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Block #315,118

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2013, 8:38:04 AM Β· Difficulty 10.0850 Β· 6,516,544 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a0dafca6e0da819aa884d59888bb3f5741889755d77dc9c11ca05167bf710acd
View on Chainz β†—

Height

#315,118

Difficulty

10.084999

Transactions

1

Size

205 B

Version

2

Bits

0a15c279

Nonce

94,571

Timestamp

12/16/2013, 8:38:04 AM

Confirmations

6,516,544

Merkle Root

9a30ce7d7a69ee922cf008cbef62c82e97c32e79cb545489320a1275b54b2f9a
Transactions (1)
Coinbase9a30ce7d7a69ee…0a1275b54b2f9a
1 in β†’ 1 out9.8200 XPM116 B
AbwWkWZt…kawDhufa
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.

2.861 Γ— 10⁹³(94-digit number)
28611342850718296077…83414981078558083240
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
2.861 Γ— 10⁹³(94-digit number)
28611342850718296077…83414981078558083239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.861 Γ— 10⁹³(94-digit number)
28611342850718296077…83414981078558083241
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
5.722 Γ— 10⁹³(94-digit number)
57222685701436592155…66829962157116166479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.722 Γ— 10⁹³(94-digit number)
57222685701436592155…66829962157116166481
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
1.144 Γ— 10⁹⁴(95-digit number)
11444537140287318431…33659924314232332959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.144 Γ— 10⁹⁴(95-digit number)
11444537140287318431…33659924314232332961
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
2.288 Γ— 10⁹⁴(95-digit number)
22889074280574636862…67319848628464665919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.288 Γ— 10⁹⁴(95-digit number)
22889074280574636862…67319848628464665921
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
4.577 Γ— 10⁹⁴(95-digit number)
45778148561149273724…34639697256929331839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.577 Γ— 10⁹⁴(95-digit number)
45778148561149273724…34639697256929331841
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 315118

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 a0dafca6e0da819aa884d59888bb3f5741889755d77dc9c11ca05167bf710acd

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 #315,118 on Chainz β†—
Circulating Supply:57,897,403 XPMΒ·at block #6,831,661 Β· updates every 60s
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