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Block #855,931

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2014, 5:41:17 PM Β· Difficulty 10.9681 Β· 5,988,150 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5f159b52a01498f4ea5753c86edee3f903aef0bbd159639e0a1c075af0080330
View on Chainz β†—

Height

#855,931

Difficulty

10.968051

Transactions

1

Size

199 B

Version

2

Bits

0af7d236

Nonce

1,207,572,520

Timestamp

12/16/2014, 5:41:17 PM

Confirmations

5,988,150

Merkle Root

38d3d00b572d74b6163e2b56c6e705dcfa4efaae9143f957be1544ff240e7a5d
Transactions (1)
Coinbase38d3d00b572d74…1544ff240e7a5d
1 in β†’ 1 out8.3000 XPM109 B
AULY2pjc…ephkB2qi
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.

1.864 Γ— 10⁹⁴(95-digit number)
18649591491009033923…59792761142847551040
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
1.864 Γ— 10⁹⁴(95-digit number)
18649591491009033923…59792761142847551039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.864 Γ— 10⁹⁴(95-digit number)
18649591491009033923…59792761142847551041
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
3.729 Γ— 10⁹⁴(95-digit number)
37299182982018067846…19585522285695102079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.729 Γ— 10⁹⁴(95-digit number)
37299182982018067846…19585522285695102081
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
7.459 Γ— 10⁹⁴(95-digit number)
74598365964036135693…39171044571390204159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.459 Γ— 10⁹⁴(95-digit number)
74598365964036135693…39171044571390204161
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
1.491 Γ— 10⁹⁡(96-digit number)
14919673192807227138…78342089142780408319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.491 Γ— 10⁹⁡(96-digit number)
14919673192807227138…78342089142780408321
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
2.983 Γ— 10⁹⁡(96-digit number)
29839346385614454277…56684178285560816639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.983 Γ— 10⁹⁡(96-digit number)
29839346385614454277…56684178285560816641
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
5.967 Γ— 10⁹⁡(96-digit number)
59678692771228908554…13368356571121633279
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 855931

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 5f159b52a01498f4ea5753c86edee3f903aef0bbd159639e0a1c075af0080330

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 #855,931 on Chainz β†—
Circulating Supply:57,997,023 XPMΒ·at block #6,844,080 Β· updates every 60s
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