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Block #210,238

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/15/2013, 12:28:18 AM Β· Difficulty 9.9129 Β· 6,592,440 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5ce8176e2449548e4d3d57f7c71c837bd653e75db51d8982984517e6a6d123bc
View on Chainz β†—

Height

#210,238

Difficulty

9.912872

Transactions

1

Size

199 B

Version

2

Bits

09e9b1f7

Nonce

147,698

Timestamp

10/15/2013, 12:28:18 AM

Confirmations

6,592,440

Mined by

⛏️ P2SHAK9vVy2joHqUBrbiHFhRPZZcZJniNoc5U8

Merkle Root

7598ab8eb780b623bf6464dd1e0db02e74aa7fe1e800f90906b92714d5822af4
Transactions (1)
Coinbase7598ab8eb780b6…b92714d5822af4
1 in β†’ 1 out10.1600 XPM109 B
AK9vVy2j…niNoc5U8
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.

4.235 Γ— 10⁹⁡(96-digit number)
42350627778875852591…17432454826718687359
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
4.235 Γ— 10⁹⁡(96-digit number)
42350627778875852591…17432454826718687359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.235 Γ— 10⁹⁡(96-digit number)
42350627778875852591…17432454826718687361
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
8.470 Γ— 10⁹⁡(96-digit number)
84701255557751705182…34864909653437374719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.470 Γ— 10⁹⁡(96-digit number)
84701255557751705182…34864909653437374721
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
1.694 Γ— 10⁹⁢(97-digit number)
16940251111550341036…69729819306874749439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.694 Γ— 10⁹⁢(97-digit number)
16940251111550341036…69729819306874749441
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
3.388 Γ— 10⁹⁢(97-digit number)
33880502223100682072…39459638613749498879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.388 Γ— 10⁹⁢(97-digit number)
33880502223100682072…39459638613749498881
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
6.776 Γ— 10⁹⁢(97-digit number)
67761004446201364145…78919277227498997759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.776 Γ— 10⁹⁢(97-digit number)
67761004446201364145…78919277227498997761
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:57,665,445 XPMΒ·at block #6,802,677 Β· updates every 60s
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