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Block #2,045,987

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/31/2017, 2:07:28 AM Β· Difficulty 10.6833 Β· 4,797,009 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fcc07a0252f978d08f6e93c00bb451ee7c661c64ca22acd60199a89a7fc9f448
View on Chainz β†—

Height

#2,045,987

Difficulty

10.683272

Transactions

1

Size

200 B

Version

2

Bits

0aaeeae9

Nonce

1,366,258,508

Timestamp

3/31/2017, 2:07:28 AM

Confirmations

4,797,009

Mined by

⛏️ P2SHAaFyrFRVC2e9LGMK1v83bVhatrZPT62wku

Merkle Root

1d608f0d45fe0e684dec5f8975e2f1bf860769389ff9c7858b46351ac9c03a5c
Transactions (1)
Coinbase1d608f0d45fe0e…46351ac9c03a5c
1 in β†’ 1 out8.7500 XPM109 B
AaFyrFRV…ZPT62wku
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.

2.671 Γ— 10⁹⁷(98-digit number)
26717154509930479510…48716259546873651199
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
2.671 Γ— 10⁹⁷(98-digit number)
26717154509930479510…48716259546873651199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.671 Γ— 10⁹⁷(98-digit number)
26717154509930479510…48716259546873651201
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
5.343 Γ— 10⁹⁷(98-digit number)
53434309019860959021…97432519093747302399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.343 Γ— 10⁹⁷(98-digit number)
53434309019860959021…97432519093747302401
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
1.068 Γ— 10⁹⁸(99-digit number)
10686861803972191804…94865038187494604799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.068 Γ— 10⁹⁸(99-digit number)
10686861803972191804…94865038187494604801
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
2.137 Γ— 10⁹⁸(99-digit number)
21373723607944383608…89730076374989209599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.137 Γ— 10⁹⁸(99-digit number)
21373723607944383608…89730076374989209601
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
4.274 Γ— 10⁹⁸(99-digit number)
42747447215888767217…79460152749978419199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.274 Γ— 10⁹⁸(99-digit number)
42747447215888767217…79460152749978419201
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.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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
Cross-reference on Chainz Explorer
Circulating Supply:57,988,323 XPMΒ·at block #6,842,995 Β· updates every 60s
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