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Block #2,047,645

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/1/2017, 4:49:16 AM Β· Difficulty 10.6875 Β· 4,794,589 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dada797a40b29db332f1c076cf3cd19f57bd8e572bf22dec65b07404f7bb32da
View on Chainz β†—

Height

#2,047,645

Difficulty

10.687495

Transactions

1

Size

199 B

Version

2

Bits

0aafffb0

Nonce

1,845,228,117

Timestamp

4/1/2017, 4:49:16 AM

Confirmations

4,794,589

Mined by

⛏️ P2SHAa2mQdHnvsYNRmibLtJ8HGrDgEtKHZUaJa

Merkle Root

3687e84fa9d3e3ee8a1deddc366a62830a557d40f71e41cc084a44b73cecc5ed
Transactions (1)
Coinbase3687e84fa9d3e3…4a44b73cecc5ed
1 in β†’ 1 out8.7400 XPM109 B
Aa2mQdHn…tKHZUaJa
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.

1.347 Γ— 10⁹⁴(95-digit number)
13475922680495789618…29651998991263879199
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
1.347 Γ— 10⁹⁴(95-digit number)
13475922680495789618…29651998991263879199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.347 Γ— 10⁹⁴(95-digit number)
13475922680495789618…29651998991263879201
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
2.695 Γ— 10⁹⁴(95-digit number)
26951845360991579236…59303997982527758399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.695 Γ— 10⁹⁴(95-digit number)
26951845360991579236…59303997982527758401
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
5.390 Γ— 10⁹⁴(95-digit number)
53903690721983158472…18607995965055516799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.390 Γ— 10⁹⁴(95-digit number)
53903690721983158472…18607995965055516801
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
1.078 Γ— 10⁹⁡(96-digit number)
10780738144396631694…37215991930111033599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.078 Γ— 10⁹⁡(96-digit number)
10780738144396631694…37215991930111033601
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
2.156 Γ— 10⁹⁡(96-digit number)
21561476288793263389…74431983860222067199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.156 Γ— 10⁹⁡(96-digit number)
21561476288793263389…74431983860222067201
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:57,982,270 XPMΒ·at block #6,842,233 Β· updates every 60s
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