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Block #1,811,258

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/17/2016, 1:03:28 PM Β· Difficulty 10.7878 Β· 5,031,099 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
01c1de69c95ee737c9b32d6967cf061d118e84e6d4dc997e52942ceb6909b91f
View on Chainz β†—

Height

#1,811,258

Difficulty

10.787784

Transactions

1

Size

199 B

Version

2

Bits

0ac9ac3a

Nonce

1,214,249,948

Timestamp

10/17/2016, 1:03:28 PM

Confirmations

5,031,099

Mined by

⛏️ P2SHARs8qdYFba1o52wV1wbiEVzvsbjRxzP86z

Merkle Root

05b6de47d72b66cadafb89934ece64705597dcfd090cea7c0034c8f2eceaedfa
Transactions (1)
Coinbase05b6de47d72b66…34c8f2eceaedfa
1 in β†’ 1 out8.5800 XPM109 B
ARs8qdYF…jRxzP86z
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.

2.247 Γ— 10⁹⁴(95-digit number)
22470648272275216511…47480586828414639679
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
2.247 Γ— 10⁹⁴(95-digit number)
22470648272275216511…47480586828414639679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.247 Γ— 10⁹⁴(95-digit number)
22470648272275216511…47480586828414639681
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
4.494 Γ— 10⁹⁴(95-digit number)
44941296544550433023…94961173656829279359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.494 Γ— 10⁹⁴(95-digit number)
44941296544550433023…94961173656829279361
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
8.988 Γ— 10⁹⁴(95-digit number)
89882593089100866046…89922347313658558719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.988 Γ— 10⁹⁴(95-digit number)
89882593089100866046…89922347313658558721
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
1.797 Γ— 10⁹⁡(96-digit number)
17976518617820173209…79844694627317117439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.797 Γ— 10⁹⁡(96-digit number)
17976518617820173209…79844694627317117441
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
3.595 Γ— 10⁹⁡(96-digit number)
35953037235640346418…59689389254634234879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.595 Γ— 10⁹⁡(96-digit number)
35953037235640346418…59689389254634234881
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:57,983,263 XPMΒ·at block #6,842,356 Β· updates every 60s
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