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Home/Chain Registry/Block #1,565,107

Block #1,565,107

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/30/2016, 1:07:29 AM Β· Difficulty 10.7516 Β· 5,280,085 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
198c1737fb6a3ca55e16307a178ffdfa2de145a2088a29b07b2382dc3bfe0117
View on Chainz β†—

Difficulty

10.751644

Transactions

1

Size

201 B

Version

2

Bits

0ac06bbc

Nonce

336,495,567

Timestamp

4/30/2016, 1:07:29 AM

Confirmations

5,280,085

Merkle Root

3e882098ebdbd88d0ac913120f1d3aeb1b2599b4bec762b4a5457fffd68ed70a
Transactions (1)
Coinbase3e882098ebdbd8…457fffd68ed70a
1 in β†’ 1 out8.6400 XPM110 B
AcWmL3Vw…47vKopYL
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.

2.876 Γ— 10⁹⁷(98-digit number)
28767806726003547383…16217664959870566400
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
2.876 Γ— 10⁹⁷(98-digit number)
28767806726003547383…16217664959870566399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.876 Γ— 10⁹⁷(98-digit number)
28767806726003547383…16217664959870566401
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
5.753 Γ— 10⁹⁷(98-digit number)
57535613452007094766…32435329919741132799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.753 Γ— 10⁹⁷(98-digit number)
57535613452007094766…32435329919741132801
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
1.150 Γ— 10⁹⁸(99-digit number)
11507122690401418953…64870659839482265599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.150 Γ— 10⁹⁸(99-digit number)
11507122690401418953…64870659839482265601
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
2.301 Γ— 10⁹⁸(99-digit number)
23014245380802837906…29741319678964531199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.301 Γ— 10⁹⁸(99-digit number)
23014245380802837906…29741319678964531201
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
4.602 Γ— 10⁹⁸(99-digit number)
46028490761605675812…59482639357929062399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.602 Γ— 10⁹⁸(99-digit number)
46028490761605675812…59482639357929062401
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 1565107

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 198c1737fb6a3ca55e16307a178ffdfa2de145a2088a29b07b2382dc3bfe0117

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 #1,565,107 on Chainz β†—
Circulating Supply:58,005,967 XPMΒ·at block #6,845,191 Β· updates every 60s
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