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Block #223,916

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/23/2013, 9:30:45 AM Β· Difficulty 9.9374 Β· 6,572,033 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ee2c1094a85ed16770eb5aefb88b36ae1a846df7bd3a0fc61c599026795533e6
View on Chainz β†—

Height

#223,916

Difficulty

9.937373

Transactions

1

Size

200 B

Version

2

Bits

09eff7a8

Nonce

30,883

Timestamp

10/23/2013, 9:30:45 AM

Confirmations

6,572,033

Mined by

⛏️ P2SHAaC7FfYJ3wgrxGC78ZvTmB5mToNd6BeiX3

Merkle Root

ba2daadb7db2fdf080fbaa53ff773aab5fc26f2e85dfdf1d6bfa227bf9cf3fb1
Transactions (1)
Coinbaseba2daadb7db2fd…fa227bf9cf3fb1
1 in β†’ 1 out10.1100 XPM109 B
AaC7FfYJ…Nd6BeiX3
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.

1.710 Γ— 10⁹⁷(98-digit number)
17103862978297433053…06132245171214986239
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
1.710 Γ— 10⁹⁷(98-digit number)
17103862978297433053…06132245171214986239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.710 Γ— 10⁹⁷(98-digit number)
17103862978297433053…06132245171214986241
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
3.420 Γ— 10⁹⁷(98-digit number)
34207725956594866106…12264490342429972479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.420 Γ— 10⁹⁷(98-digit number)
34207725956594866106…12264490342429972481
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
6.841 Γ— 10⁹⁷(98-digit number)
68415451913189732212…24528980684859944959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.841 Γ— 10⁹⁷(98-digit number)
68415451913189732212…24528980684859944961
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
1.368 Γ— 10⁹⁸(99-digit number)
13683090382637946442…49057961369719889919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.368 Γ— 10⁹⁸(99-digit number)
13683090382637946442…49057961369719889921
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
2.736 Γ— 10⁹⁸(99-digit number)
27366180765275892884…98115922739439779839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.736 Γ— 10⁹⁸(99-digit number)
27366180765275892884…98115922739439779841
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:57,611,681 XPMΒ·at block #6,795,948 Β· updates every 60s
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