637752238499329791…64529550888017167359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.863 Γ— 10⁹⁷(98-digit number)
18637752238499329791…64529550888017167361
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
3.727 Γ— 10⁹⁷(98-digit number)
37275504476998659582…29059101776034334719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.727 Γ— 10⁹⁷(98-digit number)
37275504476998659582…29059101776034334721
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
7.455 Γ— 10⁹⁷(98-digit number)
74551008953997319165…58118203552068669439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.455 Γ— 10⁹⁷(98-digit number)
74551008953997319165…58118203552068669441
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
1.491 Γ— 10⁹⁸(99-digit number)
14910201790799463833…16236407104137338879
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 118218

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 15a47835336097c0fdb774eec03a5f0e79b93f93760dace90f84442fce2e37c1

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 #118,218 on Chainz β†—
Circulating Supply:57,760,440 XPMΒ·at block #6,814,545 Β· updates every 60s
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