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Block #2,100,364

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/5/2017, 3:59:52 AM Β· Difficulty 10.8553 Β· 4,710,141 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
13e2e3c18ca9f4f7af72007ae258b6591038ad048d386e4846096d964222ff00
View on Chainz β†—

Height

#2,100,364

Difficulty

10.855267

Transactions

2

Size

46.49 KB

Version

2

Bits

0adaf2bf

Nonce

23,442,960

Timestamp

5/5/2017, 3:59:52 AM

Confirmations

4,710,141

Mined by

⛏️ P2SHANzYAuCXPFAPzhDimfcnpYwkPD2j9YypAr

Merkle Root

3e5d57167167e8aaafee525fd235bf242642e5c2924e682caab5a1fcfd0c2014
Transactions (2)
Coinbase9d890d05a8a9b9…82f6b20c28caa3
1 in β†’ 1 out9.3100 XPM109 B
ANzYAuCX…2j9YypAr
336c384e72a586…7f8ce6ce9b4346
320 in β†’ 1 out6.3652 XPM46.30 KB
AKGxoSP8…8oH3hVLd
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.

1.110 Γ— 10⁹³(94-digit number)
11102571982514332189…17615097500292086479
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
1.110 Γ— 10⁹³(94-digit number)
11102571982514332189…17615097500292086479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.110 Γ— 10⁹³(94-digit number)
11102571982514332189…17615097500292086481
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
2.220 Γ— 10⁹³(94-digit number)
22205143965028664378…35230195000584172959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.220 Γ— 10⁹³(94-digit number)
22205143965028664378…35230195000584172961
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
4.441 Γ— 10⁹³(94-digit number)
44410287930057328756…70460390001168345919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.441 Γ— 10⁹³(94-digit number)
44410287930057328756…70460390001168345921
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
8.882 Γ— 10⁹³(94-digit number)
88820575860114657512…40920780002336691839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.882 Γ— 10⁹³(94-digit number)
88820575860114657512…40920780002336691841
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
1.776 Γ— 10⁹⁴(95-digit number)
17764115172022931502…81841560004673383679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.776 Γ— 10⁹⁴(95-digit number)
17764115172022931502…81841560004673383681
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:57,728,123 XPMΒ·at block #6,810,504 Β· updates every 60s
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